math curriculum map kindergarten student …...math curriculum map domain clusters key vocabulary d...

Math

Curriculum Map

Kindergarten

Domain Clusters Key Vocabulary

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Counting and

Cardinality

Know number names and the

count sequence.

Number words, skip

counting, even, odd,

twos, fives, tens

K.CC

1a

I/R ODE Count to 100 by ones and by tens. 1,2,3,4 CD, manipulatives,

100s chart,

internet4classrooms.

com, calendar time

Counting and

Cardinality

Know how to skip count. Number words, skip

counting, even, odd,

twos, fives, tens

K.CC

1b

I/R TC Skip count by 2s to 20, by 5s to 100. 1,2,3,4 CD, manipulatives,

100s chart,


com, calendar time

Counting and

Cardinality

Know how to count backwards

from twenty.

Number words,

counting back

K.CC

1c

I/R TC Count back from 20 to 0. 1,2,3,4 CD, manipulatives,

100s chart,


com, calendar time

Counting and

Cardinality


count sequence.

Number words,

counting on

K.CC

2

I/R ODE Count forward beginning from a given number

within the known sequence (instead of having

to begin at 1).

1,2,3,4 silent line up, adding

on, calendar

Counting and

Cardinality


count sequence.

Number words,

rhymes

K.CC

3

I/R ODE Write numbers from 0 to 20. Represent a

number of objects with a written numeral 0–20

(with 0 representing a count of no objects).

1,2,3,4 rhymes, journal

pages, number

worksheets, practice

in shaving cream and

others

Counting and

Cardinality

Count to tell the number of

objects.

Number Words, one

to one

K.CC

4a

I/R ODE Understand the relationship between numbers

and quantities; connect counting to cardinality.

a. When counting objects, say the number

names in the standard order, pairing each

object with one and only one number name

and each number name with one and only one

object.

1,2,3,4 one to one counting,

using various

manipulatives to

count (food)

1

Math

Curriculum Map

Kindergarten


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Counting and

Cardinality


objects.

Number Words, one

to one

K.CC

4b



b. Understand that the last number name said

tells the number of objects counted. The

number of objects is the same regardless of

their arrangement or the order in which they

were counted.


using various

manipulatives to

count (food)

Counting and

Cardinality


objects.

Number Words, one

to one

K.CC

4c



c. Understand that each successive number

name refers to a quantity that is one larger.


using various

manipulatives to

count (food)

Counting and

Cardinality


objects.

Match K.CC

5

I/R ODE Count to answer “how many?” questions about

as many as 20 things arranged in a line, a

rectangular array, or a circle, or as many as 10

things in a scattered configuration; given a

number from 1–20, count out that many

objects.

1,2,3,4 Worksheets -

pictures with

numbers

Counting and

Cardinality

Compare numbers. Graph, more, less,

same as, equal to,

greater than, less

than

K.CC

6

I/R ODE Identify whether the number of objects in one

group is greater than, less than, or equal to the

number of objects in another group, e.g., by

using matching and counting strategies.

1,2,3,4 weather graph,

theme graphs

Counting and

Cardinality

Compare numbers. Graph, more, less,

same as, equal to,

greater than, less

than

K.CC

7

I/R ODE Compare two numbers between 1 and 10

presented as written numerals.

1,2,3,4 graphs - weather

2

Math

Curriculum Map

Kindergarten


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Observations

and Algebraic

Thinking

Understand addition as putting

together and adding to, and

understand subtraction as taking

apart and taking from.

Equation, plus sign,

minus sign, equal

sign, number

sentence

K.OA

1

I/R ODE Represent addition and subtraction with

objects, fingers, mental images, drawings1,

sounds (e.g., claps), acting out situations,

verbal explanations, expressions, or

equations.

1,2,3,4 calendar, various

worksheets, hands

on activities (food),

graphing

Observations

and Algebraic

Thinking






minus sign, equal

sign, number

sentence

K.OA

2

I/R ODE Solve addition and subtraction word problems,

and add and subtract within 10, e.g., by using

objects or drawings to represent the problem.

1,2,3,4 calendar, various

worksheets, hands

on activities (food),

graphing

Observations

and Algebraic

Thinking






minus sign, equal

sign, number

sentence, number

words

K.OA

3

I/R ODE Decompose numbers less than or equal to 10

into pairs in more than one way, e.g., by using

objects or drawings, and record each

decomposition by a drawing or equation (e.g.,

5 = 2 + 3 and 5 = 4 + 1).

1,2,3,4 number worksheets

(journal pages),

probability

Observations

and Algebraic

Thinking





Tens, ones, number

words, place value

K.OA

4

I/R ODE For any number from 1 to 9, find the number

that makes 10 when added to the given

number, e.g., by using objects or drawings,

and record the answer with a drawing or

equation.

1,2,3,4 calendar, money,

straws

Observations

and Algebraic

Thinking






minus sign, equal

sign, number

sentence

K.OA

5

I/R ODE Fluently add and subtract within 5. 1,2,3,4 worksheets, hands

on, calendar,

computer games

Observations

and Algebraic

Thinking

Recognize a pattern and

describe the pattern.

pattern, repeating,

AB, AABB, ABC,

etc.

K.OA

6a

I/R TC Describe orally the pattern of a given sequence. 1,2,3,4 unifix cubes, bears,

drawing, calendar, I

spy, motion patterns

Observations

and Algebraic

Thinking

Recognize a pattern and

describe the pattern.

pattern, repeating,

AB, AABB, ABC,

etc.

K.OA

6b

I/R TC Identify, create and extend a pattern 1,2,3,4 unifix cubes, bears,

drawing, calendar, I

spy, motion patterns

3

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Curriculum Map

Kindergarten


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Numbers and

Operations in

Base Ten

Work with numbers 11-19 to

gain foundations for place value.

ones, tens, place

value, add, subtract

K.NBT

1

I/R ODE Compose and decompose numbers from 11

to 19 into ten ones and some further ones,

e.g., by using objects or drawings, and record

each composition or decomposition by a

drawing or equation (such as 18 = 10 + 8);

understand that these numbers are composed

of ten ones and one, two, three, four, five, six,

seven, eight, or nine ones.

1,2,3,4 calendar straws,

money

Measurement

and Data

Describe and compare

measurable attributes.

length, width,

height, weight, unit,

circumfrence,

balance

K.MD

1

I/R ODE Describe measurable attributes of objects,

such as length or weight. Describe several

measurable attributes of a single object.

1,2,3,4 bears, pumpkins,

science table - gold

rocks, bats

Measurement

and Data

Describe and compare

measurable attributes.

more, less, equal,

taller, shorter

K.MD

2

I/R ODE Directly compare two objects with a

measurable attribute in common, to see which

object has “more of”/“less of” the attribute, and

describe the difference. For example, directly

compare the heights of two children and

describe one child as taller/shorter.

1,2,3,4 bears, scale, kids

with pumpkins

Measurement

and Data

Classify objects and count the

number of objects in each

category.

sorting, alike,

different, attribute,

same, shape, size,

number words, label

K.MD

3

I/R ODE Classify objects into given categories; count

the numbers of objects in each category and

sort the categories by count.

1,2,3,4 sorting bears,

shapes, graphs -

m&ms, bugs, fine

motor

Measurement

and Data

Work with time and money. clock, hour hand,

minute hand, to the

hour

K.MD

4

I/R TC Identify time to the hour. 1,2,3,4 journal pages, clock

worksheets, hands

on clock practice,

books

Measurement

and Data

Work with time and money. coin, penny, nickel,

dime, quarter,

cents, value

K.MD

5

I/R TC Identify and state value of penny, nickel, dime,

quarter.

1,2,3,4 calendar, piggy

banks, journal

worksheets, hands,

simon says

4

Math

Curriculum Map

Kindergarten


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Geometry Identify and describe shapes

(squares, circles, triangles,

rectangles, hexagons, cubes,

cones, cylinders, and spheres).

shape names, 3D

shapes, position

words

K.G 1 I/R ODE Describe objects in the environment using

names of shapes, and describe the relative

positions of these objects using terms such as

above , below , beside , in front of , behind , and

next to .

1,2,3,4 poems, worksheets,

x hunt, calendar,

shape hunt, animal

cookie activity,

geoboards





shape names, 3D

shapes, position

words

K.G 2 I/R ODE Correctly name shapes regardless of their

orientations or overall size.

1,2,3,4 poems, worksheets,

x hunt, calendar,

shape hunt, animal

cookie activity,

geoboards





3D, names, shapes K.G 3 I/R ODE Identify shapes as two-dimensional (lying in a

plane, “flat”) or three-dimensional (“solid”).

1,2,3,4 calendar

Geometry Analyze, compare, create, and

compose shapes.

3D, names, shapes K.G 4 I/R ODE Analyze and compare two- and three-

dimensional shapes, in different sizes and

orientations, using informal language to

describe their similarities, differences, parts

(e.g., number of sides and vertices/“corners”)

and other attributes (e.g., having sides of

equal length).

1,2,3,4 shape poems,

shapes with food

(licorice, pretzels)


compose shapes.

3D, names, shapes K.G 5 I/R ODE Model shapes in the world by building shapes

from components (e.g., sticks and clay balls)

and drawing shapes.

1,2,3,4 math journal, art

center, blocks,

calendar


compose shapes.

3D, names, shapes K.G 6 I/R ODE Compose simple shapes to form larger

shapes. For example, “Can you join these two

triangles with full sides touching to make a

rectangle?”

1,2,3,4 tangrams, block

shapes

5

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Operations and

Algebraic

Thinking

Represent and solve

problems involving addition

and subtraction.

symbol,equal, plus,

minus, sum ,

difference, together,

in all, how many

more, addition,

subtraction,

1.OA

1

I/R/M ODE Use addition and subtraction within

20 to solve word problems involving

situations of adding to, taking

from, putting together, taking apart,

and comparing, with unknowns in all

positions, e.g., by using objects,

drawings, and equations with a

symbol for the unknown number to

represent the problem.

1,2,3,4 Use of manipulatives and

mats, stories involving

putting together and taking

apart, math journals in

which to draw pictures and

number sentences to

represent stories, Smart

Board e-tools to represent

stories about combining

and taking apart.

Operations and

Algebraic

Thinking

Represent and solve


and subtraction.

equal, sum, plus,

together, in all,

addends, symbol,

1.0A

2

R/M ODE Solve word problems that call for

addition of three whole numbers

whose sum is less than or equal to

20, e.g., by using objects, drawings,

and equations with a symbol for the

unknown number to


2,3,4 Manipulatives such as

goldfish, candy corn,

m&m's, cubes, counters,

mats and journals to

represent word problems

that call for three addend

addition. Smartboard

pictures that can be

manipulated to represent

stories.

Operations and

Algebraic

Thinking

Understand and apply

properties of operations and

the relationship between

addition and subtraction.

Commutative

property, Associative

property, add,

subtract, plus,

minus, equal

1.OA

3

I/R/M ODE Apply properties of operations as

strategies to add and subtract.

Examples: If 8 + 3 = 11 is known,

then 3 + 8 = 11 is also known

(commutative property of addition).To

add 2 + 6 + 4, the second two

numbers can be added to make a

ten, so 2 + 6 + 4 = 2 + 10 = 12

(associative property of addition).

2,3,4 manipulatives, such as

linking cubes, counters,

journals,modeling,

practice.

1

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Operations and

Algebraic

Thinking

Understand and apply

properties of operations and

the relationship between

addition and subtraction.

addend, subtraction 1.OA

4

I/R ODE Understand subtraction as an

unknown-addend problem. For

example, subtract 10 – 8 by finding

the number that makes 10 when

added to 8.

2,3,4 manipulatives, journals,

modeling, guided practice

Operations and

Algebraic

Thinking

Add and subtract within 20. plus, minus, equal,

sum, difference,

counting on,

counting back

1.OA

5

I/R ODE Relate counting to addition and

subtraction (e.g., by counting on 2 to

add 2).

2,3,4 manipulatives, such as

linking cubes, counters,

journals,modeling, practice

Operations and

Algebraic

Thinking

Add and subtract within 20. Counting on, making

a ten, decomposing,

addition, subtraction,

equal, equivalent,

counting back

1.OA

6

I/R ODE Add and subtract within 20,

demonstrating fluency for addition

and subtraction within 10. Use

strategies such as counting on;

making ten (e.g., 8 + 6 = 8 + 2 + 4 =

10 + 4 = 14); decomposing a number

leading to a ten (e.g., 13 – 4 = 13 – 3

– 1 = 10 – 1 = 9); using the

relationship between addition and

subtraction (e.g., knowing that 8 + 4 =

12, one knows 12 – 8 = 4); and

creating equivalent but easier or

known sums (e.g., adding 6 + 7 by

creating the known equivalent 6 + 6 +

1 = 12 + 1 = 13).

3,4 manipulatives, particularly

linking cubes, number

lines, tens frames,

counters, e tools on the

Smart Board, Sites such

as

Illuminations.NCTM.org,


Operations and

Algebraic

Thinking

Work with addition and

subtraction equations.

equal, plus, minus,

equation, addition,

subtraction, false,

true

1.OA

7

I/R ODE Understand the meaning of the equal

sign, and determine if equations

involving addition and subtraction are

true or false. For example, which of

the following equations are true and

which are false? 6 = 6, 7 = 8 – 1, 5 +

2 = 2 + 5, 4 + 1 = 5 + 2.

2,3,4 manipulatives, journals,


2

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Operations and

Algebraic

Thinking

Work with addition and

subtraction equations.

addition, subtraction,

equation, true, false,

1.OA

8

I/R ODE Determine the unknown whole

number in an addition or subtraction

equation relating three whole

numbers. For example, determine the

unknown number that makes the

equation true in each of the equations

3,4 manipulaticves, journals,


Operations and

Algebraic

Thinking

Identify, create and extend

patterns

pattern unit, extend,

grow

1.TC

9

R/M TC Create a patten unit. Identify and

label the pattern unit. Extend the unit

by making it again or growing a part

of the unit.

1, 2 manipulatives, particularly

pattern blocks, Smart

Board etools, modeling,

guided and independent

practice, journals.

Number and

Operations in

Base Ten

Extend the counting

sequence.

numeral 1.NB

T1

I/R ODE Count to 120, starting at any number

less than 120. In this range, read and

write numerals and represent a

number of objects with a written

numeral.

1,2,3,4 120 number chart, 1 inch

graph paper,blank

counting charts,modeling,

practice

3

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Number and

Operations in

Base Ten

Understand place value. digits, ones, tens,

bundle

1.

NBT

2

I/R ODE Understand that the two digits of a

two-digit number represent amounts

of tens and ones. Understand the

following as special cases:a. 10 can

be thought of as a bundle of ten ones

— called a “ten.”b. The numbers from

11 to 19 are composed of a ten and

one, two, three, four, five, six, seven,

eight, or nine ones.c. The numbers

10, 20, 30, 40, 50, 60, 70, 80, 90 refer

to one, two, three, four, five, six,

seven, eight, or nine tens (and 0

ones).

2,3,4 Manipulatives such as

linking cubes, straws or

other materials to bundle,

place value mats,

Smartboard teacher

resources,

Illumiinations.NCTM.org,

tenmarks.com,

ohiotreasurechest.org,

Internetforschool.com,

Funbrain.com.

Number and

Operations in

Base Ten

Understand place value. digit, tens, ones,

place value, equal,

greater than , less

than, fewer than

1.NB

T 3

I/R ODE Compare two two-digit numbers

based on meanings of the tens and

ones digits, recording the results of

comparisons with the symbols >, =,

and <.

2,3,4 Base ten blocks, linking

cubes, tens frames,

counting chart, teacher

modeling, practice

4

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Number and

Operations in

Base Ten

Use place Value

Understanding and

properties of operations to

add and subtract.

Place value, digits,

tens, ones, compose

1.NB

T4

I/R ODE Add within 100, including adding a

two-digit number and a one-digit

number, and adding a two-digit

number and a multiple of 10, using

concrete models or drawings and

strategies based on place value,

properties of operations, and/or the


subtraction; relate the strategy to a

written method and explain the

reasoning used. Understand that in

adding two-digit numbers, one adds

tens and tens, ones and ones; and

sometimes it is necessary to

compose a ten.

3,4 Manipulatives such as



place value mats,

Smartboard teacher

resources,


tenmarks.com,



Funbrain.com.

Number and

Operations in

Base Ten

Use place Value

Understanding and


add and subtract.

more, less 1.NB

T 5

I/R ODE Given a two-digit number, mentally

find 10 more or 10 less than the

number, without having to count;

explain the reasoning used.

3, 4 Number chart, teacher

modeling, practice

5

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Number and

Operations in

Base Ten

Use place Value

Understanding and


add and subtract.

tens, plus, minus,

sum, difference,

subtract, add

1.NB

T 6

I/R ODE Subtract multiples of 10 in the

range 10-90 from multiples of 10

in the range 10-90 (positive or

zero differences), using concrete

models or drawings and


properties of operations, and/or

the relationship between addition

and subtraction; relate the

strategy to a written method and


3,4 Manipulatives such as



place value mats,

Smartboard teacher

resources,


tenmarks.com,



Funbrain.com.

Measurement

and Data

Measure lengths indirectly

and by interating length units

length, longer,

longest, compare

1.MD

1

I/R/M ODE Order three objects by length;

compare the lengths of two objects

indirectly by using a third object.

2,3,4 Objects of different

lengths, teacher modeling,

practice

Measurement

and Data

Measure lengths indirectly

and by interating length units.

Length unit, non

standard unit,

standard unit,

centimeter, meter,

inch, foot, yard

1.MD

1

I/R/M ODE Express the length of an object as a

whole number of length units, by

laying multiple copies of a shorter

object (the length unit) end to end;

understand that the length

measurement of an object is the

number of same-size length units that

span it with no gaps or overlaps. Limit

to contexts where the object being

measured is spanned by a whole

number of length units with no gaps

or overlaps.

3, 4 Objects of different

lengths, cubes, paperclips,

ruler, yardstick, centimeter

and meter stick,

Smartboard resources,

teacher modeling, practice

6

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Measurement

and Data

Tell and write time. second, minute,

hour, half hour,

analog, digital

1.MD

2

I/R ODE Tell and write time in hours and half-

hours using analog and digital clocks.

3,4 Judy teaching clocks,

analog and digital clocks,

Smartboard resources,

teacher modeling, practice

Measurement

and Data

Represent and Interpret

Data.

data, category 1.MD

3

I/R/M ODE Organize, represent, and interpret

data with up to three categories; ask

and answer questions about the total

number of data points, how many in

each category, and how many more

or less are in one category than in

another.

1,2,3,4 Smartboard tools, teacher

modeling, practice,

http://nlvm.usu.edu/en/nav/

vlibrary.html

Measurement

and Data

Identify and count coins penny, nickel, dime,

quarter, equal,

cents, dollar, equal

value, amount

1.MD

4

I/R/M TC Identify, name value, and determine

the value of a small collection of coins

(with a total value up to one dollar)

using 1 or 2 different type

coins, including pennies, nickels,

dimes and quarters. Identify different

combinations of coins with equal

values.

2,3,4 Coins, Smartboard

resources, teacher

modeling, teacher

resources,


tenmarks.com,


Internetforscho

Measurement

and Data

Identify and count coins penny, nickel, dime,

quarter, equal,

cents, dollar, equal

value, amount

1.MD

5

I/R/M TC Identify different combinations of

coins with equal values.

2,3,4 Coins, Smartboard

resources, teacher

modeling,

practice,resources at




Funbrain.com.

7

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Geometry Reason with shapes and

their attributes.

closed, open

attribute, sides,

angles

1. G 1 I/R/M ODE Distinguish between defining

attributes (e.g., triangles are closed

and three-sided) versus non-defining

attributes (e.g., color, orientation,

overall size) ; build and draw shapes

to possess defining attributes.

2,3,4 Pattern blocks, Paper

shapes that may be folded,

Geoboards, and bands,

Resources such as




Funbrain.com.


their attributes.

rectangle, square,

trapezoid, triangle,

half circle, quarter

circle, cubes, cones,

cylinders

1. G 2 I/R ODE Compose two-dimensional shapes

(rectangles, squares, trapezoids,

triangles, half-circles, and quarter-

circles) or three-dimensional shapes

(cubes, right rectangular prisms, right

circular cones, and right circular

cylinders) to create a composite

shape, and compose new shapes

from the composite shape.

3,4 Pattern blocks, Paper


Geoboards and bands,

Teacher modeling,

practice, Resources such

as,




Funbrain.com.


their attributes.

circle, rectangle,

decomposing,

fractional part,

equal, half, fourth,

quarter

1. G 3 I/R ODE Partition circles and rectangles into

two and four equal shares, describe

the shares using the words halves,

fourths, and quarters, and use the

phrases half of, fourth of, and quarter

of. Describe the whole as two of, or

four of the shares. Understand for

these examples that decomposing

into more equal shares creates

smaller shares.

3,4 Pattern blocks, paper


cut, Geoboards and

bands, Smartboard

resources and websites

such as

http://nlvm.usu.edu/en/nav/

vlibrary.html, ABCya.com,

Illuminations.NCTM.org,

Ohiotreasurechest.org,

Internetforschool

8

Math

Curriculum Map

Grade 2


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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Operations

and Algebraic

Thinking

Represent and solve


and subtraction.

add, subtract,

altogether, in all,

difference, how

many more, more,

less, minus, equal,

addend, sum, join,

related fact, regroup

2.OA1 R/M ODE Use addition and subtraction within

100 to solve one- and two-step word

problems involving situations of

adding to, taking from, putting

together, taking apart, and

comparing, with unknowns in all

positions, e.g., by using drawings and

equations with a symbol for the

unknown number to represent the

problem.

1, 2, 3, 4 Text book word

problems, unifix

cubes, numberlines, i-

pads, smartboard,

math-4-today, minute

math.

Operations and

Algebraic

Thinking

Add and subtract within 20 add, subtract,

altogether, in all,

difference, how

many more, more,

less, minus, addend,

sum, join, equal,

related fact

2.0A2 R/M ODE Fluently add and subtract within 20

using mental strategies.2 By end of

Grade 2, know from memory all sums

of two one-digit numbers.

1, 2, 3, 4 Textbook, unifix

cubes, numberlines,

minute math, math-4-

today, strategy

instruction,

smartboard.

1

Math

Curriculum Map

Grade 2


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Specific Standard

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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Operations and

Algebraic

Thinking

Work with equal groups of

objects to gain foundations

for multiplication.

even, odd 2.OA3 I/R/M ODE Determine whether a group of objects

(up to 20) has an odd or even number

of members, e.g., by pairing objects

or counting them by 2s; write an

equation to express an even number

as a sum of two equal addends.

1, 2, 3, 4 textbook,

manipulatives,

smartboard

Operations and

Algebraic

Thinking

Work with equal groups of

objects to gain foundations

for multiplication.

array, column, row 2.OA4 I/R ODE Use addition to find the total number

of objects arranged in rectangular

arrays with up to 5 rows and up to 5

columns; write an equation to express

the total as a sum of equal addends.

1, 2, 3, 4 Array activities:

manipulatives, graph

paper, smartboard.

Number and

Operations in

Base 10

Understand Place Value ones, tens,

hundreds,

thousands, digit

2.NBT

1

I/R ODE Understand that the three digits of a

three-digit number represent amounts

of hundreds, tens, and ones; e.g.,

706 equals 7 hundreds, 0 tens, and 6

ones. Understand the following as

special cases:

100 can be thought of as a bundle of

ten tens — called a “hundred.”

The numbers 100, 200, 300, 400,

500, 600, 700, 800, 900 refer to one,

two, three, four, five, six, seven, eight,

or nine hundreds (and 0 tens and 0

ones).

1, 2, 3, 4 Smartboard, base

ten blocks.

2

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Curriculum Map

Grade 2


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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Number and

Operations in

Base 10


hundreds,

thousands, digit,

pattern

2.NBT

2

R/M ODE Count within 1000; skip-count by 5s,

10s, and 100s.

1, 2, 3, 4 Smartboard,

textbook, hundreds

chart, patterning

activities.

Number and

Operations in

Base 10


hundreds,

thousands, digit

2.NBT

3

I/R/M ODE Read and write numbers to 1000

using base-ten numerals, number

names, and expanded form.


textbook, modeling,

guided practice.

Number and

Operations in

Base 10

Understand Place Value greater than, less

than, equal,

equivalence

2.NBT

4

I/R/M ODE Compare two three-digit numbers

based on meanings of the hundreds,

tens, and ones digits, using >, =, and

< symbols to record the results of

comparisons.


manipulatives, visual

aid ie. Alligator

mouth,pacmann,

arrow pointing to

smaller number.

Number and

Operations in

Base 10

Use place value

understanding and properties

of operations to add and

subtract.

ones, tens,

hundreds,

thousands, digit

2.NBT

5

I/R/M ODE Fluently add and subtract within 100

using strategies based on place

value, properties of operations, and/or

the relationship between addition and

subtraction.

1, 2, 3, 4 Smartboard, base 10

blocks, 100's chart,

addition/subtraction

strategies.

Number and

Operations in

Base 10

Use place value



subtract.

ones, tens,

hundreds,

thousands, digit

2.NBT

6

I/R/M ODE Add up to four two-digit numbers

using strategies based on place value

and properties of operations.

1, 2, 3, 4 Practice w/ paper

and pencil, online,

games, study island,

base ten blocks.

3

Math

Curriculum Map

Grade 2


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Specific Standard

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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Number and

Operations in

Base 10

Use place value



subtract.

ones, tens,

hundreds,

thousands, digit

2.NBT

7

I/R ODE Add and subtract within 1000, using

concrete models or drawings and


properties of operations, and/or the


subtraction; relate the strategy to a

written method. Understand that in

adding or subtracting three-digit

numbers, one adds or subtracts

hundreds and hundreds, tens and

tens, ones and ones; and sometimes

it is necessary to compose or

decompose tens or hundreds.

1, 2, 3, 4 Practice w/ paper

and pencil, online,

games, study island,

base ten blocks.

Number and

Operations in

Base 10

Use place value



subtract.

ones, tens,

hundreds,

thousands, digit

2.NBT

8

R/M ODE Mentally add 10 or 100 to a given

number 100–900, and mentally

subtract 10 or 100 from a given

number 100–900.

1, 2, 3, 4 Arrow Math, Block

Math, Fill in the 100

Chart, Online math

games.

Number and

Operations in

Base 10

Use place value



subtract.

ones, tens,

hundreds,

thousands, digit

2.NBT

9

I/RM ODE Explain why addition and subtraction

strategies work, using place value

and the properties of operations.

1, 2, 3, 4 Manipulatives.

Number and

Operations in

Base 10

Represent fractions using

words, numerals and physical

models.

halves,thirds,

fourths, sixths,

eighths

2.N BT

9a

I TC Compare and order physical models

of halves, thirds and fourths in

relation to 0 and 1.

2,3 Manipulatives

4

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Grade 2


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Specific Standard

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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Measurement

& Data

Measure and estimate

lengths in standard units.

Measure, length 2.MD1 R/M ODE Measure the length of an object by

selecting and using appropriate tools

such as rulers, yardsticks, meter

sticks, and measuring tapes.

2, 3, 4 Use rulers,

yardsticks, meter

sticks to measure

classroom objects.

Measurement

& Data



liter, cup, pint, quart 2.M

D1a

R TC Measure volume (capacity) using

liters, cups, pints, or quarts

2, 3, 4 Use measuring cups,

liters to measure

volume. Estimate

and compare like

quantities (ie. Quarts

and liters).

Measurement

& Data



grams, ounces,

pound

2.M

D1b

R TC Measure weight using grams,

ounces, or pounds.

2, 3, 4 Use scales, balance

beams to weigh

classroom objects.

Measurement

& Data



2.MD2 R/M ODE Measure the length of an object twice,

using length units of different lengths

for the two measurements; describe

how the two measurements relate to

the size of the unit chosen.

2, 3, 4 Measure with rulers,

yardsticks, meter

sticks.

Measurement

& Data



inches, feet,

centimeter, meter

2.MD3 I/R/M ODE Estimate lengths using units of

inches, feet, centimeters, and meters.


yardsticks, meter

sticks. Instruction in

common references.

5

Math

Curriculum Map

Grade 2


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Engagement/

Learning Activity /

Special Resource /

Web Link

Measurement

& Data



standard unit 2.MD4 I/R/M ODE Measure to determine how much

longer one object is than another,

expressing the length difference in

terms of a standard length unit.


yardsticks, meter

sticks. Instruction in

common references.

Measurement

& Data

Relate addition and

subtraction to length

equivalent 2.MD5 R/M ODE Use addition and subtraction within

100 to solve word problems involving

lengths that are given in the same

units, e.g., by using drawings (such

as drawings of rulers) and equations

with a symbol for the unknown

number to represent the problem.

2, 3, 4 Smartboard, ODE

website, ORC.

Measurement

& Data

Relate addition and

subtraction to length

2.MD6 R/M ODE Represent whole numbers as lengths

from 0 on a number line diagram with

equally spaced points corresponding

to the numbers 0, 1, 2, ..., and

represent whole-number sums and

differences within 100 on a number

line diagram.

2, 3, 4 Use numberline with

standard

measurement (ruler,

yardstick, etc.)

Measurement

& Data

Work with time and money. analog, digital,

minute, hour

2.MD7 I/R/M ODE Tell and write time from analog and

digital clocks to the nearest five

minutes, using a.m. and p.m.

2, 3, 4 Classroom clock,

Judy Clocks,

smartboard tools,

online math websites.

6

Math

Curriculum Map

Grade 2


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Specific Standard

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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Measurement

& Data

Work with time and money. penney, nickel,

dime, quarter, dollar,

2.MD8 I/R/M ODE Solve word problems involving dollar

bills, quarters, dimes, nickels, and

pennies, using $ and ¢ symbols

appropriately. Example: If you have 2

dimes and 3 pennies, how many

cents do you have?

2, 3, 4 School money, play

money, smartboard

tools, online

websites.

Measurement

& Data

Work with time and money. change 2.MD8

a

I/R TC Count money and make change

using coins and a dollar bill.

2, 3, 4 School money, play

money, smartboard

tools, online

websites, class store.

Measurement

& Data

Represent and interpret data. data, graph, 2.MD9 R/M ODE Generate measurement data by

measuring lengths of several objects

to the nearest whole unit, or by

making repeated measurements of

the same object. Show the

measurements by making a line plot,

where the horizontal scale is marked

off in whole-number units.

2, 3, 4 Graph paper, online

websites.

7

Math

Curriculum Map

Grade 2


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Student

Engagement/

Learning Activity /

Special Resource /

Web Link

Measurement

& Data

Represent and interpret data. data, graph, 2.MD

10

R/M ODE Draw a picture graph and a bar graph

(with single-unit scale) to represent a

data set with up to four categories.

Solve simple put-together, take-apart,

and compare problems1 using

information presented in a bar graph.

2, 3, 4 Blank graphs, graph

paper.

Geometry Reason with shapes and their

attributes.

angle, side, vertex,

edge, face, plane

shape, solid figure,

cube, rectangular

prism, sphere,

pyramid, cylinder,

cone, flat surface,

2.G1 I/R ODE Recognize and draw shapes having

specified attributes, such as a given

number of angles or a given number

of equal faces. Identify triangles,

quadrilaterals, pentagons, hexagons,

and cubes.

2, 3, 4 Pattern blocks, solid

figures,smartboard

tools, online

websites.


attributes.

array, column, row 2.G2 R/M ODE Partition a rectangle into rows and

columns of same-size squares and

count to find the total number of

them.

2, 3, 4 Manipulatives, online

websites.

8

Math

Curriculum Map

Grade 2


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Specific Standard

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Student

Engagement/

Learning Activity /

Special Resource /

Web Link


attributes.

fraction, equal,

halves, thirds,

fourths, unequal

2.G3 R/M ODE Partition circles and rectangles into

two, three, or four equal shares,

describe the shares using the words

halves, thirds, half of, a third of, etc.,

and describe the whole as two

halves, three thirds, four fourths.

Recognize that equal shares of

identical wholes need not have the

same shape.

2, 3, 4 Manipulatives, online

websites.

9

Math

Curriculum Map

Grade 3


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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Operations and

Algebraic Thinking

Represent and solve problems

involving multiplication and

division.

array, product,

factor, dividend,

divisor, quotient

3.OA

1

I/R

/M

ODE Interpret products of whole numbers,

e.g., interpret 5 × 7 as the total

number of objects in 5 groups of 7

objects each

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

Operations and

Algebraic Thinking



division.

array, product,

factor, dividend,

divisor, quotient

3.OA

2

I/R

/M

ODE Interpret whole-number quotients of

whole numbers, e.g., interpret 56 ÷ 8

as the number of objects in each

share when 56 objects are partitioned

equally into 8 shares, or as a number

of shares when 56 objects are

partitioned into equal shares of 8

objects each.

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

Operations and

Algebraic Thinking



division.

array, product,

factor, dividend,

divisor, quotient

3.OA

3

I/R ODE Use multiplication and division within

100 to solve word problems in

situations involving equal groups,

arrays, and measurement quantities,

e.g., by using drawings and equations

with a symbol for the unknown

number to represent the problem.

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

Operations and

Algebraic Thinking



division.

array, product,

factor, dividend,

divisor, quotient

3.OA

4

I/R ODE Determine the unknown whole

number in a multiplication or division

equation relating three whole

numbers.

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

Operations and

Algebraic Thinking

Understand properties of

multiplication and the relationship

between multiplication and

division.

associative property,

commutative

property, distributive

property

3.OA

5

I/R

/M

ODE Apply properties of operations as

strategies to multiply and divide.

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

1

Math

Curriculum Map

Grade 3


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Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Operations and

Algebraic Thinking

Understand properties of

multiplication and the relationship

between multiplication and

division.

property 3.OA

6

I/R ODE Understand division as an unknown-

factor problem

1,2,3,4 Counters,

tiles,cereal,

candies,number

lines, arrays

Operations and

Algebraic Thinking

Multiply and divide within 100. rectangular array,

multiply, divide,

product, factor,

dividend, divisor,

quotient

3.OA

7

I/R ODE Fluently multiply and divide within

100, using strategies such as the

relationship between multiplication

and division

1,2,3,4 Unifix cubes, graph

paper, counters

Operations and

Algebraic Thinking

Solve problems involving the four

operations, and identify and

explain patterns in arithmetic.

operation, multiply,

divide, add, subtract,

sum, difference,

assocaitive proprty,

commutative

property, product

3.OA

8

I/R ODE Solve two-step word problems using

the four operations. Represent these

problems using equations with a letter

standing for the unknown quantity.

Assess the reasonableness of

answers using mental computation

and estimation strategies including

rounding.

1,2,3,4 Dice, cards

Operations and

Algebraic Thinking

Solve problems involving the four

operations, and identify and

explain patterns in arithmetic.

addends, products 3.OA

9

I/R

/M

ODE Identify arithmetic patterns (including

patterns in the addition table or

multiplication table), and explain them

using properties of operations.

1,2,3,4 Addition and

multiplication charts

Number and

Operations in Base

Ten

Use place value understanding

and properties of operations to

perform multi-digit arithmetic.

round up, round

down, estimate

3.NB

T1

R/

M

ODE Use place value understanding to

round whole numbers to the nearest

10 or 100.

1,2,3,4 Place value chart,

number line, 100's

chart

Number and

Operations in Base

Ten




alogorithm 3.NB

T2

R/

M

ODE Fluently add and subtract within 1000

using strategies and algorithms

based on place value, properties of

operations, and/or the relationship

between addition and subtraction.


number line, 100's

chart

2

Math

Curriculum Map

Grade 3


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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

Operations in Base

Ten




3.NB

T3

I/R

/M

ODE Multiply one-digit whole numbers by

multiples of 10 in the range 10–90

(e.g., 9 × 80, 5 × 60) using strategies

based on place value and properties

of operations.


number line, 100's

chart

Number and

Operations-

Fractions

Develop understanding of

fractions as numbers.

whole number,

mixed number,

numerator,

denominator,

equivalent, greater

than, less than

3.NF

1

I/R

/M

ODE Understand a fraction 1/b as the

quantity formed by 1 part when a

whole is partitioned into b equal parts;

understand a fraction a/b as the

quantity formed by a parts of size 1/b.

3,4 Fraction bars or

strips, geoboards,

venn diagram,grid

paper, models

Number and

Operations-Fractions



number line,

numerator,

denominator

3.

NF2

I/R ODE Understand a fraction as a number on

the number line; represent fractions

on a number line diagram.


strips, geoboards,

venn diagram,grid

paper, models

Number and




number line 3.2

NF a

I/R ODE a. Represent a fraction 1/b on a

number line diagram by defining the

interval from 0 to 1 as the whole and

partitioning it into b equal parts.

Recognize that each part has size 1/b

and that the endpoint of the part

based at 0 locates the number 1/b on

the number line.


strips, geoboards,

venn diagram,grid

paper, models

Number and




number line 3.2

NF b

I/R ODE b. Represent a fraction a/b on a

number line diagram by marking off a

lengths 1/b from 0. Recognize that

the resulting interval has size a/b and

that its endpoint locates the number

a/b on the number line.


strips, geoboards,

venn diagram,grid

paper, models

3

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Curriculum Map

Grade 3


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Learning

Activity / Special

Resource / Web

Link

Number and




greater than, less

than, equivalent

fractions

3.3

NF

I/R

/M

ODE Explain equivalence of fractions in

special cases, and compare fractions

by reasoning about their size.


strips, geoboards,

venn diagram,grid

paper, models

Number and

Operation-Fractions



equivalent fractions 3.3N

F a

I/R ODE a. Understand two fractions as

equivalent (equal) if they are the

same size, or the same point on a

number line.


strips, geoboards,

venn diagram,grid

paper, models

Number and




equivalent fractions 3.3

NF b

I/R ODE b. Recognize and generate simple

equivalent fractions, e.g., 1/2 = 2/4,

4/6 = 2/3). Explain why the fractions

are equivalent, e.g., by using a visual

fraction model.


strips, geoboards,

venn diagram,grid

paper, models

Number and




equivalent fractions 3.3

NF c

I/R ODE c. Express whole numbers as

fractions, and recognize fractions that

are equivalent to whole

numbers.Examples: Express 3 in the

form 3 = 3/1; recognize that 6/1 = 6;

locate 4/4 and 1 at the same point of

a number line diagram.


strips, geoboards,

venn diagram,grid

paper, models

4

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Curriculum Map

Grade 3


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Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and




greater than, less

than, equivalent

fractions

3.3

NF d

I/R ODE d. Compare two fractions with the

same numerator or the same

denominator by reasoning about their

size. Recognize that comparisons are

valid only when the two fractions refer

to the same whole. Record the results

of comparisons with the symbols >, =,

or <, and justify the conclusions, e.g.,

by using a visual fraction model.


strips, geoboards,

venn diagram,grid

paper, models

Measurement and

Data

Solve problems involving

measurement and estimation of

intervals of time, liquid volumes,

and masses of objects.

hour hand, minute

hand, elasped time

3.

MD 1

I/R

/M

ODE Tell and write time to the nearest

minute and measure time intervals in

minutes. Solve word problems

involving addition and subtraction of

time intervals in minutes, e.g., by

representing the problem on a

number line diagram.

1,2,3,4 clocks- analog and

digital

Measurement and

Data


measurement and estimation of


and masses of objects.

mass, volume 3.

MD 2

I/R ODE Measure and estimate liquid volumes

and masses of objects using

standard units of grams (g),

kilograms (kg), and liters (l). Add,

subtract, multiply, or divide to solve

one-step word problems involving

masses or volumes that are given in

the same units, e.g., by using

drawings (such as a beaker with a

measurement scale) to represent the

problem.

3,4 beakers, graduated

cylinders, measuring

cups, balnce scales,

weights (g or kg),

objects to weigh

5

Math

Curriculum Map

Grade 3


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Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data

Represent and interpret data. pictograph, bar

graph, line plot

graph, symbol

3.3

MD 3

I/R

/M

ODE Draw a scaled picture graph and a

scaled bar graph to represent a data

set with several categories. Solve one-

and two-step “how many more” and

“how many less” problems using

information presented in scaled bar

graphs.

2 bar graphs, counters,

Measurement and

Data

Represent and interpret data. measure, length,

inch

3.4

MD 4

I/R

/M

ODE Generate measurement data by

measuring lengths using rulers

marked with halves and fourths of an

inch. Show the data by making a line

plot, where the horizontal scale is

marked off in appropriate

units—whole numbers, halves, or

quarters

3,4 rulers

Measurement and

Data

Geometric measurement:

understand concepts of area and

relate area to multiplication and to

addition.

area 3.5

MD a

I/R

/M

ODE Recognize area as an attribute of

plane figures and understand

concepts of area measurement.

a. A square with side length 1 unit,

called “a unit square,” is said to have

“one square unit” of area, and can be

used to measure area.

b. A plane figure which can be

covered without gaps or overlaps by n

unit squares is said to have an area

of n square units

3,4 tiles, Cheeze-its

Measurement and

Data




addition.

area 3.6

MD

I/R

/M

ODE Measure areas by counting unit

squares (square cm, square m,

square in, square ft, and improvised

units).

3,4 tiles, Cheeze-its

6

Math

Curriculum Map

Grade 3


Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

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Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data




addition.

perimeter, area 3.7 I/R

/M

ODE Relate area to the operations of

multiplication and addition.

3,4

Measurement and

Data




addition.

area 3.7 a I/R

/M

ODE a. Find the area of a rectangle with

whole-number side lengths by tiling it,

and show that the area is the same

as would be found by multiplying the

side lengths.

3,4 tiles

Measurement and

Data




addition.

perimeter 3.7 b I/R

/M

ODE b. Multiply side lengths to find areas

of rectangles with whole number side

lengths in the context of solving real

world and mathematical problems,

and represent whole-number

products as rectangular areas in

mathematical reasoning.

3,4 tiles

Measurement and

Data




addition.

area 3.7

MD c

I/R ODE c. Use tiling to show in a concrete

case that the area of a rectangle with

whole-number side lengths a and b +

c is the sum of a × b and a × c. Use

area models to represent the

distributive property in mathematical

reasoning.

3,4 tiles

Measurement and

Data




addition.

area 3.7

MD d

I/R ODE d. Recognize area as additive. Find

areas of rectilinear figures by

decomposing them into non-

overlapping rectangles and adding

the areas of the non-overlapping

parts, applying this technique to solve

real world problems.

3,4

7

Math

Curriculum Map

Grade 3


Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

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Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data


recognize perimeter as an

attribute of plane figures and

distinguish between linear and

area measures.

perimeter, area 3.8

MD

I/R ODE Solve real world and mathematical

problems involving perimeters of

polygons, including finding the

perimeter given the side lengths,

finding an unknown side length, and

exhibiting rectangles with the same

perimeter and different areas or with

the same area and different

perimeters.

3,4 tiles, 1 inch/cm grid

paper, string,

geoboards, rubber

bands

Measurement and

Data

Counting back change to $10.00 penny, nickel,

quarter, dime, bills

3.9

MD

I/R TC Ability to count back change using

coins and bills the simplest way.

Money (bills and

coins)


attributes

two dimensional,

attributes, rhombus,

rectangle,

quadrilateral

3. G

1

I/R

/M

ODE Understand that shapes in different

categories (e.g., rhombuses,

rectangles, and others) may share

attributes (e.g., having four sides),

and that the shared attributes can

define a larger category (e.g.,

quadrilaterals). Recognize

rhombuses, rectangles, and squares

as examples of quadrilaterals, and

draw examples of quadrilaterals that

do not belong to any of these

subcategories

3,4 attribute blocks


attributes

equal parts 3.G 2 I/R

/M

ODE Partition shapes into parts with equal

areas. Express the area of each part

as a unit fraction of the whole.

3,4 Fraction bars,

Fraction circles

8

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Operations and

Algebraic Thinking

Use the four operations

with whole numbers to

solve problems.

multiplication

equation, number

sentence, array,

product, factors,

Commutative

Property, Zero

Property, Identity

Property,

operations,

inverse operation,

fact family, mental

computation

4.OA.1 R/M ODE Interpret a multiplication equation

as a comparison, e.g., interpret 35

= 5 × 7 as a statement that 35 is 5

times as many as 7 and 7 times as

many as 5. Represent verbal

statements of multiplicative

comparisons as multiplication

equations.

1,2,3,4 grid paper, place

value blocks, coloring

tools, counters, index

cards, technology

Operations and

Algebraic Thinking



solve problems.

equations,

symbol,

multiplication,

division, product,

factors, partial

product,

quotients,

dividend, divisor

4.AO.2 I/R ODE Multiply or divide to solve word

problems involving multiplicative

comparison, e.g., by using drawings

and equations with a symbol for the

unknown number to represent the

problem, distinguishing

multiplicative comparison from

additive comparison.

1,2,3,4 grid paper, coloring

tools, counters,

technology

1

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Operations and

Algebraic Thinking



solve problems.

multistep,

remainders,

operations,

reasonableness,

estimate

4.AO.3 I/R ODE Solve multistep word problems

posed with whole numbers and

having whole-number answers

using the four operations, including

problems in which remainders must

be interpreted. Represent these

problems using equations with a

letter standing for the unknown

quantity. Assess the

reasonableness of answers using

mental computation and estimation

strategies including rounding.


tools, counters,

technology

Operations and

Algebraic Thinking

Gain familiarity with

factors and multiples.

factors, multiples,

prime, composite,

range, Distributive

Property

4.AO.4 I/R ODE Find all factor pairs for a whole

number in the range 1-100.

Recognize that a whole number is a

multiple of each of its factors.

Determine whether a given whole

number is the range 1-100 is a

multiple of a given one-digit

number. Determine whether a given

whole number in the range 1-100 is

prime or composite.


tools, counters, index

cards, technology

2

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Operations and

Algebraic Thinking

Generate and analyze

patterns.

pattern, shape

pattern, number

pattern, multiple,

sequence,

repeating rule

4.AO.5 I/R ODE Generate a number or shape

pattern that follows a given rule.

Identify apparent features of the

pattern that were not explicit in the

rule itself.

For example, given the rule “Add 3”

and the starting number 1, generate

terms in the resulting sequence and

observe that the terms appear to

alternate between odd and even

numbers. Explain informally why the

numbers will continue to alternate in

this way.

1,2,3,4 hundred chart,

pattern blocks,

tangram pieces, two-

color counters, grid

paper, cubes,

technology

Number and

operations in base

ten

Generalize place value

understanding for multi-

digit whole numbers.

place value,

mental multiplying

and dividing by

10's, multi-digit

number

4.NBT.

1

I/R ODE Recognize that in a multi-digit whole

number, a digit in one place

represents ten times what it

represents in the place to its right.

For example, recognize that 700 ÷

70 = 10 by applying concepts of

place value and division.

1,2,3,4 place value chart,

place value blocks,

index card, coloring

tools, two-color

counters, technology

Number and

operations in base

ten




place value, base

ten, expanded

form, standard

form, word form,

greater than, less

than, equal to,

compare, order,

symbols

4.NBT.

2

I/R/M ODE

TC

Read and write multi-digit whole

numbers using base-ten numerals,

number names, and expanded

form. Compare two multi-digit

numbers based on meanings of the

digits in each place, using >, =, and

< symbols to record the results of

comparisons.


place value blocks,

technology

3

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

operations in base

ten




place value,

rounding,

breaking apart

4.NBT.

3

R/M ODE Use place value understanding to

round multi-digit whole numbers to

any place.

1,2,3,4 number lines, place

value chart, place


tools, technology

Number and

operations in base

ten

Use place value

understanding and

properties of operations

to perform multi-digit

arithmetic.

addend, sum,

difference, digit,

numeral,

regrouping,

inverse operation,

addition,

subtraction

4.NBT.

4

R/M ODE Fluently add and subtract multi-digit

whole numbers using the standard

algorithm.


place value blocks,

technology

Number and

operations in base

ten

Use place value

understanding and


perform multi-digit

arithmetic.

Distributive,

Associative,

Commutative,

Identity Properties

of multiplication,

array, regrouping,

partial products,

compensation,

equation,

compatible

numbers,

calculation,

illustrate

4.NBT.

5

I/R ODE Multiply a whole number of up to

four digits by a one-digit whole

number, and multiply two two-digit

numbers, using strategies based on

place value and the properties of

operations. Illustrate and explain the

calculation by using equations,

rectangular arrays, and/or area

models.

1,2,3,4 grid paper, block


tools, number lines,

calculators,

technology

4

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

operations in base

ten

Use place value

understanding and


perform multi-digit

arithmetic.

divide, quotient,

dividend, divisor,

remainder,

models, arrays,

equations, inverse

operation,

repeated

subtraction, area

models, arrays

4.NBT.

6

I/R ODE Find whole-number quotients and

remainders with up to four-digit

dividends and one-digit divisors,

using strategies based on place

value, the properties of operations,

and/or the relationship between

multiplication and division. Illustrate

and explain the calculation by using

equations, rectangular arrays,

and/or area models.

1,2,3,4 calculators, coloring

tools, two-color

counters, place value

blocks, grid paper,

technology

Number and

Operations –

Fractions

Extend understanding of

fraction equivalence and

ordering.

fraction,

equivalent

fractions,

numerator,

denominator,

models

4.NF.1 I/R ODE Explain why a fraction a/b is

equivalent to a fraction (n × a)/(n ×

b) by using visual fraction models,

with attention to how the number

and size of the parts differ even

though the two fractions themselves

are the same size. Use this

principle to recognize and generate

equivalent fractions.

1,2,3,4 fraction strips,

number lines, strips

of paper, masking

tape, technology

5

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

Operations –

Fractions

Extend understanding of

fraction equivalence and

ordering.

fraction,

equivalent

fractions,

numerator,

denominator,

benchmark

fractions, fraction

models, compare,

common

denominator

4.NF.2 I/R ODE Compare two fractions with different

numerators and different

denominators, e.g., by creating

common denominators or

numerators, or by comparing to a

benchmark fraction such as 1/2.

Recognize that comparisons are

valid only when the two fractions

refer to the same whole. Record the

results of comparisons with symbols

>, =, or <, and justify the

conclusions, e.g., by using a visual

fraction model.

1,2,3,4 fraction strips,

number lines, strips

of paper, masking

tape, technology

6

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

Operations –

Fractions

Build fractions from unit

fractions by applying and

extending previous

understandings of

operations on whole

numbers.

fraction,

numerator,

denominator,

improper fraction,

mixed number,

simplify, reduce,

decompose

4.NF.3 I/R ODE Understand a fraction a/b with a > 1

as a sum of fractions 1/b.

a. Understand addition and

subtraction of fractions as joining

and separating parts referring to the

same whole.

b. Decompose a fraction into a sum

of fractions with the same

denominator in more than one way,

recording each decomposition by

an equation. Justify

decompositions, e.g., by using a

visual fraction model.

Examples: 3/8 = 1/8 + 1/8 + 1/8 ;

3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8

= 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers

with like denominators, e.g., by

replacing each mixed number with

an equivalent fraction, and/or by

using properties of operations and

the relationship between addition

and subtraction.

d. Solve word problems involving

addition and subtraction of fractions

referring to the same whole and

having like denominators, e.g., by

using visual fraction models and

equations to represent the problem.

1,2,3,4 fraction strips or

circles, number lines,

strips of paper,

masking tape,

coloring tools,

scissors, grid paper,

technology

7

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

Operations –

Fractions

Build fractions from unit

fractions by applying and

extending previous

understandings of

operations on whole

numbers.

fraction, whole

number, unit

fraction,

numerator,

denominator,

models,

equations

4.NF.4 I/R ODE Apply and extend previous

understandings of multiplication to

multiply a fraction by a whole

number.

a. Understand a fraction a/b as a

multiple of 1/b.

For example, use a visual fraction

model to represent 5/4 as the

product 5 × (1/4), recording the

conclusion by the equation 5/4 = 5 ×

(1/4).

b. Understand a multiple of a/b as a

multiple of 1/b, and use this

understanding to multiply a fraction

by a whole number.

For example, use a visual fraction

model to express 3 × (2/5) as 6 ×

(1/5), recognizing this product as

6/5. (In general, n × (a/b) = (n ×

a)/b.)

c. Solve word problems involving

multiplication of a fraction by a

whole number, e.g., by using visual

fraction models and equations to


For example, if each person at a

party will eat 3/8 of a pound of roast

beef, and there will be 5 people at

the party, how many pounds of

roast beef will be needed? Between

what two whole numbers does your

answer lie?

1,2,3,4 paper strips,

scissors, fraction

strips, technology

8

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Number and

Operations –

Fractions

Understand decimal

notation for fractions,

and compare decimal

fractions.

fraction,

numerator,

denominator,

equivalent

fraction, express

4.NF.5 I/R ODE Express a fraction with denominator

10 as an equivalent fraction with

denominator 100, and use this

technique to add two fractions with

respective denominators 10 and

100.

For example, express 3/10 as

30/100, and add 3/10 + 4/100 =

34/100.

1,2,3,4 decimals models,

number lines, grid

paper, coloring tools,

decimal place value

chart, technology

Number and

Operations –

Fractions

Understand decimal

notation for fractions, and

compare decimal fractions.

decimal, decimal

point, decimal

notation, fraction,

tenths,

hundredths,

convert

4.NF.6 I/R ODE Use decimal notation for fractions

with denominators 10 or 100.

For example, rewrite 0.62 as

62/100; describe a length as 0.62

meters; locate 0.62 on a number

line diagram.

1,2,3,4 rulers, number line

diagrams, decimal

place value chart,

technology

Number and

Operations –

Fractions

Understand decimal

notation for fractions, and

compare decimal fractions.

tenths,

hundredths,

decimal point

4.NF.7 I/R ODE Compare two decimals to

hundredths by reasoning about their

size. Recognize that comparisons

are valid only when the two

decimals refer to the same whole.

Record the results of comparisons

with the symbols >, =, or <, and

justify the conclusions, e.g., by

using a visual model.

1,2,3,4 base 10 blocks,

number line, grid

paper

9

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data


measurement and

conversion of

measurement from a

larger unit to a smaller

unit.

length, inch (in),

foot (ft.), yard

(yd.), mile (mi),

millimeter (mm),

centimeter

(cm),decimeter

(dm), meter (m),

kilometer (km),

capacity,

gallon(gal) , quart

(qt), pint (pt.), cup

(c), tablespoon

Tbsp.), liter (l),

milliliter (ml),

weight, ton (T),

pound (lb.), ounce

(oz.), mass, gram

(g), milligram

(mg), time, hour

(hr.), minute

(min), seconds

(sec), conversion,

measurement

system,

equivalent,

elapsed time,

scale, equivalent

measurement,

money, quantity

4.MD.

1

I/R ODE Know relative sizes of

measurement units within one

system of units including km, m,

cm; kg, g; lb., oz.; l, ml; hr., min,

sec. Within a single system of

measurement, express

measurements in a larger unit in

terms of a smaller unit. Record

measurement equivalents in a two

column table.

For example, know that 1 ft. is 12

times as long as 1 in. Express the

length of a 4 ft. snake as 48 in.

Generate a conversion table for feet

and inches listing the number pairs

(1, 12), (2, 24), (3, 36), ...

1,2,3,4 ruler, yardstick,

meter stick, masking

tape, containers

(gallon, quart, pint,

cup, tablespoon), liter

bottle, eyedropper,

funnel, scale,

weights, clock face,

place value blocks,

technology

10

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data


measurement and

conversion of

measurement from a larger

unit to a smaller unit.

distance, length,

time intervals

(elapsed), liquid

volume, mass,

money, fractions,

decimals,

4.MD.

2

I/R ODE Use the four operations to solve

word problems involving distances,


masses of objects, and money,

including problems involving simple

fractions or decimals, and problems

that require expressing

measurements given in a larger unit

in terms of a smaller unit.

Represent measurement quantities

using diagrams such as number

line diagrams that feature a

measurement scale.

1,2,3,4 grid paper, bills and

coins, ruler,

yardstick, meter

stick, masking tape,

containers (gallon,

quart, pint, cup,

tablespoon), liter

bottle, eyedropper,

funnel, scale,

weights, clock face,

place value blocks,

technology

Measurement and

Data


measurement and

conversion of

measurement from a larger

unit to a smaller unit.

perimeter, area,

formulas,

rectangles,

length, width,

squared, tiles

4.MD.

3

I/R ODE Apply the area and perimeter

formulas for rectangles in real world

and mathematical problems.


tools, cut out shapes,

technology

Measurement and

Data

Represent and interpret

data

line plot, data set

fractions, range

4.MD.

4

I/R ODE Make a line plot to display a data

set of measurements in fractions of

a unit (1/2, 1/4, 1/8). Solve

problems involving addition and

subtraction of fractions by using

information presented in line plots.

For example, from a line plot find

and interpret the difference in length

between the longest and shortest

specimens in an insect collection.

1,2,3,4 graph paper,

technology

11

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data


understand concepts of

angle and measure

angles.

degree, angle,

endpoint, vertex,

angle

measurement,

circle, circular arc

4.MD.

5

I/R ODE Recognize angles as geometric

shapes that are formed wherever

two rays share a common endpoint,

and understand concepts of angle

measurement:

a. An angle is measured with

reference to a circle with its center

at the common endpoint of the rays,

by considering the fraction of the

circular arc between the points

where the two rays intersect the

circle. An angle that turns through

1/360 of a circle is called a “one-

degree angle,” and can be used to

measure angles.

b. An angle that turns through n one-

degree angles is said to have an

angle measure of n degrees.

1,2,3,4 clock face, pattern

blocks, technology

Measurement and

Data



angle and measure angles.

protractor,

degree, angle,

4.MD.

6

I/R ODE Measure angles in whole-number

degrees using a protractor. Sketch

angles of specified measure.

1,2,3,4 protractor, ruler

12

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Measurement and

Data



angle and measure angles.

angle, additive,

decompose, non-

overlapping parts,

sum, diagram,

symbol, equation,

angle

measurement

4.MD.

7

I/R ODE Recognize angle measure as

additive. When an angle is

decomposed into non-overlapping

parts, the angle measure of the

whole is the sum of the angle

measures of the parts. Solve

addition and subtraction problems

to find unknown angles on a

diagram in real world and

mathematical problems, e.g., by

using an equation with a symbol for

the unknown angle measure.

1,2,3,4 coloring tools,

protractor,

technology

Geometry Draw and identify lines

and angles, and classify

shapes by properties of

their lines and angles.

point, plane, line,

line segment, ray,

angle, vertex,

endpoint,

perpendicular

lines, parallel

lines, intersecting

lines, right angle,

acute angle,

obtuse angle,

straight angle, two-

dimensional

figure

4.G.1 I/R/M ODE Draw points, lines, line segments,

rays, angles (right, acute, obtuse),

and perpendicular and parallel lines.

Identify these in two-dimensional

figures.


tools, straws,

Playdoh, dot paper,

technology

13

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Geometry Draw and identify lines and

angles, and classify shapes

by properties of their lines

and angles.

classify, category,

sort, two-

dimensional

figure, parallel

lines,

perpendicular

lines, angle,

triangle, right

triangle, acute

angle, obtuse

angle, equilateral

triangle, isosceles

triangle, scalene

triangle, polygon,

regular, irregular,

quadrilateral,

pentagon,

hexagon,

octagon,

parallelogram,

rectangle, square,

rhombus,

trapezoid,

geometric shapes

4.G.2 I/R ODE Classify two-dimensional figures

based on the presence or absence

of parallel or perpendicular lines, or

the presence or absence of angles

of a specified size. Recognize right

triangles as a category, and identify

right triangles.

1,2,3,4 geoboards, graph

paper, cut out

shapes, spaghetti,

Playdoh, straws,

pattern blocks, ruler,

protractor,

technology

14

Math

Curriculum Map

Grade 4

Domain ClustersKey

Vocabulary

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Geometry Draw and identify lines and

angles, and classify shapes

by properties of their lines

and angles.

line symmetry,

two-dimensional

figure, matching

parts, fold

4.G.3 I/R/M ODE Recognize a line of symmetry for a

two-dimensional figure as a line

across the figure such that the

figure can be folded along the line

into matching parts. Identify line-

symmetric figures and draw lines of

symmetry.

1,2,3,4 cut out shapes,

technology

15

Math

Curriculum Map

Grade 5

Domain Cluster Key Vocabulary

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Student Engagement/

Learning Activity /

Special Resource / Web

Link

Operations &

Algebraic

Thinking

Write and interpret

numerical

expressions.

order of operations,

numerical

expressions,

equations, evaluate

5.OA.

1

I, R ODE Use parentheses, brackets, or braces in

numerical expressions, and evaluate

expressions with these symbols.

1, 2, 3, 4 modeling, student practice,

technology

Operations &

Algebraic Thinking

Write and interpret

numerical

expressions.

variable, algebraic

expressions

5.OA.

2

R ODE Write simple expressions that record

calculations with numbers, and interpret

numerical expressions without

evaluating them. For example, express

the calculation “add 8 and 7, then

multiply by 2” as 2 × (8 + 7). Recognize

that 3 × (18932 + 921) is three times as

large as 18932 + 921, without having to

calculate the indicated sum or product.


technology

Operations &

Algebraic Thinking

Analyze patterns

and relationships.

corresponding,

sequence, term,

coordinate plane,

ordered pairs, origin,

x-axis, y-axis

5.OA.

3

I, R ODE Generate two numerical patterns using

two given rules. Identify apparent

relationships between corresponding

terms. Form ordered pairs consisting of

corresponding terms from the two

patterns, and graph the ordered pairs on

a coordinate plane. For example, given

the rule “Add 3” and the starting number

0, and given the rule “Add 6” and the

starting number 0, generate terms in the

resulting sequences, and observe that

the terms in one sequence are twice the

corresponding terms in the other

sequence. Explain informally why this is

so.


technology, grid paper, rulers

1

Math

Curriculum Map

Grade 5


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Student Engagement/

Learning Activity /


Link

Number &

Operations in

Base Ten

Understand the

place value system.

digits, value, standard

form, expanded form,

word form

5.NB

T.1

R, M ODE Recognize that in a multi-digit number, a

digit in one place represents 10 times as

much as it represents in the place to its

right and 1/10 of what it represents in the

place to its left.


technology, grid paper, place

value chart

Number &

Operations in Base

Ten

Understand the place

value system.

factors, product,

multiple, exponential

notation, exponent,

base, standard form,

expanded form,

squared, cubed,

power

5.NB

T.2

I, R ODE Explain patterns in the number of zeros

of the product when multiplying a

number by powers of 10, and explain

patterns in the placement of the decimal

point when a decimal is multiplied or

divided by a power of 10. Use whole-

number exponents to denote powers of

10.


technology, number cards or

tiles, calculators

Number &

Operations in Base

Ten


value system.

decimals, tenths,

hundredths,

thousandths

5.NB

T.3

I, R ODE Read, write, and compare decimals to

thousandths.


technology, grid paper, place

value chart

Number &

Operations in Base

Ten


value system.

equivalent decimals 5.NB

T.3.a

I, R ODE Read and write decimals to thousandths

using base-ten numerals, number

names, and expanded form, e.g.,

347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 ×

(1/10) + 9 × (1/100) + 2 × (1/1000).


technology

Number &

Operations in Base

Ten


value system.

greater than, less

than

5.NB

T.3.b

I, R ODE Compare two decimals to thousandths

based on meanings of the digits in each

place, using >, =, and < symbols to

record the results of comparisons.


technology, grid paper

2

Math

Curriculum Map

Grade 5


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Student Engagement/

Learning Activity /


Link

Number &

Operations in Base

Ten


value system

rounding 5.NB

T.4

I, R ODE Use place value understanding to round

decimals to any place.


technology, number line,

rounding rap

Number &

Operations in Base

Ten

Perform operations

with multi-digit whole

numbers and with

decimals to

hundredths.

underestimate,

overestimate,

distributive property,

partial products

5.NB

T.5

I, R ODE Fluently multiply multi-digit whole

numbers using the standard algorithm.


technology, grid paper,

whiteboards

Number &

Operations in Base

Ten

Perform operations


numbers and with

decimals to

hundredths.

commutative property

of multiplication,

associative property

of multiplication,

identity property of

multiplication, zero

property of

multiplication,

dividend, divisor,

quotient

5.NB

T.6

R ODE Find whole-number quotients of whole

numbers with up to four-digit dividends

and two-digit divisors, using strategies

based on place value, the properties of


between multiplication and division.

Illustrate and explain the calculation by

using equations, rectangular arrays,

and/or area models.


technology, grid paper, arrays,

whiteboards, division acrostic

Number &

Operations in Base

Ten

Perform operations


numbers and with

decimals to

hundredths.

commutative

property, associative

property, compatible

numbers,

compensation

5.NB

T.7

I, R ODE Add, subtract, multiply, and divide

decimals to hundredths, using concrete

models or drawings and strategies

based on place value, properties of


between addition and subtraction; relate

the strategy to a written method and



technology, base-ten blocks

3

Math

Curriculum Map

Grade 5


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Specific Standard

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Student Engagement/

Learning Activity /


Link

Number &

Operations -

Fractions

Use equivalent

fractions as a

strategy to add and

subtract fractions.

equivalent fractions,

simplest form,

common multiple,

least common

multiple (LCM),

common

denominator, least

common

denominator (LCD),

proper fraction,

improper fraction,

mixed number

5.NF.

1

R ODE Add and subtract fractions with unlike

denominators (including mixed

numbers) by replacing given fractions

with equivalent fractions in such a way

as to produce an equivalent sum or

difference of fractions with like

denominators. For example, 2/3 + 5/4 =

8/12 + 15/12 = 23/12. (In general, a/b +

c/d = (ad + bc)/bd.)


technology, fraction strips,

fraction circles

Number &

Operations -

Fractions

Use equivalent

fractions as a strategy

to add and subtract

fractions.

benchmark fraction 5.NF.

2

R ODE Solve word problems involving addition

and subtraction of fractions referring to

the same whole, including cases of

unlike denominators, e.g., by using

visual fraction models or equations to

represent the problem. Use benchmark

fractions and number sense of fractions

to estimate mentally and assess the

reasonableness of answers. For

example, recognize an incorrect result

2/5 + 1/2 = 3/7, by observing that 3/7 <

1/2.



fraction circles, measuring

cups

4

Math

Curriculum Map

Grade 5


Co

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Specific Standard

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Student Engagement/

Learning Activity /


Link

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and

division to multiply

and divide fractions.

numerator,

denominator,

improper fraction,

mixed number

5.NF.

3

I, R ODE Interpret a fraction as division of the

numerator by the denominator (a/b = a ÷

b). Solve word problems involving

division of whole numbers leading to

answers in the form of fractions or mixed

numbers, e.g., by using visual fraction

models or equations to represent the

problem. For example, interpret 3/4 as

the result of dividing 3 by 4, noting that

3/4 multiplied by 4 equals 3, and that

when 3 wholes are shared equally

among 4 people each person has a

share of size 3/4. If 9 people want to

share a 50-pound sack of rice equally

by weight, how many pounds of rice

should each person get? Between what

two whole numbers does your answer

lie?



fraction circles

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



numerator,

denominator,

improper fraction,

mixed number

5.NF.

4

I, R ODE Apply and extend previous

understandings of multiplication to

multiply a fraction or whole number by a

fraction.



fraction circles

5

Math

Curriculum Map

Grade 5


Co

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Grade Level

Specific Standard

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Student Engagement/

Learning Activity /


Link

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



equation, product,

quotient, order of

operations

5.NF.

4.a

I, R ODE Interpret the product (a/b) × q as a parts

of a partition of q into b equal parts;

equivalently, as the result of a sequence

of operations a × q ÷ b. For example,

use a visual fraction model to show (2/3)

× 4 = 8/3, and create a story context for

this equation. Do the same with (2/3) ×

(4/5) = 8/15. (In general, (a/b) × (c/d) =

ac/bd.)



fraction circles

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



area, square units 5.NF.

4.b

I, R ODE Find the area of a rectangle with

fractional side lengths by tiling it with unit

squares of the appropriate unit fraction

side lengths, and show that the area is

the same as would be found by

multiplying the side lengths. Multiply

fractional side lengths to find areas of

rectangles, and represent fraction

products as rectangular areas.


technology, color tiles, grid

paper

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



resizing, scaling, 5.NF.

5

R ODE Interpret multiplication as scaling

(resizing), by:


technology

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



factors, product 5.NF.

5.a

R ODE Comparing the size of a product to the

size of one factor on the basis of the

size of the other factor, without

performing the indicated multiplication.


technology

6

Math

Curriculum Map

Grade 5


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Grade Level

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Student Engagement/

Learning Activity /


Link

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



resizing, scaling,

equivalent fractions

5.NF.

5.b

R ODE Explaining why multiplying a given

number by a fraction greater than 1

results in a product greater than the

given number (recognizing multiplication

by whole numbers greater than 1 as a

familiar case); explaining why multiplying

a given number by a fraction less than 1

results in a product smaller than the

given number; and relating the principle

of fraction equivalence a/b = (n × a)/(n ×

b) to the effect of multiplying a/b by 1.


technology

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



equations, improper

fractions, mixed

numbers

5.NF.

6

R ODE Solve real world problems involving

multiplication of fractions and mixed

numbers, e.g., by using visual fraction

models or equations to represent the

problem.



fraction circles

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and



fraction, numerator,

denominator,

reciprocal

5.NF.

7

I, R ODE Apply and extend previous

understandings of division to divide unit

fractions by whole numbers and whole

numbers by unit fractions. (Students

able to multiply fractions in general can

develop strategies to divide fractions in

general, by reasoning about the

relationship between multiplication and

division. But division of a fraction by a

fraction is not a requirement at this

grade.)


technology

7

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Curriculum Map

Grade 5


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Specific Standard

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Student Engagement/

Learning Activity /


Link

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and




denominator,

reciprocal

5.NF.

7.a

I, R ODE Interpret division of a unit fraction by a

non-zero whole number, and compute

such quotients. For example, create a

story context for (1/3) ÷ 4, and use a

visual fraction model to show the

quotient. Use the relationship between

multiplication and division to explain that

(1/3) ÷ 4 = 1/12 because (1/12) × 4 =

1/3.


technology, fractions strips,

fraction circles

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and




denominator,

reciprocal

5.NF.

7.b

I, R ODE Interpret division of a whole number by a

unit fraction, and compute such

quotients. For example, create a story

context for 4 ÷ (1/5), and use a visual

fraction model to show the quotient. Use

the relationship between multiplication

and division to explain that 4 ÷ (1/5) =

20 because 20 × (1/5) = 4.



fraction circles

Number &

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and




denominator,

reciprocal

5.NF.

7c.

I, R ODE Solve real world problems involving

division of unit fractions by non-zero

whole numbers and division of whole

numbers by unit fractions, e.g., by using

visual fraction models and equations to

represent the problem. For example,

how much chocolate will each person

get if 3 people share 1/2 lb of chocolate

equally? How many 1/3-cup servings

are in 2 cups of raisins?



fraction circles

8

Math

Curriculum Map

Grade 5


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Student Engagement/

Learning Activity /


Link

Measurement &

Data

Convert like

measurement units

within a given

measurement

system.

metric, customary,

meters, liters, grams,

kilo-, centi-, milli-

5.MD.

1

R ODE Convert among different-sized standard

measurement units within a given

measurement system (e.g., convert 5

cm to 0.05 m), and use these

conversions in solving multi-step, real

world problems.


technology, metric acrostic,

rulers, meter sticks, measuring

cups, empty containers (pint,

quart, liter, etc.)

Measurement &

Data

Represent and

interpret data.

line plot, outlier,

survey, data, sample,

frequency table

5.MD.

2

R ODE Make a line plot to display a data set of

measurements in fractions of a unit (1/2,

1/4, 1/8). Use operations on fractions for

this grade to solve problems involving

information presented in line plots. For

example, given different measurements

of liquid in identical beakers, find the

amount of liquid each beaker would

contain if the total amount in all the

beakers were redistributed equally.


technology, rulers

Measurement &

Data

Geometric

measurement:

understand

concepts of volume

and relate volume to

multiplication and

to addition.

volume, three-

dimensional shape,

cube, face, edge,

vertex, vertices,

prism, cylinder, cone,

pyramid

5.MD.

3

I, R ODE Recognize volume as an attribute of

solid figures and understand concepts of

volume measurement.


technology, solids

Measurement &

Data

Geometric

measurement:

understand concepts

of volume and relate

volume to

multiplication and to

addition.

volume, cubic unit 5.MD.

3.a

I, R ODE A cube with side length 1 unit, called a

“unit cube,” is said to have “one cubic

unit” of volume, and can be used to

measure volume.


technology, centimeter cubes

9

Math

Curriculum Map

Grade 5


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Student Engagement/

Learning Activity /


Link

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.


3.b

I, R ODE A solid figure which can be packed

without gaps or overlaps using n unit

cubes is said to have a volume of n

cubic units.


technology, centimeter cubes,

small cardboard boxex

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.


4

I, R ODE Measure volumes by counting unit

cubes, using cubic cm, cubic in, cubic ft,

and improvised units.



rulers, meter sticks

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.


5

I, R ODE Relate volume to the operations of

multiplication and addition and solve real

world and mathematical problems

involving volume.


technology

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.


5.a

I, R ODE Find the volume of a right rectangular

prism with whole-number side lengths by

packing it with unit cubes, and show that

the volume is the same as would be

found by multiplying the edge lengths,

equivalently by multiplying the height by

the area of the base. Represent

threefold whole-number products as

volumes, e.g., to represent the

associative property of multiplication.



small cardboard boxes

10

Math

Curriculum Map

Grade 5


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Grade Level

Specific Standard

Qu

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Student Engagement/

Learning Activity /


Link

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.

volume, cubic unit,

rectangular prism

5.MD.

5.b

I, R ODE Apply the formulas V = l × w × h and V =

b × h for rectangular prisms to find

volumes of right rectangular prisms with

whole-number edge lengths in the

context of solving real world and

mathematical problems.


technology

Measurement &

Data

Geometric

measurement:

understand concepts


volume to


addition.

volume, cubic unit,

rectangular prism

5.MD.

5.c

I, R ODE Recognize volume as additive. Find

volumes of solid figures composed of

two non-overlapping right rectangular

prisms by adding the volumes of the non-

overlapping parts, applying this

technique to solve real world problems.


technology,

11

Math

Curriculum Map

Grade 5


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Grade Level

Specific Standard

Qu

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Student Engagement/

Learning Activity /


Link

Geometry Graph points on the

coordinate plane to

solve real-world and

mathematical

problems.

coordinate grid, x-

axis, y-axis, origin,

ordered pair, x-

coordinate, y-

coordinate

5.G.1 I, R ODE Use a pair of perpendicular number

lines, called axes, to define a coordinate

system, with the intersection of the lines

(the origin) arranged to coincide with the

0 on each line and a given point in the

plane located by using an ordered pair of

numbers, called its coordinates.

Understand that the first number

indicates how far to travel from the origin

in the direction of one axis, and the

second number indicates how far to

travel in the direction of the second axis,

with the convention that the names of

the two axes and the coordinates

correspond (e.g., x -axis and x -

coordinate, y -axis and y -coordinate).


technology, grid paper, rulers,

Geometry Graph points on the

coordinate plane to

solve real-world and

mathematical

problems.

coordinate grid, x-

axis, y-axis, origin,

ordered pair, x-

coordinate, y-

coordinate, quadrant

I

5.G.2 I, R ODE Represent real world and mathematical

problems by graphing points in the first

quadrant of the coordinate plane, and

interpret coordinate values of points in

the context of the situation.


technology, grid paper

12

Math

Curriculum Map

Grade 5


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Grade Level

Specific Standard

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Student Engagement/

Learning Activity /


Link

Geometry Classify two-

dimensional figures

into categories

based on their

properties.

polygon, regular

polygon, triangle,

quadrilateral,

pentagon, hexagon,

octagon, equilateral

triange, isosceles

triangle, scalene

triangle, right triangle,

acute triangle, obtuse

triangle,

parallelogram,

trapezoid, rectangle,

rhombus, square,

generalization

5.G.3 R, M ODE Understand that attributes belonging to a

category of two-dimensional figures also

belong to all subcategories of that

category. For example, all rectangles

have four right angles and squares are

rectangles, so all squares have four

right angles.


technology, quadrilateral

flowchart, pattern blocks, The

Greedy Triangle by Marilyn

Burns

Geometry Classify two-

dimensional figures

into categories based

on their properties.

congruent, parallel

sides, right angles

5.G.4 R, M ODE Classify two-dimensional figures in a

hierarchy based on properties.


technology, pattern blocks,

geoboards

13

Math

Curriculum Map

Grade 6


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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Ratio &

Proportions

Understand ratio concepts

and use ratio reasoning to

solve problems.

ratio, unit rate,

proportion,

equivalent ratios

6.RP.1 I ODE Understand the concept of a ratio

and use ratio language to describe

a ratio relationship between two

quantities. For example, “The ratio

of wings to beaks in the bird house

at the zoo was 2:1, because for

1,2,3,4 Interactive smart

board activities with

whole group

instruction

Ratio &

Proportions

Understand ratio concepts

and use ratio reasoning to

solve problems.

ratio, unit rate,

proportion,

equivalent ratios

6.RP.2 I ODEUnderstand the concept of a unit

rate a/b associated with a ratio a:b

with b ≠ 0, and use rate language in

the context of a ratio relationship.

For example, “This recipe has a

ratio of 3 cups of flour to 4 cups of

sugar, so there is 3/4 cup of flour

for each cup of sugar.” “We paid

$75 for 15 hamburgers, which is a

rate of $5 per hamburger.”1

1,2,3,4 Use real world

example to

demonstrate

relationship

Ratio &

Proportions

Understand ratio concepts and

use ratio reasoning to solve

problems.

ratio, unit rate,

proportion,

equivalent ratios,

6.RP.3 I ODE Use ratio and rate reasoning to solve

real-world and mathematical

problems, e.g., by reasoning about

tables of equivalent ratios, tape

diagrams, double number line

diagrams, or equations.

1,2,3,4 Use real world

example to

demonstrate

relationship using

tables, number lines,

diagrams

1

Math

Curriculum Map

Grade 6


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Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number

system

Apply and extend previous

understandings of

multiplication and division

to divide fractions by

fractions.

Factors, Prime

Factorization,

Estimation, Greatest

Common Factor,

Least Common

Multiple ,Quotient,

Divident

6.NS.1. R ODEInterpret and compute quotients

of fractions, and solve word

problems involving division of

fractions by fractions, e.g., by

using visual fraction models and

equations to represent the

problem. For example, create a

story context for (2/3) ÷ (3/4) and

use a visual fraction model to

show the quotient; use the

relationship between

multiplication and division to

explain that (2/3) ÷ (3/4) = 8/9

because 3/4 of 8/9 is 2/3. (In

general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each

person get if 3 people share 1/2 lb

of chocolate equally? How many

3/4-cup servings are in 2/3 of a

cup of yogurt? How wide is a

rectangular strip of land with

length 3/4 mi and area 1/2 square

mi? Compute fluently with multi-

digit numbers and find common

factors and multiples.

1,2,3,4 Interactive smart

board activities with

whole group

instruction

2

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number

system

Compute fluently with multi-

digit numbers and find

common factors and multiples

Factors, Prime

Factorization,


Common Factor,

Least Common

Multiple ,Quotient,

Divident

6.NS.2 I ODE

Fluently divide multi-digit numbers

using the standard algorithm

1,2,3,4 Interactive smart board

activities with whole

group instruction

Number

systemApply and extend previous

understandings of


divide fractions by fractions.

Factors, Prime

Factorization,


Common Factor,

Least Common

Multiple ,Quotient,

Divident

6.NS.3. R ODE

TC

Fluently add, subtract, multiply, and

divide multi-digit decimals using the

standard algorithm for each operation

1,2,3,4 multiplication charts

& Calculators

Number

system


understandings of


divide fractions by fractions.

Factors, Prime

Factorization,


Common Factor,

Least Common

Multiple ,Quotient,

Divident

6.NS.4. R ODE

Find the greatest common factor

of two whole numbers less than

or equal to 100 and the least

common multiple of two whole

numbers less than or equal to 12.

Use the distributive property to

express a sum of two whole

numbers 1–100 with a common

factor as a multiple of a sum of

two whole numbers with no

common factor. For example,

express 36 + 8 as 4 (9 + 2).


understandings of numbers to the

system of rational numbers.

1,2,3,4 multiplication charts

& Calculators

3

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number

system


understandings of numbers

to the system of rational

numbers.

Positive & Negative

integers,

6.NS.5. R ODEUnderstand that positive and

negative numbers are used

together to describe quantities

having opposite directions or values

(e.g., temperature above/below

zero, elevation above/below sea

level, credits/debits,

positive/negative electric charge);

use positive and negative numbers

to represent quantities in real-world

contexts, explaining the meaning of

0 in each situation.

1,2,3,4 Number lines using

positive and negative

integers, counters,

thermometer

Number


understandings of numbers

to the system of rational

numbers.

Positive & Negative

integers, origin,

quadrants

6.NS.6. R ODE Understand a rational number as a

point on the number line. Extend

number line diagrams and coordinate

axes familiar from previous grades to

represent points on the line and in the

plane with negative number

coordinates

1,2,3,4

Number

system


understandings of numbers to

the system of rational numbers

Positive & Negative

integers, origin,

quadrants

6.NS.6. a R ODE Recognize opposite signs of numbers

as indicating locations on opposite

sides of 0 on the number line;

recognize that the opposite of the

opposite of a number is the number

itself, e.g., –(–3) = 3, and that 0 is its

own opposite

1,2,3,4 Number lines using

positive and negative

integers, counters,

thermometer

4

Math

Curriculum Map

Grade 6


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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number

system




Positive & Negative

integers, origin,

quadrants

6.NS.6. b R ODE

Understand signs of numbers in

ordered pairs as indicating locations

in quadrants of the coordinate plane;

recognize that when two ordered

pairs differ only by signs, the

locations of the points are related by

reflections across one or both axes



group instruction, graph

paper

Number

system




Positive & Negative

integers, origin,

quadrants

6.NS.6. c R ODE Find and position integers and other

rational numbers on a horizontal or

vertical number line diagram; find and

position pairs of integers and other

rational numbers on a coordinate

plane

1,2,3,4 Use real world example

to demonstrate

relationship using

tables, number lines,

diagrams

Number




Positive & Negative

integers, origin,

quadrants

6.NS.7 R ODE

Understand ordering and absolute

value of rational numbers.

1,2,3,4 Small group flash cards

and have students put

in order without talking

each has a number

card

Number

system




Positive & Negative

integers, origin,

quadrants

6.NS.7 a R ODE Interpret statements of inequality as

statements about the relative

position of two numbers on a

number line diagram. For example,

interpret –3 > –7 as a statement

that –3 is located to the right of –7

on a number line oriented from left

to right.

1,2,3,4 Smart board activity

with number line

5

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Number

system




Positive & Negative

integers, origin,

quadrants

6.NS.7 b I ODE Write, interpret, and explain

statements of order for rational

numbers in real-world contexts. For

example, write –3 co. > –7 co. to

express the fact that –3 co. is warmer

than –7 co.

1,2,3,4 Small group to

collaborate on writing

and statements using

real-world examples

Number

system




Positive & Negative

integers, origin,

quadrants, absolute

value

6.NS.7 c R ODE

Understand the absolute value of a

rational number as its distance from 0

on the number line; interpret absolute

value as magnitude for a positive or

negative quantity in a real-world

situation. For example, for an

account balance of –30 dollars, write

1,2,3,4 Tutorial video using

real world situations

Number

system




Positive & Negative

integers, origin,

quadrants

6.NS.7 d R Distinguish comparisons of absolute

value from statements about order.

For example, recognize that an

account balance less than –30

dollars represents a debt greater

than 30 dollars



group instruction

Number

system




Positive & Negative

integers, origin,

quadrants, absolute

value

6.NS.8. R ODESolve real-world and

mathematical problems by

graphing points in all four

quadrants of the coordinate plane.

Include use of coordinates and

absolute value to find distances

between points with the same first

coordinate or the same second

coordinate.



group instruction

Expressions

& Equations


understandings of arithmetic to

algebraic expressions

Algebra, evaluate,

exponents, variable

6.EE.1. R ODE Write and evaluate numerical

expressions involving whole-

number exponents.

1,2,3,4 Smart board activities

6

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions &

Equations




Algebra, coefficient,

evaluate, exponents,

quotient, variable

6.EE.2. R ODE Write, read, and evaluate expressions

in which letters stand for numbers.

1,2,3,4 Smart board activities

Expressions &

Equations






quotient, variable

6.EE.2. a R ODE Write expressions that record

operations with numbers and with

letters standing for numbers. For

example, express the calculation

“Subtract y from 5” as 5 – y.

1,2,3,4 smart board

activities, copies,

calculators

Expressions &

Equations






quotient, variable

6.EE.2. b R ODE Identify parts of an expression using

mathematical terms (sum, term,

product, factor, quotient,

coefficient); view one or more parts

of an expression as a single entity.

For example, describe the

expression 2 (8 + 7) as a product of

two factors; view (8 + 7) as both a

single entity and a sum of two

terms.

1,2,3,4 smart board

activities, copies,

calculators

7

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Tau

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions

& Equations






quotient, variable

6.EE.2. c R ODE Evaluate expressions at specific

values of their variables. Include

expressions that arise from formulas

used in real-world problems. Perform

arithmetic operations, including those

involving whole-number exponents, in

the conventional order when there are

no parentheses to specify a particular

order (Order of Operations). For

example, use the formulas V = s3

and A = 6 s2 to find the volume and

surface area of a cube with sides of

length s = 1/2.

1,2,3,4 smart board activities,

copies, calculators

Expressions

& Equations






quotient, variable

6.EE.3. RApply the properties of operations

to generate equivalent expressions.

For example, apply the distributive

property to the expression 3 (2 + x)

to produce the equivalent

expression 6 + 3x; apply the

distributive property to the

expression 24x + 18y to produce

the equivalent expression 6 (4x +

3y); apply properties of operations

to y + y + y to produce the

equivalent expression 3y.

1,2,3,4 Smart board

interactive, copies

8

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions

& Equations






quotient, variable

6.EE.4. ODEIdentify when two expressions are

equivalent (i.e., when the two

expressions name the same

number regardless of which value

is substituted into them). For

example, the expressions y + y +

y and 3y are equivalent because

they name the same number

regardless of which number y

stands for. Reason about and

solve one-variable equations and

inequalities.

1,2,3,4 Smart board

interactive, copies

Expressions &

Equations

Reason about and solve one-

variable equations and

inequalities.



quotient, variable

6.EE.5. I

Understand solving an equation or

inequality as a process of answering

a question: which values from a

specified set, if any, make the

equation or inequality true? Use

substitution to determine whether a

given number in a specified set

makes an equation or inequality true

1,2,3,4 Smart board

interactive, copies

Expressions

& Equations



inequalities.

6.EE.6.Use variables to represent numbers

and write expressions when solving

a real-world or mathematical

problem; understand that a variable

can represent an unknown number,

or, depending on the purpose at

hand, any number in a specified

set.

1,2,3,4 Smart board

interactive, copies

9

Math

Curriculum Map

Grade 6


Co

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dard

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Grade Level

Specific Standard

Qu

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Tau

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions

& Equations



quotient, variable

6.EE.7. ODESolve real-world and mathematical

problems by writing and solving

equations of the form x + p = q and

px = q for cases in which p , q and x

are all nonnegative rational number

1,2,3,4 Real world tutorial,

small group work

Expressions &

Equations



inequalities.



quotient, variable

6.EE.8. I ODEWrite an inequality of the form x >

c or x < c to represent a

constraint or condition in a real-

world or mathematical problem.

Recognize that inequalities of the

form x > c or x < c have infinitely

many solutions; represent

solutions of such inequalities on

number line diagrams.

1,2,3,4 Smart board, small

group work

10

Math

Curriculum Map

Grade 6


Co

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dard

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C

Grade Level

Specific Standard

Qu

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Tau

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions &

Equations

Represent and analyze

quantitative relationships

between dependent and

independent variables.



quotient, variable

6.EE.9. I ODEUse variables to represent two

quantities in a real-world problem

that change in relationship to one

another; write an equation to

express one quantity, thought of

as the dependent variable, in

terms of the other quantity,

thought of as the independent

variable. Analyze the relationship

between the dependent and

independent variables using

graphs and tables, and relate

these to the equation. For

example, in a problem involving

motion at constant speed, list and

graph ordered pairs of distances

and times, and write the equation

d = 65t to represent the

relationship between distance and

time.

1,2,3,4 Smart board, small

group work

Geometry Solve real-world and

mathematical problems

involving area, surface area,

and volume

triangles,

quadrilaterals,

polygon

6.G.1. R ODE Find the area of right triangles,

other triangles, special

quadrilaterals, and polygons by

composing into rectangles or

decomposing into triangles and

other shapes; apply these

techniques in the context of solving


problems.

1,2,3,4 Smart board, Thee

dimensional shapes

11

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link




and volume

volume, triangles,

quadrilaterals,

polygons

6.G.2. R ODEFind the volume of a right

rectangular prism with fractional

edge lengths by packing it with unit

cubes of the appropriate unit

fraction edge lengths, and show

that the volume is the same as

would be found by multiplying the

edge lengths of the prism. Apply the

formulas V = l w h and V = b h to

find volumes of right rectangular

prisms with fractional edge lengths

in the context of solving real-world

and mathematical problems.


dimensional shapes




and volume

volume, triangles,

quadrilaterals,

polygons

6.G.3. I ODE Draw polygons in the coordinate

plane given coordinates for the

vertices; use coordinates to find the

length of a side joining points with the

same first coordinate or the same

second coordinate. Apply these

techniques in the context of solving


problems


dimensional shapes




and volume

volume, triangles,

quadrilaterals,

polygons

6.G.4. R ODE Represent three-dimensional

figures using nets made up of

rectangles and triangles, and use

the nets to find the surface area

of these figures. Apply these

techniques in the context of

solving real-world and



dimensional shapes

12

Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Statistics &

Probability


statistical variability.

mean, median,

mode, histograms,

range, box plots,

outliers, statistics,

stem-and- leaf plot

6.SP.1. I ODE Recognize a statistical question as

one that anticipates variability in the

data related to the question and

accounts for it in the answers. For

example, “How old am I?” is not a

statistical question, but “How old are

the students in my school?” is a

statistical question because one

anticipates variability in students’

ages

1,2,3,4 Smart board tutorial,

small group Q/A

Statistics &

Probability



mean, median,

mode, histograms,

range, box plots,


stem-and- leaf plot

6.SP.2. I ODE Understand that a set of data

collected to answer a statistical

question has a distribution which

can be described by its center,

spread, and overall shape.

1,2,3,4 smart board, Graphing

Statistics &

Probability



mean, median,

mode, range,


6.SP.3. I ODERecognize that a measure of

center for a numerical data set

summarizes all of its values with a

single number, while a measure

of variation describes how its

values vary with a single number.

1,2,3,4 smart board, Graphing

Statistics &

Probability

Summarize and describe

distributions

histograms, box

plots, outliers,

statistics, stem-and-

leaf plot

6.SP.4 I ODEDisplay numerical data in plots on a

number line, including dot plots,

histograms, and box plots.

1,2,3,4 smart board,

Graphing

Statistics &

Probability


distributions

mean, median,

mode, histograms,

range, box plots,


stem-and- leaf plot

6.SP.5 R ODE Summarize numerical data sets in

relation to their context


Graphing

13

http://corestandards.org/the-standards/mathematics/grade-6/statistics-and-probability/










Math

Curriculum Map

Grade 6


Co

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Grade Level

Specific Standard

Qu

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Engagement/

Learning

Activity / Special

Resource / Web

Link

Statistics &

Probability


distributions

6.SP.5 a R ODE Reporting the number of

observations.


Graphing

Statistics &

Probability


distributions

measurement 6.SP.5b R ODE Describing the nature of the attribute

under investigation, including how it

was measured and its units of

measurement.


Graphing

Statistics &

Probability


distributions

mean, median,

mode, histograms,

absolute deviation,


6.SP.5c R ODE Giving quantitative measures of

center (median and/or mean) and

variability (interquartile range and/or

mean absolute deviation), as well

as describing any overall pattern

and any striking deviations from the

overall pattern with reference to the

context in which the data were

gathered.

1,2,3,4 Smart board activity ,

small group work on

gathering data

Statistics &

Probability


distributions

mean, median,

mode, histograms,

range, box plots,


stem-and- leaf plot

6.SP.5d I ODERelating the choice of measures

of center and variability to the

shape of the data distribution

and the context in which the

data were gathered.

1,2,3,4 Smart board,

graphing, small group

activity

14









Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

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C

Grade Level

Specific Standard

Qu

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Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Ratios &

Proportional

Relationships

Analyze proportional

realtionships and use

them to solve real-worls

and mathematical

problems

rate, ratio, unit

rate

7.RP.

1

R ODE Compute unit rates associated with

ratios of fractions, including ratios of

lengths, areas and other quantities

measured in like or different units.

For example, if a person walks 1/2

mile in each 1/4 hour, compute the

unit rate as the complex fraction 1/2

/ 1/4 miles per hour, equivalently 2

miles per hour.

1,2,3,4 Interactive

Smartboard,

Calculators

Ratios & Proportional

Relationships




and mathematical

problems

rate, ratio, unit

rate

7.RP.

2

R ODE Recognize and represent proportional

relationships between quantities

1,2,3,4 Interactive

Smartboard,

Calculators


Relationships




and mathematical

problems

proportion,

coordinate plane,

linear, origin

7.RP.

2a

R ODE Decide whether two quantities are in

a proportional relationship, e.g., by

testing for equivalent ratios in a table

or graphing on a coordinate plane

and observing whether the graph is a

straight line through the origin.

1,2,3,4 Interactive

Smartboard,

Calculators, graph

paper


Relationships




and mathematical

problems

unit rate, slope,

scale

7.RP.

2b

R ODE Identify the constant of proportionality

(unit rate) in tables, graphs,

equations, diagrams, and verbal

descriptions of proportional

relationships.

1,2,3,4 Interactive

Smartboard,

Calculators

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

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tan

dard

I/R

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E / T

C

Grade Level

Specific Standard

Qu

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Tau

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Student

Engagement/

Learning

Activity / Special

Resource / Web

Link


Relationships




and mathematical

problems

rate of change 7.RP.

2c

R ODE Represent proportional relationships

by equations. For example, if total

cost t is proportional to the number n

of items purchased at a constant

price p, the relationship between the

total cost and the number of items

can be expressed as t = pn.

1,2,3,4 Interactive

Smartboard,

Calculators, news

advertisements/catal

ogues


Relationships




and mathematical

problems

slope 7.RP.

2d

I ODE Explain what a point (x , y ) on the

graph of a proportional relationship

means in terms of the situation, with

special attention to the points (0, 0)

and (1, r ) where r is the unit rate.

1,2,3,4 Interactive

Smartboard, graph

paper


Relationships




and mathematical

problems

percent, interest,

mark up/down,

gratuity,

commission, %

change

(increase/decrea

se), % error

7.RP.

3

R ODE Use proportional relationships to

solve multistep ratio and percent

problems. Examples: simple interest,

tax, markups and markdowns,

gratuities and commissions, fees,

percent increase and decrease,

percent error.

1,2,3,4 Interactive

Smartboard,

Calculators,

newsprint

advertisements,

banking APR, credit

card advertisements,

catalogue, auto

trader

Number System Apply and extend

previous

understandings of

operations with

fractions to add,

subtract, multiply, and

divide rational

numbers.

rational numbers,

number line

7.NS.

1

M ODE Apply and extend previous

understandings of addition and

subtraction to add and subtract

rational numbers; represent addition

and subtraction on a horizontal or

vertical number line diagram.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

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Tau

gh

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Student

Engagement/

Learning

Activity / Special

Resource / Web

Link


previous

understandings of

operations with

fractions to add,


divide rational

numbers.

integers,

opposite, additive

inverse

7.NS.

1a

R ODE Describe situations in which opposite

quantities combine to make 0. For

example, a hydrogen atom has 0

charge because its two constituents

are oppositely charged.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer

Number SystemApply and extend

previous

understandings of

operations with

fractions to add,


divide rational

numbers.

absolute value,

additive inverse

7.NS.

1b

R ODE Understand p + q as the number

located a distance |q | from p , in the

positive or negative direction

depending on whether q is positive or

negative. Show that a number and its

opposite have a sum of 0 (are

additive inverses). Interpret sums of

rational numbers by describing real-

world contexts.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer


previous

understandings of

operations with

fractions to add,


divide rational

numbers.

additive inverse,

absolute value

7.NS.

1c

R ODE Understand subtraction of rational

numbers as adding the additive

inverse, p – q = p + (–q ). Show that

the distance between two rational

numbers on the number line is the

absolute value of their difference, and

apply this principle in real-world

contexts.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link


previous

understandings of

operations with

fractions to add,


divide rational

numbers.

rational numbers 7.NS.

1d

R ODE Add properties of operations as

strategies to add and subtract rational

numbers.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer


previous

understandings of

operations with

fractions to add,


divide rational

numbers.


2

M ODE Apply and extend previous

understandings of multiplication and

division and of fractions to multiply

and divide rational numbers.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer


previous

understandings of

operations with

fractions to add,


divide rational

numbers.

distributive

property

7.NS.

2a

R ODE Understand that multiplication is

extended from fractions to rational

numbers by requiring that operations

continue to satisfy the properties of

operations, particularly the distributive

property, leading to products such as

(–1)(–1) = 1 and the rules for

multiplying signed numbers. Interpret

products of rational numbers by

describing real-world contexts.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

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Tau

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Student

Engagement/

Learning

Activity / Special

Resource / Web

Link


previous

understandings of

operations with

fractions to add,


divide rational

numbers.


2b

R ODE Understand that integers can be

divided, provided that the divisor is

not zero, and every quotient of

integers (with non-zero divisor) is a

rational number. If p and q are

integers, then –(p /q ) = (–p )/q =

p /(–q ). Interpret quotients of rational

numbers by describing real-world

contexts.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer


previous

understandings of

operations with

fractions to add,


divide rational

numbers.

properties of

operations

7.NS.

2c

R ODE Apply properties of operations as

strategies to multiply and divide

rational numbers.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field,

thermometer


previous

understandings of

operations with

fractions to add,

long division,

terminating

decimal

7.NS.

2d

R ODE Convert a rational number to a

decimal using long division; know that

the decimal form of a rational number

terminates in 0s or eventually

repeats.

1,2,3,4 Interactive

Smartboard,

Calculators


previous

understandings of

operations with

fractions to add,


3

R ODE Solve real-world and mathematical

problems involving the four

operations with rational numbers.

1,2,3,4 Interactive

Smartboard,

Calculators, number

lines, counters,

football field, Expressions &

Equations

Use properties of

operations to generate

equivalent expressions.

linear,

coefficients

7.EE.

1

I ODE Apply properties of operations as

strategies to add, subtract, factor, and

expand linear expressions with

rational coefficients.

1,2,3,4 Interactive

Smartboard,

Calculators

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions &

Equations

Use properties of

operations to

generate equivalent

expressions.

percent 7.EE.

2

I ODE Understand that rewriting an

expression in different forms in a

problem context can shed light on the

problem and how the quantities in it

are related. For example, a + 0.05a =

1.05a means that “increase by 5%” is

the same as “multiply by 1.05.”

1,2,3,4 Interactive

Smartboard,

Calculators

Expressions &

Equations

Solve real-life and


using numerical and


and equations.

coefficient,

variable,

7.EE.

3

I ODE Understand that rewriting an

expression in different forms in a

problem context can shed light on the

problem and how the quantities in it

are related. For example, a + 0.05a =

1.05a means that “increase by 5%” is

the same as “multiply by 1.05.”

1,2,3,4 Interactive

Smartboard,

Calculators

Expressions &

Equations

Solve real-life and


using numerical and


and equations.

variable,

inequalities

7.EE.

4

I ODE Use variables to represent quantities

in a real-world or mathematical

problem, and construct simple

equations and inequalities to solve

problems by reasoning about the

quantities.

1,2,3,4 Interactive

Smartboard,

Calculators

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions &

Equations

Solve real-life and


using numerical and


and equations.

product 7.EE.

4a

R ODE Solve word problems leading to

equations of the form px + q = r and

p (x + q ) = r , where p , q , and r are

specific rational numbers. Solve

equations of these forms fluently.

Compare an algebraic solution to an

arithmetic solution, identifying the

sequence of the operations used in

each approach. For example, the

perimeter of a rectangle is 54 cm. Its

length is 6 cm. What is its width?

1,2,3,4 Interactive

Smartboard,

Calculators,

Geoboards, graph

paper

Expressions &

Equations

Solve real-life and


using numerical and


and equations.

sequence 7.EE.

4b

R ODE Solve word problems leading to

equations of the form px + q = r and

p(x + q) = r, where p, q, and r are

specific rational numbers. Solve

equations of these forms fluently.

Compare an algebraic solution to an

arithmetic solution, identifying the

sequence of the operations used in

each approach.

1,2,3,4 Interactive

Smartboard,

Calculators,

Geometry Draw, construct and

describe geometrical

figures and describe

the relationships

between them.

scale drawings,

scale

7.G.

1

I ODE Solve problems involving scale

drawings of geometric figures,

including computing actual lengths

and areas from a scale drawing and

reproducing a scale drawing at a

different scale.

1,2,3,4 Interactive

Smartboard,

Calculators,

Geoboards, graph

paper, copier

enlargement,

Matchbox car

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link




the relationships

between them.

protractor,

straight edge

7.G.

2

I ODE Draw (freehand, with ruler and

protractor, and with technology)

geometric shapes with given

conditions. Focus on constructing

triangles from three measures of

angles or sides, noticing when the

conditions determine a unique

triangle, more than one triangle, or no

triangle.

1,2,3,4 Interactive

Smartboard,

Calculators, ruler,

protractor




the relationships

between them.

2D, 3D, slicing,

prisms, pyramids,

plane

7.G.

3

I ODE Describe the two-dimensional figures

that result from slicing three-

dimensional figures, as in plane

sections of right rectangular prisms

and right rectangular pyramids.

1,2,3,4 Geometric figures,

Interactive

Smartboard, nets

Geometry Solve real-life and


involving angle

measure, area, surface

area, and volume.

formulas, area,

circumference

7.G.

4

I ODE Know the formulas for the area and

circumference of a circle and use

them to solve problems; give an

informal derivation of the relationship

between the circumference and area

of a circle.

1,2,3,4 round object, ruler,

string, calculator,

pizza, Interactive

Smartboard, graph

paper, Geoboard,

lemon, scissors,

paper



involving angle


area, and volume.

Angles:

supplementary,

complementary,

vertical, adjacent

7.G.

5

I ODE Use facts about supplementary,

complementary, vertical, and

adjacent angles in a multi-step

problem to write and solve simple

equations for an unknown angle in a

figure.

1,2,3,4 Interactive

Smartboard,

protractor, railroad

tracks, bridge, maps

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link



involving angle


area, and volume.

area, volume,

surface area,

quadrilateral,

triangle, polygon,

cube, right prism

7.G.

6

I ODE Solve real-world and mathematical

problems involving area, volume and

surface area of two- and three-

dimensional objects composed of

triangles, quadrilaterals, polygons,

cubes, and right prisms.

1,2,3,4 Interactive

Smartboard,

Calculators, nets,

containers, tape,

graph paper, scissors

Statistics &

Probability

Use random sampling

to draw inferences

about a population.

statistics,

population,

random sample

7.SP.

1

I ODE Understand that statistics can be

used to gain information about a

population by examining a sample of

the population; generalizations about

a population from a sample are valid

only if the sample is representative of

that population. Understand that

random sampling tends to produce

representative samples and support

valid inferences.

1,2,3,4 Interactive

Smartboards,

Calculators

Statistics & Probability Use random sampling

to draw inferences

about a population.

random sample,

population

7.SP.

2

I ODE Use data from a random sample to

draw inferences about a population

with an unknown characteristic of

interest. Generate multiple samples

(or simulated samples) of the same

size to gauge the variation in

estimates or predictions. For

example, estimate the mean word

length in a book by randomly

sampling words from the book;

predict the winner of a school

election based on randomly sampled

survey data. Gauge how far off the

estimate or prediction might be.

1,2,3,4 Interactive

Smartboard,

Calculators

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Statistics & Probability Draw informal

comparative inferences

about two populations.

measures of

center,

distribution,

mean, median,

absolute

deviation, dot

plot, distributors,

range

7.SP.

3

R ODE Informally assess the degree of visual

overlap of two numerical data

distributions with similar variabilities,

measuring the difference between the

centers by expressing it as a multiple

of a measure of variability. For

example, the mean height of players

on the basketball team is 10 cm

greater than the mean height of

players on the soccer team, about

twice the variability (mean absolute

deviation) on either team; on a dot

plot, the separation between the two

distributions of heights is noticeable.

1,2,3,4 Interactive

Smartboard,

Calculators

Statistics & Probability Draw informal

comparative inferences

about two populations.

measures of

center/variability,

inference,

random samples,

population

7.SP.

4

R ODE Use measures of center and

measures of variability for numerical

data from random samples to draw

informal comparative inferences

about two populations. For example,

decide whether the words in a

chapter of a seventh-grade science

book are generally longer than the

words in a chapter of a fourth-grade

science book.

1,2,3,4 Interactive

Smartboard,

Calculators

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Statistics & Probability Investigate chance

processes and develop,

use, and evaluate

probability models.

probability 7.SP.

5

I ODE Understand that the probability of a

chance event is a number between 0

and 1 that expresses the likelihood of

the event occurring. Larger numbers

indicate greater likelihood. A

probability near 0 indicates an unlikely

event, a probability around 1/2

indicates an event that is neither

unlikely nor likely, and a probability

near 1 indicates a likely event.

1,2,3,4 Interactive

Smartboard,

Calculators, spinners,

dice



use, and evaluate

probability models.

relative frequency 7.SP.

6

R ODE Approximate the probability of a

chance event by collecting data on

the chance process that produces it

and observing its long-run relative

frequency, and predict the

approximate relative frequency given

the probability. For example, when

rolling a number cube 600 times,

predict that a 3 or 6 would be rolled

roughly 200 times, but probably not

exactly 200 times.

1,2,3,4 Interactive

Smartboard,


dice



use, and evaluate

probability models.

probability model,

frequencies

7.SP.

7

I ODE Develop a probability model and use

it to find probabilities of events.

Compare probabilities from a model

to observed frequencies; if the

agreement is not good, explain

possible sources of the discrepancy.

1,2,3,4 Interactive

Smartboard,


dice

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link



use, and evaluate

probability models.

uniform

probability

7.SP.

7a

I ODE Develop a uniform probability model

by assigning equal probability to all

outcomes, and use the model to

determine probabilities of events. For

example, if a student is selected at

random from a class, find the

probability that Jane will be selected

and the probability that a girl will be

selected.

1,2,3,4 Interactive

Smartboard,


dice



use, and evaluate

probability models.

chance process 7.SP.

7b

I ODE Develop a probability model (which

may not be uniform) by observing

frequencies in data generated from a

chance process. For example, find

the approximate probability that a

spinning penny will land heads up or

that a tossed paper cup will land open-

end down.

1,2,3,4 Interactive

Smartboard,


dice



use, and evaluate

probability models.

compound

probability, tree

diagram,

simulation

7.SP.

8

I ODE Find probabilities of compound

events using organized lists, tables,

tree diagrams, and simulation.

1,2,3,4 Interactive

Smartboard,


dice



use, and evaluate

probability models.

compound event 7.SP.

8a

I ODE Understand that, just as with simple

events, the probability of a compound

event is the fraction of outcomes in

the sample space for which the

compound event occurs.

1,2,3,4 Interactive

Smartboard,


dice

Math Curriculum Map

Grade 7

Domain ClusterKey

Vocabulary

Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t

Student

Engagement/

Learning

Activity / Special

Resource / Web

Link



use, and evaluate

probability models.

sample space,

event

7.SP.

8b

R ODE Represent sample spaces for

compound events using methods

such as organized lists, tables and

tree diagrams. For an event

described in everyday language (e.g.,

“rolling double sixes”), identify the

outcomes in the sample space which

compose the event.

1,2,3,4 Interactive

Smartboard,


dice



use, and evaluate

probability models.

frequency,

compound

events,

simulation

7.SP.

8c

I ODE Design and use a simulation to

generate frequencies for compound

events. For example, use random

digits as a simulation tool to

approximate the answer to the

question: If 40% of donors have type

A blood, what is the probability that it

will take at least 4 donors to find one

with type A blood?

1,2,3,4 Interactive

Smartboard,


dice

Math Curriculum Map

Grade 8 - Integrated Math A


Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

The Number System Know that there are numbers that

are not rational, and approximate

them by numbers

rational numbers,

irrational numbers

8.NS.

1

R ODE Know that numbers that are not

rational are called irrational.

Understand informally that every

number has a decimal expansion; for

rational numbers show that the

decimal expansion repeats

eventually,

and convert a decimal expansion

which repeats eventually into a

rational number.

1,2,3,4 Interactive

SmartBoard, Venn

diagram

The Number System Know that there are numbers that

are not rational, and approximate

them by numbers

rational numbers,

irrational numbers,

square roots,

truncating, decimal

expansion

8.NS.

2

R ODE Use rational approximations of

irrational numbers to compare the

size

of irrational numbers, locate them

approximately on a number line

diagram, and estimate the value of

expressions (e.g., π2). For example,

by truncating the decimal expansion

of √2, show that √2 is between 1 and

2, then between 1.4 and 1.5, and

explain how to continue on to get

better

approximations.

1,2,3,4 interactive

Smartboard, number

lines, calculators

Expressions and

Equations

Work with radicals and integer

exponents.

exponents,

numerical

expressions,

powers, base

8.EE.

1

I ODE Know and apply the properties of

integer exponents to generate

equivalent numerical expressions.

For example, 32 × 3–5 = 3–3 = 1/33 =

1/27.

1,2,3,4 interactive

Smartboard,

calculators

1

Math Curriculum Map



Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions and

EquationsWork with radicals and integer

exponents.

square roots, cube

roots, perfect

squares, rational

and irrational

numbers

8.EE.

2

R ODE Use square root and cube root

symbols to represent solutions to

equations of the form x2 = p and x

3 =

p, where p is a positive rational

number. Evaluate square roots of

small perfect squares and cube roots

of small perfect cubes. Know that √2

is irrational.

1,2,3,4 interactive

Smartboard,

calculators

Expressions and


exponents.

integers 8.EE.

3

R ODE Use numbers expressed in the form

of a single digit times an integer

power of 10 to estimate very large or

very small quantities, and to

express how many times as much

one is than the other. For example,

estimate the population of the United

States as 3 × 108 and the population

of the world as 7 × 109, and

determine that the world population is

more

than 20 times larger.

1,2,3,4 interactive

Smartboard,

calculators, NASA

website

2

Math Curriculum Map



Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions and


exponents.

scientific notation,

units of appropriate

size

8.EE.

4

R ODE Perform operations with numbers

expressed in scientific notation,

including problems where both

decimal and scientific notation are

used. Use scientific notation and

choose units of appropriate size

for measurements of very large or

very small quantities (e.g., use

millimeters per year for seafloor

spreading). Interpret scientific

notation that has been generated by

technology.

1,2,3,4 interactive

Smartboard,

calculator, NASA

website

Expressions and

EquationsUnderstand the connections

between proportional

relationships,

lines, and linear equations.

proportional

relationships, unit

rate, slope, rate of

change

8.EE.

5

I ODE Graph proportional relationships,

interpreting the unit rate as the

slope of the graph. Compare two

different proportional relationships

represented in different ways. For

example, compare a distance-time

graph to a distance-time equation to

determine which of two moving

objects has greater speed.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Expressions and

EquationsUnderstand the connections

between proportional

relationships,

similar, distinct,

coordinate plane,

lines, linear

equations, vertical

and horizonal lines

8.EE.

6

I ODE Use similar triangles to explain why

the slope m is the same between

any two distinct points on a non-

vertical line in the coordinate plane;

derive the equation y = mx for a line

through the origin and the

equation y = mx + b for a line

intercepting the vertical axis at b.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Expressions and

Equationslines, and linear equations. linear equations,

variable

8.EE.

7

R ODE Solve linear equations in one variable. interactive

Smartboard,

calculator, balance

3

Math Curriculum Map



Co

re S

tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions and

EquationsAnalyze and solve linear

equations and pairs of

simultaneous linear

equations.

linear equations,

variable, infinite

many solutions,

equivalent equations

8.EE.

7a

I ODE Give examples of linear equations in

one variable with one

solution, infinitely many solutions, or

no solutions. Show which

of these possibilities is the case by

successively transforming the

given equation into simpler forms,

until an equivalent equation of

the form x = a, a = a, or a = b results

(where a and b are different

numbers).

1,2,3,4 interactive

Smartboard,

graphing paper,

graphing calculator

Expressions and



simultaneous linear equations.

linear equations,

coefficients,

distributive property,

collecting like terms

8.EE.

7b

I ODE Solve linear equations with rational

number coefficients, including

equations whose solutions require

expanding expressions using

the distributive property and collecting

like terms.

1,2,3,4 interactive

Smartboard,

calculator

Expressions and



simultaneous linear

equations.

simultaneous linear

equations

8.EE.

8

I ODE Analyze and solve pairs of

simultaneous linear equations.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculatorExpressions and



simultaneous linear

equations.

system of linear

equations,

intersections of

linear equations,

simultaneously

8.EE.

8a

I ODE Understand that solutions to a system

of two linear equations

in two variables correspond to points

of intersection of their

graphs, because points of

intersection satisfy both equations

simultaneously.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

4

Math Curriculum Map



Co

re S

tan

dard

I/R

/M

OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Expressions and



simultaneous linear

equations.

linear equations,

algebraically

8.EE.

8b

I ODE Solve systems of two linear equations

in two variables

algebraically, and estimate solutions

by graphing the equations.

Solve simple cases by inspection. For

example, 3x + 2y = 5 and 3x +

2y = 6 have no solution because 3x +

2y cannot simultaneously be 5

and 6.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Expressions and



simultaneous linear

equations.

linear equations,

coordinates

8.EE.

8c

I ODE Solve real-world and mathematical

problems leading to two linear

equations in two variables. For

example, given coordinates for two

pairs of points, determine whether the

line through the first pair of

points intersects the line through the

second pair.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Functions Define, evaluate, and compare

functions.

functions, input,

output

8.F.1 I ODE Understand that a function is a rule

that assigns to each input exactly

one output. The graph of a function is

the set of ordered pairs

consisting of an input and the

corresponding output.

1,2,3,4 interactive

Smartboard, function

machine, tables,

graph paper,

graphing calculators

5

Math Curriculum Map



Co

re S

tan

dard

I/R

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C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link


functions.

functions, rate of

change, algebraic

expressions, linear

function

8.F.2 I ODE Compare properties of two functions

each represented in a different

way (algebraically, graphically,

numerically in tables, or by verbal

descriptions). For example, given a

linear function represented by a table

of values and a linear function

represented by an algebraic

expression,

determine which function has the

greater rate of change.

1,2,3,4 interactive

Smartboard,

graphing calculators,

graph paper


functions.

linear function, non-

linear functions

8.F.3 I ODE Interpret the equation y = mx + b as

defining a linear function, whose

graph is a straight line; give examples

of functions that are not linear.

For example, the function A = s2

giving the area of a square as a

function

of its side length is not linear because

its graph contains the points (1,1),

(2,4) and (3,9), which are not on a

straight line.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

6

Math Curriculum Map



Co

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tan

dard

I/R

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OD

E / T

C

Grade Level

Specific Standard

Qu

art

er

Tau

gh

t Student

Engagement/

Learning

Activity / Special

Resource / Web

Link

Functions Use functions to model

relationships between quantities.

function, linear, rate

of change, initial

value

8.F.4 I ODE Construct a function to model a linear

relationship between two

quantities. Determine the rate of

change and initial value of the

function from a description of a

relationship or from two (x, y) values,

including reading these from a table

or from a graph. Interpret the rate

of change and initial value of a linear

function in terms of the situation

it models, and in terms of its graph or

a table of values.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Functions Use functions to model

relationships between quantities.

linear, non-linear 8.F.5 I ODE Describe qualitatively the functional

relationship between two

quantities by analyzing a graph (e.g.,

where the function is increasing

or decreasing, linear or nonlinear).

Sketch a graph that exhibits the

qualitative features of a function that

has been described verbally.

1,2,3,4 graph paper,

graphing calculator,

interactive

Smartboard

Geometry Understand congruence and

similarity using physical models,

transparencies,

or geometry software.

rotations, reflections,

translations

8.G1 R ODE Verify experimentally the properties of

rotations, reflections, and

translations:

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch

pad softwareGeometry Understand congruence and


transparencies,


lines and line

segments

8.G.1

a

R ODE Lines are taken to lines, and line

segments to line segments of the

same length.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch

pad software

7

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transparencies,


angles 8.G.1

b

R ODE Angles are taken to angles of the

same measure.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch



transparencies,


parallel lines 8.G.1

c

R ODE Parallel lines are taken to parallel

lines.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch



transparencies,


congruent figures,

rotations, reflections,

translations

8.G.2 R ODE Understand that a two-dimensional

figure is congruent to another if

the second can be obtained from the

first by a sequence of rotations,

reflections, and translations; given

two congruent figures, describe a

sequence that exhibits the

congruence between them.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch

pad software



transparencies,


diliations,

translations,

rotations, reflections

8.G.3 R ODE Describe the effect of dilations,

translations, rotations, and reflections

on two-dimensional figures using

coordinates.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch

pad software



transparencies,


similar, rotaions,

reflections,

translations,

dilations, sequence

8.G.4 I ODE Understand that a two-dimensional

figure is similar to another if the

second can be obtained from the first

by a sequence of rotations,

reflections, translations, and dilations;

given two similar two dimensional

figures, describe a sequence that

exhibits the similarity

between them.

1,2,3,4 interactive

Smartboard, graph

paper, Geosketch

pad software

8

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transparencies,


exterior angles and

interior angles,

parallel lines,

transversal,

8.G.5 I ODE Use informal arguments to establish

facts about the angle sum and

exterior angle of triangles, about the

angles created when parallel lines

are cut by a transversal, and the

angle-angle criterion for similarity of

triangles. For example, arrange three

copies of the same triangle so that

the sum of the three angles appears

to form a line, and give an argument

in terms of transversals why this is

so.

1,2,3,4 students construct

and cut triangles and

regular polygons,

calculators

Geometry Understand and apply the

Pythagorean Theorem.

converse,

Pythagorean

Thereom

8.G.6 I ODE Explain a proof of the Pythagorean

Theorem and its converse.

1,2,3,4 interactive

Smartboard, graph

paperGeometry Understand and apply the


pythagorean

thereom, right

triangle

8.G.7 I ODE Apply the Pythagorean Theorem to

determine unknown side lengths

in right triangles in real-world and

mathematical problems in two and

three dimensions.

1,2,3,4 interactive

Smartboard, graph

paper, calculator

Geometry Understand and apply the


pythagorean

theorem, distance,

coordinate system

8.G.8 I ODE Apply the Pythagorean Theorem to

find the distance between two

points in a coordinate system.

1,2,3,4 interactive

Smartboard, graph

paper, calculatorGeometry Solve real-world and

mathematical problems involving

volume of

cylinders, cones, and spheres.

volume, cylinders,

cones, spheres

8.G.9 R ODE Know the formulas for the volumes of

cones, cylinders, and spheres

and use them to solve real-world and


1,2,3,4 3-D solids, interactive

Smartboard,

calculator

9

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Statistics and

Probability

Investigate patterns of association

in bivariate data.

scatter plots,

bivariate data,

clustering, outliers,

positive or negative

association, linear or

non-linear

association

8.SP.

1

R ODE Construct and interpret scatter plots

for bivariate measurement

data to investigate patterns of

association between two quantities.

Describe patterns such as clustering,

outliers, positive or negative

association, linear association, and

nonlinear association.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Statistics and

ProbabilityInvestigate patterns of association

in bivariate data.

scatter plots, linear

association

8.SP.

2

R ODE Know that straight lines are widely

used to model relationships

between two quantitative variables.

For scatter plots that suggest a

linear association, informally fit a

straight line, and informally assess

the model fit by judging the closeness

of the data points to the line.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

Statistics and


in bivariate data.

linear, bivariate data,

slope, and intercept

8.SP.

3

I ODE Use the equation of a linear model to

solve problems in the context

of bivariate measurement data,

interpreting the slope and intercept.

1,2,3,4 interactive

Smartboard, graph

paper, graphing

calculator

10

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Statistics and


in bivariate data.

bivariate data,

categorical data,

frequency and

relative frequency

tables, categorical

variables.

8.SP.

4

I ODE Understand that patterns of

association can also be seen in

bivariate

categorical data by displaying

frequencies and relative frequencies

in

a two-way table. Construct and

interpret a two-way table summarizing

data on two categorical variables

collected from the same subjects.

Use relative frequencies calculated

for rows or columns to describe

possible association between the two

variables.

1,2,3,4 interactive

Smartboard, tables,

graphing calculators

11

Quick Overview of Math Changes

Read from Top to Bottom in Each Column

Grade Level New Math Standards Tipp City Maintained Removed/Shifted

K

Operations and Algebraic Thinking

Understand addition as putting together

and adding to, and understand subtraction

as taking apart and taking from, make ten,

fluently add, subtract within 5. (K.OA.1-5)

Counting and Cardinality Know number

names and the count sequence to 100 (K.CC.1-

3) Tipp City currently meets this Common Core

Standard.

Number, Number Sense and Operations

Demonstrate joining multiple groups of objects

each containing the same number of objects.

(See Grade 2.OA.3-4)

K

Number and Operations in Base Ten

Work with numbers 11-19 to gain

foundations for place value. (K.NBT.3)

Counting and Cardinality Count to tell the

number of objects up to 20 objects. (K.CC.4-5)

Tipp City currently meets this Common Core

Standard.


Partition or share a small set of objects into

groups of equal size. (See Grade 2.OA.3-4)

K

Geometry Identify shapes as two-

dimensional or three-dimensional. (K.G.3)

Counting and Cardinality Compare numbers.

(K.CC.6-7) Tipp City currently meets this

Common Core Standard.

Data Analysis is used as a tool for working

with numbers and geometric shapes.

K

Measurement and Data Describe and

compare measurable attributes, using

direct comparison. (K.MD.1-3)

Counting and Cardinality Skip count by 2s to

20, by 5s to 100.

K

Geometry Correctly identify and describe

shapes (squares, circles, triangles,

rectangles, hexagons, cubes, cylinders,

spheres). (K.G.1-2)

Counting and Cardinality Count backwards

from 20 to 0.

K

Geometry Analyze, compare, create and

compose shapes. (K.G.4-6)

Operactions and Algerbraic Thinking

Describe orally the pattern of a given sequence.

KOperactions and Algerbraic Thinking Identify,

create and extend a pattern.

KMeasurement and Data Identify time to the

hour.

KMeasurement and Data Identify and state the

value of penny, nickel, dime and quarter.

1




1 Operations and Algebraic

Thinking Understand and apply

properties of operations and the


subtraction. (1.OA.3-4)

Number, Number Sense and

Operations Money can be used as a

tool for working with numbers.

Number, Number Sense and

Operations Model and represent

multiplication and division. (See Grade

2.OA.4 and grade 3.OA.1-4)

1 Number and Operations in Base

Ten Extend the counting

sequence. [to 120] (1.NBT.1)

Patterns, Functions and Algebra

Sequences, growing patterns

Measurement Weight (See Grade

3.MD1-2)


Ten Understand place value.

[compare two two-digit numbers

using <, =, >] (1.NBT.3)

Measurement Length with standard

units (See Grade 2.MD1-4)


Ten Use place value

understanding and properties of

operations to add and subtract.

[multiples of 10, properties and

strategies] (1.NBT.4-6)

Data Analysis is used as a tool for

working with numbers and geometric

shapes.

1 Geometry Reason with shapes

and their attributes. [foundation for

fractions using geometric shapes]

(1.G.3)

Probability (See Grade 7.SP.5-8)

1 Measurement and Data Measure

lengths indirectly and by iterating

length units. (1.MD.1)

1




2Operations and Algebraic Thinking

Add and subtract within 20. (2.OA.2)

Measurement Weight and volume (See

3.MD.1-2,) Number, Number Sense and Operations

Ten as ten ones (See Grade 1.NBT.1-4)

2


Understand place value. [bundle of ten

tens, multiples of 100s] (2.NBT.1-2)

Numbers and Operations in Base 10

Represent fractions using words, numerals,

and physical models.


Add/subtract multiples of ten (See Grade

1.NBT.4-6)

2

Measurement and Data Relate addition

and subtraction to length. (2.MD.5-6)

Measurement and Data Work with time and

money (count money and make change using

coins and a dollar bill.)


Fractions limited to partitioning circles and

rectangles 2.G.3 (See Grade 3.NF)

2Measurement and Data Represent and

interpret data. (2.MD.9)


Division (See Grade 3.OA.3)

2Geometry Reason with shapes and their

attributes. [new shapes and faces] (2.G.1-

2)


Front end estimation

2Geometry Reason with shapes and their

attributes. [partitioning wholes] (2.G.3)

Geometry Three-dimensional objects

2Number and Operations in Base Ten

Understand place value. [use , using <, =,

> (2.NBT.3-4)

Geometry Two-dimensional congruence and

line symmetry (See Grade 6-8.G)

2


Use place value understanding and

properties of operations to add and

subtract. [fluently add/subtract within 100

using strategies; add four two-digit

numbers; mentally add/subtract 10 or 100;

explain using place value and properties

of operations; no algorithms mentioned]

(2.NBT.5-9)

Patterns, Functions and Algebra

Sequences, growing patterns, quantitative and

qualitative changes

2Measurement and Data Represent and

interpret data. [picture and bar graphs]

(2.MD.10)

Data Analysis is used as a tool for working

with numbers and geometric shapes

2 Probability (See Grade 7.SP.5-8)

1




3 Operations and Algebraic Thinking

Understand properties of multiplication

and the relationship between multiplication

and division. (3.OA.6)

Measurement and Data Counting back

change to $10.00.


Decimals (See Grade 4.NF)

3 Number and Operations in Base Ten

Use place value understanding and

properties of operations to perform multi-

digit arithmetic. [range of algorithms]

(3.NBT.1-3)

Measurement and Data Ability to count back

change using coins and bills the simplest way.


Money represented as cents is a context for

solving problems. (See Grade 2.MD.8 for

money introduction and Grade 4 NF.5-7)

3 Measurement and Data Represent and

interpret data. (3.MD.3-4)


Division remainders (See Grade 4.OA.3)

3 Measurement and Data Geometric

measurement: understand concepts of

area and relate area to multiplication and

to addition. (3.MD.5-7)

Measurement Temperature

3 Measurement and Data Geometric

measurement: recognize perimeter as an

attribute of place figures and distinguish

linear and area measures. (3.MD.6)

Measurement Volume (See Grade 5.MD.3-5)

3 Geometry Reason with shapes and their

attributes. (3.G.1-2)

Geometry Three-dimensional objects (See

Grades 5-6.G)

3 Geometry Angles (See Grades 4-5.G)

3 Patterns, Functions and Algebra

Multiplicative and growing patterns,

quantitative changes

3 Data Analysis is used as a tool for working

with numbers and geometric shapes

3 Probability (See Grade 7.SP.5-8)

1


Read From Top To Bottom in Each Column

Grade Level New Math Standards Tipp City Maintained Removed/ Shifted

4 Measurement and Data: Number, Number sense and Operations:

4 Solve problems involving

addition and subtraction of

fractions by using information

presented in line plots.

Addition and subtraction of decimals-moved to

5th grade

4 Angle degree of rotation (1/360

of a circle)

Measurement and Data:

4 Fractions on a line plot Volume-moved to 5th grade

4 Measuring angles-Using a

protractor

Geometry:

4 Geometry: Transformations-Moved to 8th grade

Draw and lines and angles Coordinate Plane-moved to 5th grade

4 Classify shapes based on lines

and angles

Patterns, Functions and Algebra:

4 Inequalities-moved to 6th and 7th grade

4 Probability-move to 7th grade

4 Data Analysis:

All removed except line plots

4 Median, Mode, Mean-moved to 6-8th grade

1


Read from top to bottom in each column

Grade Level New Math Standards Tipp City Maintained Removed/ Shifted

5 Operations and Algebraic Thinking Number, Number Sense and

Operations

5 Write and interpret numerical

expressions.

Ratio, percent - moved to 6th grade

5 Number and Operations in Base Ten Angles - moved to 4th grade

5 Perform operations with multi-digit

whole numbers with decimals to

hundredths.

Surface area - moved to 4th grade

Number and Operations - Fractions Volume formulas - moved to 6th grade

5 Apply and extend previous

understandings of multiplication and

division to multiply and fivide fractions.

Geometry

5 Measurement and Data Circles - moved to 7th grade

5 Represent and interpret data. Congruent figures - moved to 7th grade

5 Geometric measurement: understand

concepts of volume and relate volume

to multiplication and to addition.

Four quadrant coordinate system -

moved to 6th grade

5 Geometry Angles - moved to 4th and 7th grade

5 Classify two-dimensional figures into

categories based on their properties.

Nets - moved to 6th grade

5 Patterns, Functions and Algebra

5 Inequalities - Moved to 6th grade

5 Data Analysis and Probability

5 Data Analysis (In 5th grade used only

as a tool for organizing numbers and

geometric shapes) - moved to 6th-8th

1

Quick Overview of Math Changes Read from Top to Bottom in Each column

Grade Level New Math Standards Tipp City Maintained Removed/shifted 6th Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems. (6RP. 1-2)

The Number System Compute fluently with multi-digit numbers and find common factors and multiples. (6NS. 2-3)

The Number System Apply and extend previous understanding of numbers to the system of rational numbers. (6.NS. 5-8)

Expressions and Equations Reason about the solve one-variable equations and inequalities. (6EE.&-8)

Geometry Solve real-world and mathematical problems involving area, surface area, and volume. ( 6.SP. 1-3)

Statistics and Probability Develop understanding of statistical variability ( 6.SP.1-3)

Statistics and Probability Summarize and described distributions. (6.SP.5c-d)

Measurement Differences between perimeter and area (reinforce differences)

Patterns, Functions and Algebra Equivalent algebraic expressions ( see grade 6-7,EE)

Number, Number Sense

and Operations - Exponents ( 7EE.1-4)

Measurement – Circles(7.G)

Geometry Classification of Two dimensional shapes (5.G.3-4)

Geometry Transformations and similar figures ( 8.G.1-5)

Patterns, Functions and Algebra Linear equations and inequalities (7-8. EE)

Patterns, Functions and Algebra Functions (8.F)

Patterns, Functions and Algebra Rate of Change ( 7.RP.2)

Probability( 7.SP 5-8)




7 Ratios & Proportional Relationships none added or removed Patterns, Functions, and Algebra

7 7.RP.1-3 Analyze proportional

relationships and use them to solve real-

world and mathematical problems7 Number System Number, Number Sense and Operations

7 7.NS.1-3 Apply and extend previous

understandings of operations with fractions

to add, subtract, multiply, and divide,

rarional numbers

Scientific notation and negative exponents--

8.EE.1-4

Irrational numbers--8.NS.1-2

Absolute valule--6.NS.7

7 Expressions & Equations Patterns functions and Algebra

7 7.EE.1-2 Use properties of operations to

generate equivalent expressions

Algebraic expressions--6&7.EE

7 7.EE.3 Solve real life and mathematical

problems using numerical and algebraic

expressions and equations

Linear equations--7&8.EE or 8.F

7 7.EE.4 Solve real-life and mathermatical

problems using numerical and algebraic

expressions and equations

Non-linear--High School

7 Geometry Geometry & Spatial Sense

7.G.1 Draw, construct, and describe

geometric figures and describe the

realtionships between them

Measurement

7.G.2-3 Draw, construct, and describe

geometric figures and describe the

realtionships between them

Precision estimates--removed

1




7.G.4-5 Solve real-life and mathematical

problems involving angle measure, area,

surface area, and volume

Area of compostie shapes--6.G.1

7.G.6 Solve real-life and mathematical

problems involving angle measure, area,

surface area, and volume

Volume of cylinders--8.G.9

Comparison of surface area and volume--

removed

Properties of 2 dimensional shapes--5.G.3-4

Properties of 3 dimensional shapes--High

School

7 Statistics & Probability Data Analysis and Probability

7.SP.1-2 Use random sampling to draw

inferences about a population

graphical representation analysis--6.SP

7.SP.3-4 Draw informal comparative

inferences about two populations

Pythagorean Theorem--8.G.6-8

7.SP.5-8 Investigate chance processes,

and develop, use, and evaluate probability

models

Transformations and symmetry--8.G.1-5

Graphical representation analysis--6.SP

2




8th Expressions and equations none added or deleted Number and Number sense

8th extend the concept of square roots

to cube roots

ratio, proportion and percent problems

are shifted to grade 7

8th interpreting the unit rate as the

slope of the graph

Measurement

8th use similar triangles to show the

slope of a line is constant

ordering and converting of units of

measures are shifted to 6th grade

8th analysis and solve a system of

linear equations including one

solution, no solutions and infinate

solutions.

problems involving rates and derived

measurements are shifted to 7th

grade

8th Functions Geometry

8th define, evaluate and compare

functions

represent and analyze shapes placed

in the coordinate plane shifted to 6th

grade8th use functions to model the

relationship between two qualities

(variables)

constructing nets of three dimensional

figures shifted to 6th grade

8th Geometry Patterns, Functions and Algebra

8th understand congruency and

similarity of figures using

transformations (translation,

rorations, reflections, or dilations).

learning is limited to linear equations,

no quadratic equations which are

shifted intirely to Algebra I

8th understand and apply the

Pythagorean Theorem and its

converse

remove non-linear growth, such as

exponential equations

1




8th Statistics and probability Data Analysis and Probability

8th more indepth study of bivariate

data and patterns of association

between the two data sets

differentiate between what types of

graphs to use in various settings

moved to grade 68th measures of center and spread of

data shifted to 7th grade

8th different types of sampling methods is

shifted to 7th grade

8th probability of simple and compound

events are shifted to 7th grade.

2

8th Grade Freshman Sophomore Junior Senior

Integrated Math A Algebra I Geometry Algebra II Pre-Calculus

Algebra I Geometry Algebra II Pre-Calculus Advanced Math

Integrated Math A Integrated Math B Algebra I Informal Algebra II Geometry

Algebra I Acc. Geometry Acc. Algebra II H. Pre-Calculus AP Calculus

AP Statistics

Acc. Geometry Acc. Algebra II H. Pre-Calculus AP Calculus

Pre-Calculus Advanced Math

AP Statistics

AP Calculus

AP Statistics

Integrated Math B

Curriculum Map

Strand Domain ClusterKey

Vocabulary

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Number and Quantity The Real Number System Extended the properties of exponents

to rational exponents

exponents,

properties

N-RN

1

R ODE Explain how the definition of the meaning

of rational exponents follows from

extending the properties of integer

exponents to those values, allowing for a

notation for radicals in terms of rational

exponents

3, 4

Number and Quantity The Real Number System Use properties of rational and

irrational numbers

sum, product,

rational, irrational,

nonzerio

N-RN

3

IR

M

ODE Explain why the sum or product of two

rational numbers is rational; that the sum

of a rational number and an irrational

number is irrational; and that the product

of a nonzero rational number and an

irrational number is irrational.

1,2

Number and Quantity Quantities Reason quantitively and use units to

solve problems

multi step

problems, units,

scale, origin

N-Q 1 IR

M

ODE Use units as a way to understand

problems and to guide the solution of multi-

step problems; choose and interpret units

consistently in formulas; choose and

interpret the scale and the origin in graphs

and data displays.

1,2,3,4

Algebra Seeing Structure in

Expressions

Interpret the structure of expressions terms, factors,

coefficients

A-

SSE

1b

IR

M

ODE Interpret expressions that represent a

quantity in terms of its context.★

Interpret parts of an expression, such as

terms, factors, and coefficients.

1,2,3,4

Algebra Seeing Structure in

Expressions

Interpret the structure of expressions terms, factors,

coefficients

A-

SSE

1a

I ODE Interpret expressions that represent a

quantity in terms of its context.

Interpret complicated expressions by

viewing one or more of their parts as a

single entity.

1, 2

1

Integrated Math B

Curriculum Map


Vocabulary

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Algebra Creating Equations Create equations that describe

numbers or relationships

equations

inequalities

A-

CED 1

I ODE Create equations and inequalities in one

variable and use them to solve problems.

1, 2


numbers or relationships

equations,

quantities, axes,

labels

A-

CED 2

I ODE Create equations in two or more variables

to represent relationships between

quantities; graph equations on coordinate

axes with labels and scales.

4

Algebra Reasoning with Equations

and Inequalities

Understand solving equations as a

process of reasoning and explain the

reasoning

steps, solution A-REI

1

IR ODE Explain each step in solving a simple

equation as following from the equality of

numbers asserted at the previous step,

starting from the assumption that the

original equation has a solution. Construct

a viable argument to justify a solution

method.

1,2,3,4


and Inequalities

Solve equations and inequalities in

one variable

linear equations A-REI

3

I ODE Solve linear equations and inequalities in

one variable, including equations with

coefficients represented by letters.

4


and Inequalities

Represent and solve equations and

inequalities graphically

graph, solutions,

coordinate plane

A-REI

10

I ODE Understand that the graph of an equation

in two variables is the set of all its

solutions plotted in the coordinate plane,

often forming a curve (which could be a

line).

4

2

Integrated Math B

Curriculum Map


Vocabulary

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Functions Interpreting Functions Understand the concept of a function

and use function notation

domain, range,

functions

F-IF 1 I ODE Understand that a function from one set

(called the domain) to another set (called

the range) assigns to each element of the

domain exactly one element of the range.

If f is a function and x is an element of its

domain, then f(x) denotes the output of f

corresponding to the input x. The graph of

f is the graph of the equation y = f(x).

3, 4



inputs, domain F-IF 2 I ODE Use function notation, evaluate functions

for inputs in their domains, and interpret

statements that use function notation in

terms of a context.

3, 4

Functions Interpreting Functions Interpret functions that arise in

applications in terms of the context

rate of change F-IF 6 I ODE Calculate and interpret the average rate of

change of a function (presented

symbolically or as a table) over a

specified interval. Estimate the rate of

change from a graph

1, 2

Functions Interpreting Functions Analyze functions using different

representations

linear, quadratic,

maxima, minima

F-IF

7a

I ODE Graph functions expressed

symbolically and show key features of

the graph, by hand in simple cases and

using technology for more complicated

cases.★

a. Graph linear and quadratic functions

and show intercepts, maxima, and

minima.

4

3

Integrated Math B

Curriculum Map


Vocabulary

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Functions Linear and Exponential

Models

Construct and compare linear and

exponential models and solve

problems

linear, exponential F-LE

1a

I Distinguish between situations that

can be modeled with linear functions

and with exponential functions.

Prove that linear functions grow by equal

differences over equal intervals, and that

exponential functions grow by equal

factors over equal intervals.

4


Models



problems


1b




Recognize situations in which one

quantity changes at a constant rate per

unit interval relative to another.

4


Models



problems


1c




Recognize situations in which a quantity

grows or decays by a constant percent

rate per unit interval relative to another.

2

Geometry Congruence Experiment with transformations in the

plane

angle, circle,

perpendicular,

parallel, segment,

line, point,

distance, arc

G-CO

1

I ODE Know precise definitions of angle, circle,

perpendicular line, parallel line, and line

segment, based on the undefined notions

of point, line, distance along a line, and

distance around a circular arc.

2,3

4

Integrated Math B

Curriculum Map


Vocabulary

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plane

plane G-CO

2

I ODE Represent transformations in the plane

using, e.g., transparencies and geometry

software; describe transformations as

functions that take points in the plane as

inputs and give other points as outputs.

Compare transformations that preserve

distance and angle to those that do not

(e.g., translation versus horizontal

stretch).

2,3


plane

rectangle,

parallelogram,

trapezoid, polygon,

rotation, reflections

G-CO

3

I ODE Given a rectangle, parallelogram,

trapezoid, or regular polygon, describe the

rotations and reflections that carry it onto

itself.

2,3


plane

rotation, reflection,

translation, angles,

cirecles,

perpendicular,

parallel, segments

G-CO

4

I ODE Develop definitions of rotations,

reflections, and translations in terms of

angles, circles, perpendicular lines,

parallel lines, and line segments.

2,3


plane


translation

G-CO

5

I ODE Given a geometric figure and a rotation,

reflection, or translation, draw the

transformed figure using, e.g., graph

paper, tracing paper, or geometry

software. Specify a sequence of

transformations that will carry a given

figure onto another.

2,3

5

Integrated Math B

Curriculum Map


Vocabulary

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Geometry Similarity, Right Triangles,

and Trigonometry

Understand similarity in terms of

similarity transformations

dilation, scale

factor

G-

SRT

1a

I ODE Verify experimentally the properties of

dilations given by a center and a scale

factor:

A dilation takes a line not passing through

the center of the dilation to a parallel line,

and leaves a line passing through the

center unchanged.

3,4


and Trigonometry



dilation, scale

factor

G-

SRT

1b



factor:

The dilation of a line segment is longer or

shorter in the ratio given by the scale

factor

3,4


and Trigonometry



similar,

proportionality

G-

SRT 2

I ODE Given two figures, use the definition of

similarity in terms of similarity

transformations to decide if they are

similar; explain using similarity

transformations the meaning of similarity

for triangles as the equality of all

corresponding pairs of angles and the

proportionality of all corresponding pairs

of sides.

3,4


and Trigonometry



congruence G-

SRT 5

I ODE Use congruence and similarity criteria for

triangles to solve problems and to prove

relationships in geometric figures.

2,3

6

Integrated Math B

Curriculum Map


Vocabulary

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Specific Standard

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Geometry Expressing Geometric

Properties with Equations

Using Coordinates to prove simple

geometric theorems algebraically

parallel and

perpendicular lines

G-

GPE 5

I ODE Prove the slope criteria for parallel and

perpendicular lines and use them to solve

geometric problems (e.g., find the

equation of a line parallel or perpendicular

to a given line that passes through a given

point).

3,4

Geometry Expressing Geometric

Properties with Equations



polygons, area of

triangles, distance

formula

G-

GPE 7

I ODE Use coordinates to compute perimeters of

polygons and areas of triangles and

rectangles, e.g., using the distance

formula

3,4

Geometry Geometric Measurement

and Dimension

Explain volume formulas and use

them to solve problems

circumference,

area, volume,

cylinder, pyramid,

cone

G-

GMD

1

I ODE Give an informal argument for the

formulas for the circumference of a circle,

area of a circle, volume of a cylinder,

pyramid, and cone. Use dissection

arguments, Cavalieri’s principle, and

informal limit arguments.

3,4

Geometry Geometric Measurement

and Dimension



cylinder, pyramids,

cones, spheres

G-

GMD

3

I ODE Use volume formulas for cylinders,

pyramids, cones, and spheres to solve

problems

3,4

Geometry Modeling with Geometry Apply geometric concepts in modeling

situations

shapes, measures G-MG

1

I ODE Use geometric shapes, their measures,

and their properties to describe objects

(e.g., modeling a tree trunk or a human

torso as a cylinder)

3,4

Statistics and

Probability

Interpreting Categorical and

Quantitative Data

Summarize, represent, and interpret

data on a single count or

measurement variable

number line S-ID 1 I ODE Represent data with plots on the real

number line (dot plots, histograms, and

box plots).

1,2

Statistics and

Probability

Conditional Probability and

the Rules of Probability

Use the rules of probability to

compute probabilities of compound

events in a uniform probability model

addition rule S-CP

7

I ODE Apply the Addition Rule, P(A or B) = P(A)

+ P(B) – P(A and B), and interpret the

answer in terms of the model.

1,2

7

Integrated Math B

Curriculum Map


Vocabulary

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Algebra I

Curriculum Map

Strand Domain Cluster Key Vocabulary

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Specific Standard

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Number and Quantity The Real Number System Extend the properties

of exponents to

rational exponents

Rational, exponent,

radical, integer

N-RN

1

I ODE Explain how the definition of the

meaning of rational exponents

follows from extending the

properties of integer exponents to

those values, allowing for a notation

for radicals in terms of rational

exponents.

3,4

Number and Quantity The Real Number System Use properties of

rational and irrational

numbers

Rational, irrational,

non zero, integer

N-RN

3

I ODE Explain why the sum or product of two






1,2

Number and Quantity Quantity Reason

quantatitatively and

use units to solve

problems

units, scale, origin N-Q 1 I ODE Use units as a way to understand

problems and to guide the solution of

multi-step problems; choose and interpret

units consistently in formulas; choose

and interpret the scale and the origin in

graphs and data displays

1,2,3,4

Algebra Seeing Structure in Expressions Interpret the structure

of expressions

expression, terms,

factors, coefficients

A-

SSE 1

I,R ODE Interpret expressions that represent a

quantity in terms of its context.

Interpret parts of an expression, such as

terms, factors, and coefficients.



single entity

1,2,3,4

1

Algebra I

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Algebra Seeing Structure in Expressions Write expressions in

equivalent forms to

solve problems

equivalent, quadratic,

complete the square,

exponential

A-

SSE 3

I ODE Choose and produce an equivalent form

of an expression to reveal and explain

properties of the quantity represented by

the expression.

a. Factor a quadratic expression to reveal

the zeros of the function it defines.

3,4

Algebra Creating Equations Create equations that

describe numbers or

relationshps

inequalities, variables,

linear, quadratic,

rational, exponential

A-

CED 1

I,R ODE Create equations and inequalities in one


Include equations arising from linear and

quadratic functions, and simple rational

and exponential functions.

1,2,3,4


describe numbers or

relationshps

graph, coordinate

axes, labels, scales

A-

CED 2

I,R ODE Create equations in two or more variables




3,4


describe numbers or

relationshps

interest A-

CED 4

I ODE Rearrange formulas to highlight a

quantity of interest, using the same

reasoning as in solving equations.

3,4

Algebra Reasoning with Equations and

Inequalites

Understand solving

equations as a

process of reasoning

and explain the

reasoning

inequalities A-REI

1

I ODE Explain each step in solving a simple

equation as following from the equality of

numbers asserted at the previous step,

starting from the assumption that the

original equation has a solution.

Construct a viable argument to justify a

solution method

1,2,3,4

2

Algebra I

Curriculum Map


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Inequalites

Solve equations and

inequalites in one

variable

linear equations,

inequalites,

coefficients

A-REI

3

I,R ODE Solve linear equations and inequalities in


coefficients represented by letters

3,4


Inequalites

Solve equations and

inequalites in one

variable

quadratic equations,

square roots, factoring,

complex solutions

A-REI

4

I ODE Solve quadratic equations in one

variable.

Solve quadratic equations by inspection

(e.g., for x2 = 49), taking square roots,

completing the square, the quadratic

formula and factoring, as appropriate to

the initial form of the equation.

3,4


Inequalites

Solve systems of

equations

system, variables,

solutions

A-REI

5

I ODE Prove that, given a system of two

equations in two variables, replacing one

equation by the sum of that equation and

a multiple of the other produces a system

with the same solutions.

3,4


Inequalites

Solve systems of

equations

system, linear

equations

A-REI

6

I ODE Solve systems of linear equations exactly

and approximately (e.g., with graphs),

focusing on pairs of linear equations in

two variables.

3,4


Inequalites

Represent and solve

equations and

inequalites graphically

graph, solutions,

coordinate plane,

curve

A-REI

10

I,R ODE Understand that the graph of an equation




line).

1,2

3

Algebra I

Curriculum Map


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Inequalites

Represent and solve

equations and


coordinates, solutions A-REI

11

I ODE Explain why the x-coordinates of the

points where the graphs of the equations

y = f(x) and y = g(x) intersect are the

solutions of the equation f(x) = g(x);

3,4


Inequalites

Represent and solve

equations and


graph, solutions, A-REI

12

I ODE Graph the solutions to a linear inequality

in two variables as a half-plane

(excluding the boundary in the case of a

strict inequality), and graph the solution

set to a system of linear inequalities in

two variables as the intersection of the

corresponding half-planes.

3,4

Functions Interpreting Functions Understand the

concept of a function

and use function

notation

domain, range,

function, input, output

F-IF 1 I,R ODE Understand that a function from one set





domain, then f(x) denotes the output of f

corresponding to the input x. The graph

of f is the graph of the equation y = f(x).

1,2

Functions Interpreting Functions Understand the

concept of a function

and use function

notation

function notation,

evaluate, functions,

inputs, domains

F-IF 2 I ODE Use function notation, evaluate functions



terms of a context.

1,2

4

Algebra I

Curriculum Map


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Functions Interpreting Functions Interprety functions

that arise in

applications in terms of

the contex

function, model,

quantities

F-IF 4 1 ODE For a function that models a relationship

between two quantities, interpret key

features of graph and tables in terms of

the quantities, and sketch graphs

showing key featrues given a verbal

description of the relationship

1,2,3,4

Functions Interpreting Functions Interpret functions that

arise in applications in

terms of the context

quantitative, function F-IF 5 I ODE Relate the domain of a function to its

graph and, where applicable, to the

quantitative relationship it describes.

1,2

Functions Interpreting Functions Interpret functions that

arise in applications in


rate of change F-IF 6 I,R ODE Calculate and interpret the average rate

of change of a function (presented



change from a graph.

1,2

Functions Intepreting Functions Build a functions that

models a relationship

between two quantities

function, quatities,

recursive function

F-BF

1a

I,R ODE Write a function that describes a

relationship between two quantities

(a) determine an explicit expression, a

recursive process, or steps for calculation

from a context

1,2,3,4

Functions Intepreting Functions Build a functions that

models a relationship

between two quantities

intercepts, max, min,

linear, quadratic

F-IF

7a



the graph, by hand in simple cases

and using technology for more

complicated cases.

(a) Graph linear and quadratic functions


minima.

3,4

5

Algebra I

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Functions Linear and Exponential Models Construct and

compare linear and

exponential models

and solve problems

linear functions, rate,

interval, decay, growth,

percent of change

F-LE

1a

I ODE Distinguish between situations that



(a) Prove that linear functions grow by

equal differences over equal intervals,

and that exponential functions grow by

equal factors over equal intervals.

3,4


compare linear and

exponential models

and solve problems



percent of change

F-LE

1b

I ODEDistinguish between situations

that can be modeled with linear

functions and with exponential

functions.

(b) Recognize situations in which one

quantity changes at a constant rate

per unit interval relative to another.

3,4


compare linear and

exponential models

and solve problems



percent of change

F-LE

1c




(c) Recognize situations in which a

quantity grows or decays by a constant

percent rate per unit interval relative to

another.

3,4

6

Algebra I

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Functions Linear and Exponential Models Interpret expressions

for functions in terms

of the situation they

model

parameters F-LE

5

I ODE Interpret the parameters in a linear or

exponential function in terms of a context.

3,4

Geometry Similarity, Right Triangles, and

Trigonometry

Understand similarity

in terms of similarity

transformations

similarity,

corresponding

G-

SRT 2

I ODE Given two figures, use the definition of








of sides.

1,2


Trigonometry

Prove theorems

involving similarity

congruence, similarity G-

SRT 5

I ODE Use congruence and similarity criteria for



1,2

Geometry Expressing Geometric Properties with

Equations

Using Coordinates to

prove simple

geometric theorems

algebraically

parallel and

perpendicular lines

G-

GPE 5

I ODE Prove the slope criteria for parallel and



equation of a line parallel or

perpendicular to a given line that passes

through a given point).

3,4

Statistics and

Probability


Quantitiative Data

Summarize, represent,

and interpret data on a

single count or


dot plots, histograms,

box plots

S-ID 1 I ODE Represent data with plots on the real


box plots).

3,4

7

Algebra I

Curriculum Map


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Statistics and

Probability


Quantitiative Data



single count or


outliers S-ID 2 I ODE Use statistics appropriate to the shape of

the data distribution to compare center

(median, mean) and spread (interquartile

range, standard deviation) of two or more

different data sets.

3,4

Statistics and

Probability


Quantitiative Data



single count or


function, analyze,

scatter plot, inear

S-ID

6a

I ODE Represent data on two quantitative

variables on a scatter plot, and

describe how the variables are related.

a. Fit a function to the data; use functions

fitted to data to solve problems in the

context of the data. Use given functions

or choose a function suggested by the

context. Emphasize linear, quadratic, and

exponential models.

3,4

Statistics and

Probability


Quantitiative Data



single count or


function, analyze,

scatter plot, inear

S-ID

6b




b. Informally assess the fit of a function

by plotting and analyzing residuals.

3,4

8

Algebra I

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Statistics and

Probability


Quantitiative Data



single count or


function, analyze,

scatter plot, inear

S-ID

6c




c. Fit a linear function for a scatter plot

that suggests a linear association.

1,2

Statistics and

Probability

Making Inferences and Justifying

Conclusions

Make inferences and

justify conclusions

from sample surveys,

experiments, and

observational studies

mean, proportion, error S-IC 4 I ODE Use data from a sample survey to

estimate a population mean or

proportion; develop a margin of error

through the use of simulation models for

random sampling.

3,4

Statistics and

Probability


Conclusions

Make inferences and

justify conclusions

from sample surveys,

experiments, and

observational studies

data S-IC 6 I ODE Evaluate Reports based on data 3,4

Statistics and

Probability

Conditional Probabilty and the Rules

of Probability

Understand

independence and

conditional probablility

and use them to

interpret data

union, intersections,

complements, and, or

S-CP

1

I ODE Describe events as subsets of a sample

space (the set of outcomes) using

characteristics (or categories) of the

outcomes, or as unions, intersections, or

complements of other events (“or,” “and,”

“not”).

3,4

9

Algebra I

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Statistics and

Probability


of Probability

Understand

independence and


and use them to

interpret data

independent events S-CP

2

I ODE Understand that two events A and B are

independent if the probability of A and B

occurring together is the product of their

probabilities, and use this

characterization to determine if they are

independent.

3,4

Statistics and

Probability


of Probability

Understand

independence and


and use them to

interpret data

conditional probabilty S-CP

3

I ODE Understand the conditional probability of

A given B as P(A and B)/P(B), and

interpret independence of A and B as

saying that the conditional probability of A

given B is the same as the probability of

A, and the conditional probability of B

given A is the same as the probability of

B.

3,4

Statistics and

Probability


of Probability

Use the rules of

probability to compute

probabilities of

compound events in a

uniform probability

model

events S-CP

7




3,4

Statistics and

Probability


of Probability

Use the rules of

probability to compute

probabilities of

compound events in a

uniform probability

model

events S-CP

8

I ODE (+) Apply the general Multiplication Rule

in a uniform probability model, P(A and B)

= P(A)P(B|A) = P(B)P(A|B), and interpret

the answer in terms of the model.

3,4

10

Geometry

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Number and Quantity The Real Number System Extend the properties of exponents to

rational exponents

radicals, exponents N-RN

1

I ODE Rewrite expressions involving radicals

and rational exponents using the

properties of exponents

3,4

Number and Quantity Quantity Reason Quantitatively and use units

to solve problems

units N-Q 1 I, R ODE Use units as a way to understand



units consistently in formulas; choose and


and data displays.

1,2

Number and Quantity Vector and Matrix Quantities Represent and model with vector

quantities

vector, magnitude,

direction

N-VM

1

I ODE (+) Recognize vector quantities as having

both magnitude and direction. Represent

vector quantities by directed line

segments, and use appropriate symbols

for vectors and their magnitudes

3,4


quantities

coordinates, initial

point, terminal point

N-VM

2

I ODE (+) Find the components of a vector by

subtracting the coordinates of an initial

point from the coordinates of a terminal

point

3,4

Number and Quantity Vector and Matrix Quantities Perform operations on Vectors vector N-VM

4c

I ODE (+) Add and subtract vectors.

Understand vector subtraction v – w as v

+ (–w), where –w is the additive inverse of

w, with the same magnitude as w and

pointing in the opposite direction.

Represent vector subtraction graphically

by connecting the tips in the appropriate

order, and perform vector subtraction

component-wise.

3,4

1

Geometry

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Number and Quantity Vector and Matrix Quantities Perform operations on Vectors scalar multiplication V-VM

5a

I ODE (+) Multiply a vector by a scalar.

Represent scalar multiplication graphically

by scaling vectors and possibly reversing

their direction; perform scalar

multiplication component-wise

3,4


plane

angle, circle,

perpendicular, parallel,

segment, line, point,

distance, arc

G-CO

1

I,

R,

M

ODE Know precise definitions of angle, circle,





1,2,3,4


plane

plane G-CO

2

I, R ODE Represent transformations in the plane








stretch).

3,4


plane

rectangle,

parallelogram,

trapezoid, polygon,


G-CO

3




itself.

3,4


plane



cirecles, perpendicular,

parallel, segments

G-CO

4

I, R ODE Develop definitions of rotations,




3,4

2

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plane


translation

G-CO

5

I, R ODE Given a geometric figure and a rotation,







1,2,3,4

Geometry Congruence Understand congruence in terms of

rigid motions

motion G-CO

6

I, R ODE Use geometric descriptions of rigid

motions to transform figures and to predict

the effect of a given rigid motion on a

given figure; given two figures, use the

definition of congruence in terms of rigid

motions to decide if they are congruent.

1,2,3,4


rigid motions

triangles,

corresponding parts

G-CO

7

I, R ODE Use the definition of congruence in terms

of rigid motions to show that two triangles

are congruent if and only if corresponding

pairs of sides and corresponding pairs of

angles are congruent.

1,2,3,4


rigid motions

ASA, SAS, SSS G-CO

8

I, R ODE Explain how the criteria for triangle

congruence (ASA, SAS, and SSS) follow

from the definition of congruence in terms

of rigid motions.

1,2,3,4

3

Geometry

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Geometry Congruence Prove Geometric Theorems vertical, corresponding,

perpendicular bisector,

equidistant

G-CO

9

I, R ODE Prove theorems about lines and angles.

Theorems include: vertical angles are

congruent; when a transversal crosses

parallel lines, alternate interior angles are

congruent and corresponding angles are

congruent; points on a perpendicular

bisector of a line segment are exactly

those equidistant from the segment’s

endpoints.

1,2

Geometry Congruence Prove Geometric Theorems interior angles, base

angles, isosceles,

midpoints, medians

G-CO

10

I, R ODE Prove theorems about triangles.

Theorems include: measures of interior

angles of a triangle sum to 180°; base

angles of isosceles triangles are

congruent; the segment joining midpoints

of two sides of a triangle is parallel to the

third side and half the length; the medians

of a triangle meet at a point.

1,2

Geometry Congruence Prove Geometric Theorems parallelogram,

diagonals, rectangles

G-CO

11

I, R ODE Prove theorems about parallelograms.

Theorems include: opposite sides are

congruent, opposite angles are congruent,

the diagonals of a parallelogram bisect

each other, and conversely, rectangles

are parallelograms with congruent

diagonals.

1,2

4

Geometry

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Geometry Congruence Make Geometric Constructions compass straightedge G-CO

12

I, R ODE Make formal geometric constructions with

a variety of tools and methods (compass

and straightedge, string, reflective

devices, paper folding, dynamic geometric

software, etc.). Copying a segment;

copying an angle; bisecting a segment;

bisecting an angle; constructing

perpendicular lines, including the

perpendicular bisector of a line segment;

and constructing a line parallel to a given

line through a point not on the line.

1,2

Geometry Congruence Make Geometric Constructions equilateral triangle,

square, hexagon,

inscribed in

G-CO

13

I ODE Construct an equilateral triangle, a

square, and a regular hexagon inscribed

in a circle.

1,2


Trigonometry



dilation, scale factor G-

SRT

1a



factor:




center unchanged.

3,4


Trigonometry




SRT

1b

I, R ODE Verify experimentally the properties of


factor:



factor

3,4

5

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Trigonometry



similar, proportionality G-

SRT 2

I, R ODE Given two figures, use the definition of








of sides.

3,4


Trigonometry



AA G-

SRT 3

I, R ODE Use the properties of similarity

transformations to establish the AA

criterion for two triangles to be similar.

3,4


Trigonometry



Pythagorean Theorem G-

SRT 4

I ODE Prove theorems about triangles.

Theorems include: a line parallel to one

side of a triangle divides the other two

proportionally, and conversely; the

Pythagorean Theorem proved using

triangle similarity.

3,4


Trigonometry



congruence G-

SRT 5

I, R ODE Use congruence and similarity criteria for



1,2,3,4


Trigonometry

Define trigonometric ratios and solve

problems invovling right angles

right triangles, acute

angles

G-

SRT 6

I,R ODE Understand that by similarity, side ratios in

right triangles are properties of the angles

in the triangle, leading to definitions of

trigonometric ratios for acute angles.

3,4

6

Geometry

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Trigonometry



sine and cosine G-

SRT 7

I,R ODE Explain and use the relationship between

the sine and cosine of complementary

angles

3,4


Trigonometry




SRT 8

I, R ODE Use trigonometric ratios and the

Pythagorean Theorem to solve right

triangles in applied problems

3,4


Trigonometry

Apply trigonometry to general

triangles

area of a triangle G-

SRT 9

I ODE (+) Derive the formula A = 1/2 ab sin(C) for

the area of a triangle by drawing an

auxiliary line from a vertex perpendicular

to the opposite side.

3,4


Trigonometry


triangles

law of sines, law of

cosines

G-

SRT

10

I ODE (+) Prove the Laws of Sines and Cosines and

use them to solve problems.

3,4


Trigonometry


triangles


cosines

G-

SRT

11

I ODE (+) Understand and apply the Law of Sines

and the Law of Cosines to find unknown

measurements in right and non-right

triangles (e.g., surveying problems,

resultant forces).

3,4

Geometry Circles Understand and apply theorems about

circles

circles G-C 1 I ODE Prove that all circles are similar. 3,4


circles

inscribed angles, radii,

chords

G-C 2 I,R ODE Identify and describe relationships among

inscribed angles, radii, and chords.

Include the relationship between central,

inscribed, and circumscribed angles;

inscribed angles on a diameter are right

angles; the radius of a circle is

perpendicular to the tangent where the

radius intersects the circle.

3,4

7

Geometry

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circles

inscribed,

circumscribed

G-C 3 I ODE Construct the inscribed and circumscribed

circles of a triangle, and prove properties

of angles for a quadrilateral inscribed in a

circle.

3,4


circles

tangent G-C 4 I ODE (+) Construct a tangent line from a point

outside a given circle to the circle.

3,4

Geometry Circles Find arc lengths and areas of sectors

of circles

arc length, area of

sector

G-C 5 I ODE Derive using similarity the fact that the

length of the arc intercepted by an angle

is proportional to the radius, and define

the radian measure of the angle as the

constant of proportionality; derive the

formula for the area of a sector.

3,4


Equations

Translate between the geometric

description and the equation for a

conic section

circle, radius,

Pythagorean Theorem

G-

GPE 1

I ODE Derive the equation of a circle of given

center and radius using the Pythagorean

Theorem; complete the square to find the

center and radius of a circle given by an

equation.

3,4


Equations



corrdinates G-

GPE 4

I ODE Use coordinates to prove simple

geometric theorems algebraically. For

example, prove or disprove that a figure

defined by four given points in the

coordinate plane is a rectangle; prove or

disprove that the point (1, √3) lies on the

circle centered at the origin and containing

the point (0, 2).

1,2

8

Geometry

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Equations



parallel and

perpendicular lines

G-

GPE 5

R ODE Prove the slope criteria for parallel and





point).

1,2


Equations



segment G-

GPE 6

R ODE Find the point on a directed line segment

between two given points that partitions

the segment in a given ratio.

1,2


Equations



polygons, area of

triangles, distance

formula

G-

GPE 7

R ODE Use coordinates to compute perimeters of



formula

1,2

Geometry Geometric Measurement and

Dimension



circumference, area,

volume, cylinder,

pyramid, cone

G-

GMD

1

R ODE Give an informal argument for the






1,2


Dimension



volume, sphere G-

GMD

2

1,R ODE (+) Give an informal argument using

Cavalieri’s principle for the formulas for

the volume of a sphere and other solid

figures.

3,4


Dimension



cylinder, pyramids,

cones, spheres

G-

GMD

3

R,

M

ODE Use volume formulas for cylinders,


problems

3,4

9

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Dimension



cross sections G-

GMD

4

I,R ODE Identify the shapes of two-dimensional

cross-sections of three-dimensional

objects, and identify three-dimensional

objects generated by rotations of two-

dimensional objects.

3,4


situations


1

I,R ODE Use geometric shapes, their measures,




3,4

Modeling with Geometry Apply geometric concepts in modeling

situations

density, area, volume G-MG

2

I ODE Apply concepts of density based on area

and volume in modeling situations (e.g.,

persons per square mile, BTUs per cubic

foot).

3,4


situations

design problems G-MG

3

I,R ODE Apply geometric methods to solve design

problems (e.g., designing an object or

structure to satisfy physical constraints or

minimize cost; working with typographic

grid systems based on ratios).

1,2,3,4

Statistics and

Probability

Using Probability to Make Decisions Use probability to evaluate outcomes

of decisions

probability S-MD

6

R ODE (+) Use probabilities to make fair decisions

(e.g., drawing by lots, using a random

number generator).

3,4

10

Accelerated Geometry

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rational exponents

radicals, exponents N-RN

1

I ODE Rewrite expressions involving radicals


properties of exponents

3,4

Number and Quantity Quantity Reason Quantitatively and use units

to solve problems

units N-Q 1 I, R ODE Use units as a way to understand





and data displays.

1,2


quantities

vector, magnitude,

direction

N-VM

1






3,4


quantities



N-VM

2




point

3,4


4c


Understand vector subtraction v – w as v

+ (–w), where –w is the additive inverse of

w, with the same magnitude as w and





component-wise.

3,4

1


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5a


Represent scalar multiplication graphically

by scaling vectors and possibly reversing

their direction; perform scalar


3,4


plane

angle, circle,

perpendicular, parallel,

segment, line, point,

distance, arc

G-CO

1

I,

R,

M

ODE Know precise definitions of angle, circle,





1,2,3,4


plane

plane G-CO

2

I, R ODE Represent transformations in the plane








stretch).

3,4


plane

rectangle,

parallelogram,

trapezoid, polygon,


G-CO

3




itself.

3,4


plane



cirecles, perpendicular,

parallel, segments

G-CO

4

I, R ODE Develop definitions of rotations,




3,4

2


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plane


translation

G-CO

5

I, R ODE Given a geometric figure and a rotation,







1,2,3,4


rigid motions

motion G-CO

6

I, R ODE Use geometric descriptions of rigid

motions to transform figures and to predict

the effect of a given rigid motion on a

given figure; given two figures, use the

definition of congruence in terms of rigid

motions to decide if they are congruent.

1,2,3,4


rigid motions

triangles,

corresponding parts

G-CO

7

I, R ODE Use the definition of congruence in terms

of rigid motions to show that two triangles

are congruent if and only if corresponding

pairs of sides and corresponding pairs of

angles are congruent.

1,2,3,4


rigid motions

ASA, SAS, SSS G-CO

8

I, R ODE Explain how the criteria for triangle

congruence (ASA, SAS, and SSS) follow

from the definition of congruence in terms

of rigid motions.

1,2,3,4

3


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Geometry Congruence Prove Geometric Theorems vertical, corresponding,

perpendicular bisector,

equidistant

G-CO

9

I, R ODE Prove theorems about lines and angles.

Theorems include: vertical angles are

congruent; when a transversal crosses

parallel lines, alternate interior angles are

congruent and corresponding angles are

congruent; points on a perpendicular

bisector of a line segment are exactly

those equidistant from the segment’s

endpoints.

1,2

Geometry Congruence Prove Geometric Theorems interior angles, base

angles, isosceles,

midpoints, medians

G-CO

10

I, R ODE Prove theorems about triangles.

Theorems include: measures of interior

angles of a triangle sum to 180°; base

angles of isosceles triangles are

congruent; the segment joining midpoints

of two sides of a triangle is parallel to the

third side and half the length; the medians

of a triangle meet at a point.

1,2

Geometry Congruence Prove Geometric Theorems parallelogram,

diagonals, rectangles

G-CO

11

I, R ODE Prove theorems about parallelograms.

Theorems include: opposite sides are

congruent, opposite angles are congruent,

the diagonals of a parallelogram bisect

each other, and conversely, rectangles

are parallelograms with congruent

diagonals.

1,2

4


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Geometry Congruence Make Geometric Constructions compass straightedge G-CO

12

I, R ODE Make formal geometric constructions with

a variety of tools and methods (compass

and straightedge, string, reflective

devices, paper folding, dynamic geometric

software, etc.). Copying a segment;

copying an angle; bisecting a segment;

bisecting an angle; constructing

perpendicular lines, including the

perpendicular bisector of a line segment;

and constructing a line parallel to a given

line through a point not on the line.

1,2

Geometry Congruence Make Geometric Constructions equilateral triangle,

square, hexagon,

inscribed in

G-CO

13

I ODE Construct an equilateral triangle, a

square, and a regular hexagon inscribed

in a circle.

1,2


Trigonometry




SRT

1a



factor:




center unchanged.

3,4


Trigonometry




SRT

1b

I, R ODE Verify experimentally the properties of


factor:



factor

3,4

5


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Trigonometry



similar, proportionality G-

SRT 2

I, R ODE Given two figures, use the definition of








of sides.

3,4


Trigonometry



AA G-

SRT 3

I, R ODE Use the properties of similarity

transformations to establish the AA

criterion for two triangles to be similar.

3,4


Trigonometry




SRT 4

I ODE Prove theorems about triangles.






3,4


Trigonometry



congruence G-

SRT 5

I, R ODE Use congruence and similarity criteria for



1,2,3,4


Trigonometry




angles

G-

SRT 6

I,R ODE Understand that by similarity, side ratios in




3,4

6


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Trigonometry



sine and cosine G-

SRT 7

I,R ODE Explain and use the relationship between


angles

3,4


Trigonometry




SRT 8

I, R ODE Use trigonometric ratios and the



3,4


Trigonometry


triangles


SRT 9





3,4


Trigonometry


triangles


cosines

G-

SRT

10



3,4


Trigonometry


triangles


cosines

G-

SRT

11





resultant forces).

3,4


circles

circles G-C 1 I ODE Prove that all circles are similar. 3,4


circles

inscribed angles, radii,

chords

G-C 2 I,R ODE Identify and describe relationships among

inscribed angles, radii, and chords.

Include the relationship between central,

inscribed, and circumscribed angles;

inscribed angles on a diameter are right

angles; the radius of a circle is

perpendicular to the tangent where the

radius intersects the circle.

3,4

7


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circles

inscribed,

circumscribed

G-C 3 I ODE Construct the inscribed and circumscribed

circles of a triangle, and prove properties

of angles for a quadrilateral inscribed in a

circle.

3,4


circles

tangent G-C 4 I ODE (+) Construct a tangent line from a point

outside a given circle to the circle.

3,4


of circles

arc length, area of

sector

G-C 5 I ODE Derive using similarity the fact that the






3,4


Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 1

I ODE Derive the equation of a circle of given




equation.

3,4


Equations



corrdinates G-

GPE 4

I ODE Use coordinates to prove simple

geometric theorems algebraically. For

example, prove or disprove that a figure

defined by four given points in the

coordinate plane is a rectangle; prove or

disprove that the point (1, √3) lies on the

circle centered at the origin and containing

the point (0, 2).

1,2

8


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Equations



parallel and

perpendicular lines

G-

GPE 5






point).

1,2


Equations



segment G-

GPE 6

R ODE Find the point on a directed line segment

between two given points that partitions

the segment in a given ratio.

1,2


Equations



polygons, area of

triangles, distance

formula

G-

GPE 7

R ODE Use coordinates to compute perimeters of



formula

1,2


Dimension



circumference, area,

volume, cylinder,

pyramid, cone

G-

GMD

1

R ODE Give an informal argument for the






1,2


Dimension



volume, sphere G-

GMD

2

1,R ODE (+) Give an informal argument using

Cavalieri’s principle for the formulas for

the volume of a sphere and other solid

figures.

3,4


Dimension



cylinder, pyramids,

cones, spheres

G-

GMD

3

R,

M



problems

3,4

9


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Dimension



cross sections G-

GMD

4

I,R ODE Identify the shapes of two-dimensional





3,4


situations


1

I,R ODE Use geometric shapes, their measures,




3,4

Modeling with Geometry Apply geometric concepts in modeling

situations

density, area, volume G-MG

2

I ODE Apply concepts of density based on area

and volume in modeling situations (e.g.,

persons per square mile, BTUs per cubic

foot).

3,4


situations

design problems G-MG

3

I,R ODE Apply geometric methods to solve design

problems (e.g., designing an object or

structure to satisfy physical constraints or

minimize cost; working with typographic

grid systems based on ratios).

1,2,3,4

Statistics and

Probability


of decisions

probability S-MD

6



number generator).

3,4

10

Informal Algebra II

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rational exponents

rational, exponent,

radical, integer

N-

RN.1

I,R ODE Explain how the definition of the meaning





exponents

4


rational exponents

rational, exponent,

radical, integer

N-

RN.2

I,R ODE Rewrite expressions involving radicals


properties of exponents.

4

Number and Quantity The Real Number System Use Properties of rational and

irrational numbers

sum, product, rational,

irrational, nonzero,

integer

N-

RN.3

I,R ODE Explain why the sum or product of two






4

Number and Quantity Quantity Reason quantatitatively and use units

to solve problems

units, scale, origin N-Q 1 I,R ODE Use units as a way to understand





and data displays

1,2,3,4

Number and Quantity Quantities Reason quantitatively and use units to

solve problems

quantities, modeling N-Q.2 R ODE Define appropriate quantities for the

purpose of descriptive modeling.

1,2,3,4


solve problems

quantities,

measurement

N-Q.3 R ODE Choose a level of accuracy appropriate to

limitations on measurement reporting

quantities

1,2,3,4

Number and Quantity The Complex Number System Perform arithmetic operations with

complex numbers

complex number, real

number

N-

CN.1

I ODE Know there is a complex number i such as

i^2 = -1, and every complex number has

the form a +bi with a and b real.

3

1

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complex numbers


number, properties:

communative,

associative, distributive

N-

CN.2

I ODE Use the relation i^2 = -1 and the

commutative, associative, and distributive

properties to add, subtract, and multiply

complex numbers.

3

Number and Quantity The Complex Number System Use complex numbers in polynomial

identities and equations

quadratic, complex

solutions, coefficients

N-

CN.7

I ODE Solve quadratic equations with real

coefficients that have complex solutions

3

Algebra Seeing Structure in Expressions Interpret the structure of expressions expression, terms,


quantity

A-

SSE.1

b


quantity in terms of its context. (b)



single entity

1,2,3,4



quantity

A-

SSE.2

I ODE Use the structure of an expression to

identify ways to rewrite it

1,2,3,4

Algebra Seeing Structure in Expressions Write expressions in equivalent forms

to solve problems.

expression, factor,

zeros of a function

A-

SSE.3

a

I ODE Choose and produce an equivalent

form of an expression to reveal and

explain properties of the quantity

represented by the expression

(a)Factor a quadratic expression to reveal

the zeros of the function it defines

3


to solve problems.

expression, complete

the square, quadratic,

maximum/minimum

A-

SSE.3

b




represented by the expression (b)

Complete the square in a quadratic

expression to reveal the maximum or

minimum value of the function it defines.

3

2

Informal Algebra II

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to solve problems.

expression, exponent,

exponential function

A-

SSE.3

c




represented by the expression (c)

Use the properties of exponents to

transform expressions for exponential

functions

4


to solve problems.

sum, infinite geometric

series

A-

SSE.4

I ODE Derive the formula for the sum of a finite

geometric series (when the common ratio

is not 1), and use the formula to solve

problems.

3,4

Algebra Arithmetic with Polynomials and

Rational Expressions

Perform arithmetic operations on

polynomials

polynomial, integer A-

AAPR

.1

I ODE Understand that polynomials form a

system analogous to the integers, namely,

they are closed under the operations of

addition, subtraction, and multiplication;

add, subtract, and multiply polynomials

3



Understand the relationshipbetween

zeros and factors of polynomials

remainder thorem,

polynomial

A-

AAPR

.2

I ODE Know and apply the Remainder Theorem:

For a polynomial p(x) and a number a, the

remainder on division by x – a is p(a), so

p(a) = 0 if and only if (x – a) is a factor of

p(x).

3





zero of a function A-

AAPR

.3

I ODE Identify zeros of polynomials when

suitable factorizations are available, and

use the zeros to construct a rough graph

of the function defined by the polynomial

3

3

Informal Algebra II

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Use polynomial identities to solve

problems

binomial theorem A-

AAPR

.5

I ODE (+) Know and apply the Binomial Theorem for

the expansion of (x + y)^n in powers of x

and y for a positive integer n, where x and

y are any numbers, with coefficients

determined for example by Pascal’s

Triangle.1

3



Rewrite polynomials expression rational expression A-

AAPR

.6

I ODE Rewrite simple rational expressions in

different forms; write a(x)/b(x) in the form

q(x) + r(x)/b(x), where a(x), b(x), q(x), and

r(x) are polynomials with the degree of r(x)

less than the degree of b(x), using

inspection, long division, or, for the more

complicated examples, a computer

algebra system.

3




AAPR

.7

I ODE Understand that rational expressions form

a system analogous to the rational

numbers, closed under addition,

subtraction, multiplication, and division by

a nonzero rational expression; add,

subtract, multiply, and divide rational

expressions.

4


numbers or relationship

equation, inequalitiy,

variable, coefficient,

constant

A-

CED.1

R ODE Create equations and inequalities in one


Include equations

arising from linear and quadratic

functions, and simple rational and

exponential functions.

1

4

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constant

A-

CED.2

R ODE Create equations in two or more variables


quantities; graph

equations on coordinate axes with labels

and scales

2





constant

A-

CED.3

R ODE Represent constraints by equations or

inequalities, and by systems of equations

and/or inequalities,

and interpret solutions as viable or non-

viable in a modeling context.

2



equation, formula,


constant

A-

CED.4

R ODE Rearrange formulas to highlight a quantity

of interest, using the same reasoning as in

solving

equations.

1,2


Inequalities



reasoning.

Rational equations,

radical equations,

variable

A-

REI.2

I ODE Solve simple rational and radical

equations in one variable, and give

examples showing how

extraneous solutions may arise.

4


Inequalities


one variable

linear equation, linear

inequality, variable,

coefficient

A-

REI.3

a

R ODE Solve linear equations and inequalities in



1,2


Inequalities


one variable

quadratic equation A-

REI.3

b


variable. (a) Use the method of

completing the square to transform any

quadratic equation in x into an equation of

the form (x – p)^2 = q that has the same

solutions. Derive the quadratic formula

from this form.

3

5

Informal Algebra II

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Inequalities


one variable


REI.4


variable.

(b) Solve quadratic equations by

inspection (e.g., for x^2 = 49), taking

square roots, completing the square, the

quadratic formula and factoring, as

appropriate to the initial form of the

equation. Recognize when the quadratic

formula gives complex solutions and write

them in a ± bi for real numbers a and b.

3


Inequalities

Solve systems of equations system, variable A-

REI.5

I ODE Prove that a system of two equations in

two variables, replacing one equation by

the sum of that equation and a multiple of

the other produces a system with the

same solutions.

2


Inequalities


REI.6




two variables.

2


Inequalities

Solve systems of equations inverse of a matrix,

system, linear equation

A-

REI.9

I ODE (+) Find the inverse of a matrix if it exists and

use it to solve systems of linear equations

(using technology for matrices of

dimension 3x3 or greater)

2


Inequalities



graph, set of all

solutions, coordinate

plane

A-

REI.1

0





line).

2

6

Informal Algebra II

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Inequalities



x-coordinate, y-

coordinate, function

A-

REI.1

1

R ODE Explain why the x-coordinates of the

points where the graphs of the equations y

= f(x) and y = g(x) intersect are the

solutions of the equation f(x) = g(x); find

the solutions approximately, e.g., using

technology to graph the functions, make

tables of values, or find successive

approximations. Include cases where f(x)

and/or g(x) are linear, polynomial, rational,

absolute value, exponential, and

logarithmic functions.

1,2


Inequalities



graph, linear inequality,

boundary, system

A-

REI.1

2

R ODE Graph the solutions to a linear inequality

in two variables as a half-plane (excluding

the boundary in the case of a strict

inequality), and graph the solution set to a

system of linear inequalities in two

variables as the intersection of the


2



domain, range, set,

function

F-IF.1 R ODE Understand that a function from one set





domain, the f(x) denotes the output of f



2



function, domain, input F-IF.2 R ODE Use function notation, evaluate functions



terms of a context.

1

7

Informal Algebra II

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intercepts; intervals

where the function is

increasing, decreasing,

positive, or negative;

relative maximums and

minimums;

symmetries; end

behavior; and

periodicity.

F-IF.4 I ODE For a function that models a relationship


features of graphs and tables in terms of

the quantities, and sketch graphs showing

key features given a verbal description of

the relationship.

3



domain, quantiative F-IF.5 R ODE Relate the domain of a function to its



2



rate of change F-IF.6 I ODE Calculate and interpret the average rate of


symbolically or as a table) over a specified

interval. Estimate the rate of change from

a graph.

1,2


representations

linear, quadratic,

intercepts, maxima,

minima

F-

IF.7a

I,R ODE Graph functions expressed




cases. (a) Graph linear and quadratic

functions and show intercepts, maxima,

and minima

1,2,3


representations

roots, piecewise, step-

function, absolute

value

F-

IF.7b





cases. b. Graph square root, cube root,

and piecewise-defined functions, including

step functions and absolute value

functions

4

8

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representations

polynomial, zeros,

factorizations

F-

IF.7c





cases. (c) Graph polynomial functions,

identifying zeros when suitable

factorizations are available, and showing

end behavior

3


representations

rational, zeros,

asymptotes

F-

IF.7d

I ODE (+) Graph functions expressed




cases. (d) Graph rational functions,

identifying zeros and asymptotes when


showing end behavior.

3


representations

logarithmic,

exponential, intercepts,

end behavior, period,

midline, amplitutde

F-

IF.7e





cases. (e) Graph exponential and

logarithmic functions, showing intercepts

and end behavior, and trigonometric

functions, showing period, midline, and

amplitude.

3,4


representations

functions, equivalent F-IF.8 R ODE Write a function defined by an expression

in different but equivalent forms to reveal

and explain different properties of the

function

1,2,3,4

9

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representations

functions, equivalent F-IF.9 R ODE Compre properties of two functions each

represented in a different way

(algebraically, graphincally, numberically

in tables, or by vertbal description)

1,2,3,4

Functions Building Functions Build a function that models a


function F-

BF.1

I ODE Write a function that describes a

relationship between two quantities. (a)

Determine an explicit expression, a


from a context. (b) Combine standard

function types using arithmetic operations

1,2,3,4



arithmetic and

geometric sequence

F-

BF.2

I ODE Write arithmetic and geometric sequences

both recursively and with an explicit

formula; use them to model situations,

and translate between the two forms.

2,3

Functions Building Functions Building new functions from existing

functions

inverse function F-

BF.4a

I ODE Find inverse functions.

(a) Solve an equation of the form f(x) = c

for a simple function f that has an inverse

and write an expression for the inverse.

3,4


functions

inverse, exponents,

logarithms

F-

BF.5

I ODE (+) Understand the inverse relationship

between exponents and logarithms and

use this relationship to solve problems

involving logarithms and exponents

3

Functions Linear and Exponential Models Construct and compare linear and

exponential modesl and solve

problems

linear functions,

intervals, exponential

functions

F-

LE.1a




a. Prove that linear functions grow by




3,4

10

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problems

rate F-

LE.1b




b. Recognize situations in which one



3,4



problems

growth, decay, rate F-

LE.1c




c. Recognize situations in which a quantity



3,4



problems

linear and exponential

functions, arithemetic

and geometric

sequence, input, output

F-

LE.2

I ODE Construct linear and exponential

functions, including arithmetic and

geometric sequences, given a graph, a

description of a relationship, or two input-

output pairs (include reading these from a

table.)

1,2,3,4



problems

linearlly, quadratically,

polynomial

F-

LE.3

I ODE Observe using graphs and tables that a

quantity increasing exponentially

eventually exceeds a quantity increasing

linearly, quadratically, or (more generally)

as a polynomial function.

1,2,3,4

11

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problems

logarithm F-

LE.4

I ODE For exponential models, express as a

logarithm the solution to abct = d where a,

c, and d are numbers and the base b is 2,

10, or e; evaluate the logarithm using

technology.

3,4

Functions Linear and Exponential Models Interpret expresiions for functions in

terms of the situation they model

parameters F-

LE.5

I ODE Interpert the parameters in a linear or

exponetial function in terms of a context

4


Equations



parallel and

perpendicular lines

G-

GPE 5

R.

M

ODE Prove the slope criteria for parallel and





point).

1,2

Statistics Interpreting Categorical and

Quantiative Data


data on two categorical and

quantiative variables

function, model S-

ID.6a



describe how the variables are related

(a) Fit a function to the data; use functions


context of the data. Use given functions or

choose a function suggested by the


exponential models

4


Quantiative Data




residuals, function S-

ID.6b




(b) Informally assess the fit of a function

by plotting and analyzing residuals

4

12

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Quantiative Data




linear function, scatter

plote

S-

ID.6c




(c) Fit a linear function for a scatter plot

that suggests a linear association

4


Quantiative Data

Interpret Linear Models slope, intercepts S-ID.7 I ODE Interpret the slope (rate of change) and

the intercept (constant term) of a linear

model in the context of the data.

4


Quantiative Data

Interpret Linear Models scatter plot, linear fit S-ID.8 I ODE Compute (using technology) and interpret

the correlation coefficient of a linear fit.

4


Quantiative Data

Interpret Linear Models correlation, causation S-ID.9 I ODE Distinguish between correlation and

causation.

4

Statistics and

Probability


of Probability

Understand independence and

conditional probablility and use them

to interpret data



S-CP

1






“not”).

4

Statistics and

Probability


of Probability



to interpret data


2




probabilities, and use this characterization

to determine if they are independent.

4

13

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Statistics and

Probability


of Probability



to interpret data


3

I ODE Understand the conditional probability of A

given B as P(A and B)/P(B), and interpret

independence of A and B as saying that

the conditional probability of A given B is

the same as the probability of A, and the

conditional probability of B given A is the

same as the probability of B.

4

Statistics and

Probability


of Probability




events S-CP

7




4

14

Algebra II

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rational exponents

rational, exponent,

radical, integer

N-

RN.1






exponents

4


rational exponents

rational, exponent,

radical, integer

N-

RN.2




4


irrational numbers



integer

N-

RN.3







4


to solve problems






and data displays

1,2,3,4


solve problems



1,2,3,4


solve problems

quantities,

measurement



quantities

1,2,3,4


complex numbers


number

N-

CN.1




3

1

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complex numbers


number, properties:

communative,


N-

CN.2




complex numbers.

3


complex numbers


number, conjugate

N-

CN.3

I ODE (+) Find the conjugate of a complex number;

use conjugates to find moduli and

quotients of complex numbers.

3



quadratic, complex


N-

CN.7



3



polynomial identities,

complex numbers

N-

CN.8

I ODE (+) Extend polynomial identities to the

complex numbers. For example, rewrite

x^2 + 4 as (x +2i)(x - 2i)

3



polynomials,

quadratics

N-

CN.9

I ODE (+) Know the Fundamental Theorem of

Algebra; show that it is true for quadratic

polynomials

3


quantities

matrix, data N-

VM.6

I ODE (+) Use matrices to represent and manipulate

data, e.g., to represent payoffs or

incidence relationships in a network.

2


quantities

matrix, scaler, product N-

VM.7

I ODE (+) Multiply matrices by scalars to produce

new matrices, e.g., as when all of the

payoffs in a game are doubled.

2


quantities

matrix, dimensions N-

VM.8

I ODE (+) Add, subtract, and multiply matrices of

appropriate dimensions

2

2

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quantities

matrix, square matrix,

commuatitive

operation, associate

and distributive

property

N-

VM.9

I ODE (+) Understand that, unlike multiplications of

numbers, matrix multiplication for square

matrices is not a commutative operation,

but still satisfies the associative and

distributive properties

2


quantities

zero matrix, identity


multiplicative inverse

N-

VM.10

I ODE (+) Understand that the zero and identity

matrices play a role in matrix addition and

multiplication similar to the role of 0 and 1

in the real numbers. The determinant of a

square matrix is nonzero if and only if the

matrix has a multiplicative inverse.

2


quantities

vector, matrix,

transformations

N-

VM.11

I ODE (+) Multiply a vector (regarded as a matrix

with one column) by matrix suitable

dimensions to produce another vector.

Work with matrices as transformations of

vectors.

3,4


quantities

transformations:

translation, rotation,

reflection, absolute

value

N-

VM.12

I ODE (+) Work with 2x2 matrices as

transformations of the plane, and interpret

the absolute value of the determinant in

terms of area.

2



quantity

A-

SSE.1

b





single entity

1,2,3,4

3

Algebra II

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quantity

A-

SSE.2



1,2,3,4


to solve problems.

expression, factor,

zeros of a function

A-

SSE.3

a







3


to solve problems.



maximum/minimum

A-

SSE.3

b








3


to solve problems.



A-

SSE.3

c







functions

4


to solve problems.


series

A-

SSE.4




problems.

3,4

4

Algebra II

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polynomials


AAPR

.1

I ODE Understand that polynomials form a





3





remainder thorem,

polynomial

A-

AAPR

.2





p(x).

3






AAPR

.3





3




problems

polynomial identities A-

AAPR

.4

I ODE Prove polynomial identities and use them

to describe numerical relationships. For

example, the polynomial identity (x^2 +

y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be

used to generate Pythagorean triples.

4




problems

binomial theorem A-

AAPR

.5


the expansion of (x + y)n in powers of x




Triangle.1

3

5

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AAPR

.6








algebra system.

3




AAPR

.7







expressions.

4





constant

A-

CED.1



Include equations




1





constant

A-

CED.2



quantities; graph


and scales

2





constant

A-

CED.3






2

6

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equation, formula,


constant

A-

CED.4



solving

equations.

1,2


Inequalities



reasoning.

Rational equations,

radical equations,

variable

A-

REI.2





4


Inequalities


one variable



coefficient

A-

REI.3

a




1,2


Inequalities


one variable


REI.3

b







from this form.

3


Inequalities


one variable


REI.4


variable.









3


Inequalities


REI.5

I ODE Prove that a system of two equations in




same solutions.

2

7

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Inequalities


REI.6




two variables.

2


Inequalities



A-

REI.9





2


Inequalities



graph, set of all


plane

A-

REI.1

0





line).

2


Inequalities



x-coordinate, y-


A-

REI.1

1












1,2


Inequalities




boundary, system

A-

REI.1

2








2

8

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domain, range, set,

function









2






terms of a context.

1








minimums;

symmetries; end

behavior; and

periodicity.






the relationship.

3






2







a graph.

1,2

9

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representations

linear, quadratic,

intercepts, maxima,

minima

F-

IF.7a

I,R ODE Graph functions expressed






and minima

1,2,3


representations


function, absolute

value

F-

IF.7b








functions

4


representations

polynomial, zeros,

factorizations

F-

IF.7c








end behavior

3


representations

rational, zeros,

asymptotes

F-

IF.7d









3

10

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representations

logarithmic,



midline, amplitutde

F-

IF.7e









amplitude.

3,4


representations




function

1,2,3,4


representations





1,2,3,4



function F-

BF.1







1,2,3,4



arithmetic and

geometric sequence

F-

BF.2





2,3


functions

inverse function F-

BF.4a





3,4

11

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functions

inverse, exponents,

logarithms

F-

BF.5





3



problems

linear functions,


functions

F-

LE.1a








3,4



problems

rate F-

LE.1b







3,4



problems


LE.1c







3,4

12

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problems



and geometric


F-

LE.2






table.)

1,2,3,4



problems


polynomial

F-

LE.3






1,2,3,4



problems

logarithm F-

LE.4





technology.

3,4



parameters F-

LE.5



4


Equations



parallel and

perpendicular lines

G-

GPE 5

R.

M






point).

1,2

13

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Quantiative Data




function, model S-

ID.6a




(a) Fit a function to the data; use functions





exponential models

4


Quantiative Data




residuals, function S-

ID.6b




(b) Informally assess the fit of a function

by plotting and analyzing residuals

4


Quantiative Data




linear function, scatter

plote

S-

ID.6c




(c) Fit a linear function for a scatter plot

that suggests a linear association

4


Quantiative Data

Interpret Linear Models slope, intercepts S-ID.7 I ODE Interpret the slope (rate of change) and



4


Quantiative Data

Interpret Linear Models scatter plot, linear fit S-ID.8 I ODE Compute (using technology) and interpret


4


Quantiative Data

Interpret Linear Models correlation, causation S-ID.9 I ODE Distinguish between correlation and

causation.

4

14

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Statistics and

Probability


of Probability



to interpret data



S-CP

1






“not”).

4

Statistics and

Probability


of Probability



to interpret data


2





to determine if they are independent.

4

Statistics and

Probability


of Probability



to interpret data


3

I ODE Understand the conditional probability of A







4

Statistics and

Probability


of Probability




events S-CP

7




4

Statistics and

Probability


of Probability




events S-CP

8

I ODE (+) Apply the general Multiplication Rule in

a uniform probability model, P(A and B) =

P(A)P(B|A) = P(B)P(A|B), and interpret the


4

15

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Statistics and

Probability


of Probability




permutations,

combinations

S-CP

9

I ODE (+)Use permutations and combinations to

compute probabilities of compound events

and solve problems.

4

16

Accelerated Algebra II

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rational exponents

rational, exponent,

radical, integer

N-

RN.1






exponents

3


rational exponents

rational, exponent,

radical, integer

N-

RN.2




3


irrational numbers



integer

N-

RN.3







1,2


to solve problems






and data displays

1,2


solve problems



1,2


solve problems

quantities,

measurement



quantities

1,2,3,4


complex numbers


number

N-

CN.1




2

1


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complex numbers


number, properties:

communative,


N-

CN.2




complex numbers.

2,3


complex numbers


number, conjugate

N-

CN.3

I ODE (+) Find the conjugate of a complex number;



2



quadratic, complex


N-

CN.7



2




complex numbers

N-

CN.8

I ODE (+) Extend polynomial identities to the


x^2 + 4 as (x +2i)(x - 2i)

2



polynomials,

quadratics

N-

CN.9

I ODE (+) Know the Fundamental Theorem of


polynomials

2


quantities

matrix, data N-

VM.6

R ODE (+) Use matrices to represent and manipulate

data, e.g., to represent payoffs or

incidence relationships in a network.

2


quantities


VM.7

R ODE (+) Multiply matrices by scalars to produce



2


quantities


VM.8

I ODE (+) Add, subtract, and multiply matrices of


2

2


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quantities


commuatitive


and distributive

property

N-

VM.9

I ODE (+) Understand that, unlike multiplications of





2


quantities




N-

VM.10

I ODE (+) Understand that the zero and identity






2


quantities

vector, matrix,

transformations

N-

VM.11





vectors.

2


quantities

transformations:



value

N-

VM.12

I ODE (+) Work with 2x2 matrices as



terms of area.

2



quantity

A-

SSE.1

b

I ODE Interpret expressions that represent a




single entity

1,2,3,4

3


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quantity

A-

SSE.2



1,2,3,4


to solve problems.

expression, factor,

zeros of a function

A-

SSE.3

a







2,3,4


to solve problems.



maximum/minimum

A-

SSE.3

b








2


to solve problems.



A-

SSE.3

c







functions

3


to solve problems.


series

A-

SSE.4




problems.

4

4


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polynomials


AAPR

.1

R ODE Understand that polynomials form a





2,3





remainder thorem,

polynomial

A-

AAPR

.2





p(x).

2






AAPR

.3





2




problems


AAPR

.4

I ODE Prove polynomial identities and use them


example, the polynomial identity (x^2 +

y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be

used to generate Pythagorean triples.

2,3




problems

binomial theorem A-

AAPR

.5






Triangle.1

2,3

5


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AAPR

.6








algebra system.

3




AAPR

.7







expressions.

2,3





constant

A-

CED.1



Include equations




1,2,3,4





constant

A-

CED.2



quantities; graph


and scales

1,2,3,4





constant

A-

CED.3

I ODE Represent constraints by equations or





1

6


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equation, formula,


constant

A-

CED.4



solving

equations.

1,2,3,4


Inequalities



reasoning.

Rational equations,

radical equations,

variable

A-

REI.2





3


Inequalities


one variable



coefficient

A-

REI.3

a




1,2


Inequalities


one variable


REI.3

b

R ODE Solve quadratic equations in one






from this form.

2


Inequalities


one variable


REI.4


variable.









3


Inequalities


REI.5

R ODE Prove that a system of two equations in




same solutions.

2

7


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Inequalities


REI.6

R ODE Solve systems of linear equations exactly



two variables.

2


Inequalities

Solve systems of equations System, variable,

matrix, linear equation

A-

REI.8

I ODE (+) Represestn a system of linear equations

as a single matrix eqation in a vector

variable.

1,2


Inequalities



A-

REI.9





2


Inequalities



graph, set of all


plane

A-

REI.1

0

R ODE Understand that the graph of an equation




line).

1


Inequalities



x-coordinate, y-


A-

REI.1

1












1


Inequalities




boundary, system

A-

REI.1

2








1

8


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domain, range, set,

function









3






terms of a context.

3








minimums;

symmetries; end

behavior; and

periodicity.






the relationship.

3



domain, quantiative F-IF.5 I ODE Relate the domain of a function to its



3



rate of change F-IF.6 R ODE Calculate and interpret the average rate of




a graph.

2,3

9


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representations

linear, quadratic,

intercepts, maxima,

minima

F-

IF.7a







and minima

2,3


representations


function, absolute

value

F-

IF.7b





cases. (b) Graph square root, cube root,



functions

2


representations

polynomial, zeros,

factorizations

F-

IF.7c








end behavior

2


representations

rational, zeros,

asymptotes

F-

IF.7d









2,3,4

10


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representations

logarithmic,



midline, amplitutde

F-

IF.7e









amplitude.

3,4


representations

functions, equivalent F-IF.8 I ODE Write a function defined by an expression



function

2


representations

functions, equivalent F-IF.9 I ODE Compre properties of two functions each




2



function F-

BF.1







2



arithmetic and

geometric sequence

F-

BF.2





4


functions

f-bf.5: I ODE Understand that inverse relationship



involving logarithms and exponents.

3

11


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functions

inverse function F-

BF.4a





2,3,4


functions

inverse, exponents,

logarithms

F-

BF.5





3



problems

linear functions,


functions

F-

LE.1a








3



problems

rate F-

LE.1b







3

12


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problems


LE.1c







3



problems



and geometric


F-

LE.2






table.)

3,4



problems


polynomial

F-

LE.3






3,4



problems

logarithm F-

LE.4





technology.

3



parameters F-

LE.5



3

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Equations



parallel and

perpendicular lines

G-

GPE 5

R.

M






point).

1,2

Statistics and

Probability


Quantitative Data





box plots

S-ID 1 I ODE Represent data with plots on the real


box plots).

4

Statistics and

Probability


Quantitative Data




mean, median,

interquartile range,

standard deviation

S-ID 2 I ODE Use statistics appropriate to the shape of





4

Statistics and

Probability


Quantitative Data




outliers S-ID 3 I ODE Interpret differences in shape, center, and

spread in the context of the data sets,

accounting for possible effects of extreme

data points (outliers).

4

Statistics and

Probability


Quantitative Data




population percentages S-ID 4 I ODE Use the mean and standard deviation of a

data set to fit it to a normal distribution

and to estimate population percentages.

Recognize that there are data sets for

which such a procedure is not

appropriate. Use calculators,

spreadsheets, and tables to estimate

areas under the normal curve.

4

14


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Statistics and

Probability


Quantitative Data



quantitative variables

frequency tables S-ID 5 I ODE Summarize categorical data for two

categories in two-way frequency tables.

Interpret relative frequencies in the

context of the data (including joint,

marginal, and conditional relative

frequencies). Recognize possible

associations and trends in the data.

4

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6a









exponential models.

1

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6b




b. Informally assess the fit of a function by

plotting and analyzing residuals.

1

15


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Statistics and

Probability


Quantitative Data




scatter plot S-ID

6c






1

Statistics and

Probability


Quantitative Data

Interpret Linear Models slope, intercept S-ID 7 I ODE Interpret the slope (rate of change) and



1

Statistics and

Probability


Quantitative Data

Interpret Linear Models correclation coefficient S-ID 8 I ODE Compute (using technology) and interpret


1

Statistics and

Probability


Quantitative Data

Interpret Linear Models correlation and

causation

S-ID 9 I ODE Distinguish between correlation and

causation.

4

Statistics and

Probability


Conclusions

Understand and evaluate random

processes underlying statistical

experiments

population parameters,

random sample

S-IC 1 I ODE Understand statistics as a process for

making inferences about population

parameters based on a random sample

from that population.

4

Statistics and

Probability


Conclusions



experiments

simulation S-IC 2 R ODE Decide if a specified model is consistent

with results from a given data-generating

process, e.g., using simulation. For

example, a model says a spinning coin

falls heads up with probability 0.5. Would

a result of 5 tails in a row cause you to

question the model?

4

16


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Statistics and

Probability


Conclusions

Make inferences and justify

conclusions from sample surveys,

experiments, and observational

studies

sample survey,

experiments,

observational studies,

randomization

S-IC 3 I ODE Recognize the purposes of and

differences among sample surveys,

experiments, and observational studies;

explain how randomization relates to

each.

4

Statistics and

Probability


Conclusions



experiments


random sample





4

Statistics and

Probability


Conclusions



experiments







question the model?

4

Statistics and

Probability


Conclusions




studies

sample survey,

experiments,


randomization





each.

4

Statistics and

Probability

Conditional Probability and the Rules

of Probability


conditional probabilty and use them to

interpret data

conditional probability,

independence

S-CP

5

I ODE Recognize and explain the concepts of

conditional probability and independence

in everyday language and everyday

situations.

4

Statistics and

Probability


of Probability





outcomes

S-CP

6

I ODE Find the conditional probability of A given

B as the fraction of B’s outcomes that also

belong to A, and interpret the answer in

terms of the model.

4

17


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Statistics and

Probability


of Probability




addition rule S-CP

7




4

Statistics and

Probability


of Probability




multiplication rule S-CP

8

I ODE (+) Apply the general Multiplication Rule in a

uniform probability model, P(A and B) =



4

Statistics and

Probability


of Probability




permutations and

combinations

S-CP

9

I ODE (+) Use permutations and combinations to


and solve problems.

4

Statistics and

Probability


of decisions

decisions S-MD

6

I ODE (+) Use probabilities to make fair decisions


number generator).

4

18

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to solve problems

units, scale, origin N-Q 1 R,

M

ODE Use units as a way to understand





and data displays

1,2,3,4


quantities



N-VM

3

I, R ODE (+) Recommended to move to the next cluster 1,2,3,4


numbers or relationshps

graph, coordinate

axes, labels, scales

A-

CED 2





1,2,3


numbers or relationshps

interest A-

CED 4

R ODE Rearrange formulas to highlight a


reasoning as in solving equations.

1,2,3

Functions Intepreting Functions Build a functions that models a


intercepts, max, min,

linear, quadratic

F-IF

7a

M ODE Graph functions expressed




cases.

(a) Graph linear and quadratic functions


minima.

1,2,3


representations

functions, equivalent F-IF.9 M ODE Compre properties of two functions each




1,2,3

1

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problems

linear functions,


functions

F-

LE.1a

M ODE Distinguish between situations that







1,2,3



problems

rate F-

LE.1b

R ODE Distinguish between situations that






1,2,3



problems


LE.1c







1,2,3



problems



and geometric


F-

LE.2

R ODE Construct linear and exponential





table.)

1,2,3

2

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problems


polynomial

F-

LE.3

R ODE Observe using graphs and tables that a





1,2,3

Statistics and

Probability


Quantitative Data




mean, median,


standard deviation

S-ID 2 R ODE Use statistics appropriate to the shape of





3,4

Statistics and

Probability


Quantitative Data





box plots

S-ID 1 R ODE Represent data with plots on the real


box plots).

3,4

Statistics and

Probability


Quantitative Data




outliers S-ID 3 R ODE Interpret differences in shape, center, and




3,4

Statistics and

Probability


Quantitative Data












3,4

3

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Statistics and

Probability


Quantitative Data











3,4

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6a

R ODE Represent data on two quantitative








exponential models.

3,4

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6b






3,4

4

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Statistics and

Probability


Quantitative Data




scatter plot S-ID

6c






3,4

Statistics and

Probability


Quantitative Data

Interpret Linear Models slope, intercept S-ID 7 R ODE Interpret the slope (rate of change) and



3,4

Statistics and

Probability


Quantitative Data

Interpret Linear Models correclation coefficient S-ID 8 R ODE Compute (using technology) and interpret


3,4

Statistics and

Probability


Quantitative Data


causation


causation.

3,4

Statistics and

Probability


Conclusions



experiments


random sample





3,4

Statistics and

Probability


Conclusions



experiments







question the model?

3,4

5

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Statistics and

Probability


Conclusions




studies

sample survey,

experiments,


randomization





each.

3,4

Statistics and

Probability


Conclusions




studies

survey, mean,

proportion, margin of

error

S-IC 4 I ODE Use data from a sample survey to

estimate a population mean or proportion;

develop a margin of error through the use

of simulation models for random

sampling.

3,4

Statistics and

Probability


Conclusions




studies

parameters S-IC 5 I ODE Use data from a randomized experiment

to compare two treatments; use

simulations to decide if differences

between parameters are significant.

3,4

Statistics and

Probability


Conclusions




studies

data S-IC 6 I ODE Evaluate reports based on data. 3,4

Statistics and

Probability


of Probability



interpret data

subsets, sample

space, outcome, union,

intersection,

complements

S-CP

1






“not”).

3,4

Statistics and

Probability


of Probability



interpret data

independent S-CP

2





to determine if they are independent

3,4

6

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Statistics and

Probability


of Probability



interpret data

conditional probability S-CP

3

R ODE Understand the conditional probability of A







3,4

Statistics and

Probability


of Probability



interpret data

frequency tables,

conditional probability

S-CP

4

I ODE Construct and interpret two-way

frequency tables of data when two

categories are associated with each

object being classified. Use the two-way

table as a sample space to decide if

events are independent and to

approximate conditional probabilities.

3,4

Statistics and

Probability


of Probability



interpret data


independence

S-CP

5




situations.

3,4

Statistics and

Probability


of Probability





outcomes

S-CP

6




terms of the model.

3,4

Statistics and

Probability


of Probability




addition rule S-CP

7




3,4

7

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Statistics and

Probability


of Probability





8





3,4

Statistics and

Probability


of Probability




permutations and

combinations

S-CP

9

R ODE (+) Use permutations and combinations to


and solve problems.

3,4

Statistics and

Probability

Using Probability to Make Decisions Calculate expected values and use


random variable, data

distributions

S-MD

1

I ODE (+) Define a random variable for a quantity of

interest by assigning a numerical value to

each event in a sample space; graph the

corresponding probability distribution

using the same graphical displays as for

data distributions.

3,4

Statistics and

Probability



expected value S-MD

2

I ODE (+) Calculate the expected value of a random

variable; interpret it as the mean of the

probability distribution.

3,4

Statistics and

Probability



probability distribution S-MD

3

I ODE (+) Develop a probability distribution for a

random variable defined for a sample

space in which theoretical probabilities

can be calculated; find the expected value

3,4

Statistics and

Probability




4



space in which probabilities are assigned

empirically; find the expected value.

3,4

8

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Statistics and

Probability


of decisions

payoff values,

expected values

S-MD

5a

I ODE (+) Weigh the possible outcomes of a

decision by assigning probabilities to

payoff values and finding expected

values.

a. Find the expected payoff for a game of

chance. For example, find the expected

winnings from a state lottery ticket or a

game at a fast-food restaurant.

3,4

Statistics and

Probability


of decisions

payoff values,

expected values

S-MD

5b




values.

b. Evaluate and compare strategies on the

basis of expected values. For example,

compare a high-deductible versus a low-

deductible automobile insurance policy

using various, but reasonable, chances of

having a minor or a major accident.

3,4

Statistics and

Probability


of decisions

decisions S-MD

6



number generator).

3,4

Statistics and

Probability


of decisions

probability concepts S-MD

7

I ODE (+) Analyze decisions and strategies using

probability concepts (e.g., product testing,

medical testing, pulling a hockey goalie at

the end of a game).

3,4

9

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The Real Number System Extend the properties of exponents to

rational exponents

rational, exponent,

radical, integer

N-

RN.2

R ODE Rewrite expressions involving radicals



1

The Complex Number System Perform arithmetic operations with

complex numbers


number

N-

CN.1

R ODE Know there is a complex number i such

as i^2 = -1, and every complex number

has the form a +bi with a and b real.

3


complex numbers


number, properties:

communative,

associative,

distributive

N-

CN.2

R ODE Use the relation i^2 = -1 and the



complex numbers.

3


complex numbers


number, conjugate

N-

CN.3

R ODE (+) Find the conjugate of a complex number;



3


complex numbers

complex numbers,

complex plane,

rectangular form, polar

form

R ODE (+) Represent complex numbers on the

complex plane in rectangular and polar

form (including real and imaginary

numbers), and explain why the

rectangular and polar forms of a given

complex number represent the same

number.

3,4

The Complex Number System Use complex numbers in polynomial


quadratic, complex


N-

CN.7

R ODE Solve quadratic equations with real


3

1

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complex numbers

N-

CN.8

R ODE (+) Extend polynomial identities to the


x^2 + 4 as (x +2i)(x - 2i)

3



polynomials,

quadratics

N-

CN.9

R ODE (+) Know the Fundamental Theorem of


polynomials

3

Vector and Matrix Quantities Represent and model with vector

quantities

vector, magnitude,

direction

N-VM

1






2


quantities



N-VM

2




point

2


quantities



N-VM

3

I ODE (+) Recommended to move to the next

cluster

2

Vector and Matrix Quantities Perform operations on Vectors vector, magnitude,

direction

N-VM

4a


(a)Add vectors end-to-end, component-

wise, and by the parallelogram rule.

Understand that the magnitude of a sum

of two vectors is typically not the sum of

the magnitudes

1,2

Vector and Matrix Quantities Perform operations on Vectors vector, magnitude,

direction

N-VM

4b


(b) Given two vectors in magnitude and

direction form, determine the magnitude

and direction of their sum

1,2

2

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Vector and Matrix Quantities Perform operations on Vectors vector N-VM

4c


(c) Understand vector subtraction v – w

as v + (–w), where –w is the additive

inverse of w, with the same magnitude as

w and pointing in the opposite direction.




component-wise.

2

Vector and Matrix Quantities Perform operations on Vectors scalar multiplication V-VM

5a


(a) Represent scalar multiplication

graphically by scaling vectors and

possibly reversing their direction; perform

scalar multiplication component-wise

2

Vector and Matrix Quantities Perform operations on Vectors scalar multiplication V-VM

5b


(b) Compute the magnitude of a scalar

multiple cv using ||cv|| = |c|v. Compute

the direction of cv knowing that when |c|v

≠ 0, the direction of cv is either along v

(for c > 0) or against v (for c < 0).

2


quantities


VM.7




3,4

3

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quantities


VM.8

R ODE (+) Add, subtract, and multiply matrices of


3,4


quantities


commuatitive


and distributive

property

N-

VM.9

R ODE (+) Understand that, unlike multiplications of





3,4


quantities




N-

VM.10

R ODE (+) Understand that the zero and identity






3,4


quantities

vector, matrix,

transformations

N-

VM.11





vectors.

3,4


quantities

transformations:



value

N-

VM.12

R ODE (+) Work with 2x2 matrices as

transformations of the plane, and

interpret the absolute value of the

determinant in terms of area.

3,4

Seeing Structure in Expressions Interpret the structure of expressions expression, terms,


quantity

A-

SSE.1

b

R ODE Interpret expressions that represent a




single entity

3

4

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Seeing Structure in Expressions Interpret the structure of expressions expression, terms,


quantity

A-

SSE.2

R ODE Use the structure of an expression to


3

Seeing Structure in Expressions Write expressions in equivalent forms

to solve problems.

expression, factor,

zeros of a function

A-

SSE.3

a

R ODE Choose and produce an equivalent






2


to solve problems.



maximum/minimum

A-

SSE.3

b








2


to solve problems.



A-

SSE.3

c







functions

2


to solve problems.


series

A-

SSE.4

R ODE Derive the formula for the sum of a finite



problems.

4

5

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Arithmetic with Polynomials and



polynomials


AAPR

.1


system analogous to the integers,

namely, they are closed under the

operations of addition, subtraction, and

multiplication; add, subtract, and multiply

polynomials

2





remainder thorem,

polynomial

A-

AAPR

.2

R ODE Know and apply the Remainder Theorem:

For a polynomial p(x) and a number a,

the remainder on division by x – a is p(a),

so p(a) = 0 if and only if (x – a) is a factor

of p(x).

2






AAPR

.3

R ODE Identify zeros of polynomials when




2




problems


AAPR

.4

R ODE Prove polynomial identities and use them


example, the polynomial identity (x2 +

y2)2 = (x2 – y2)2 + (2xy)2 can be used to

generate Pythagorean triples.

1




problems

binomial theorem A-

AAPR

.5

R ODE (+) Know and apply the Binomial Theorem

for the expansion of (x + y)n in powers of

x and y for a positive integer n, where x

and y are any numbers, with coefficients


Triangle.1

4

6

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AAPR

.6

R ODE Rewrite simple rational expressions in



r(x) are polynomials with the degree of

r(x) less than the degree of b(x), using



algebra system.

2




AAPR

.7

R ODE Understand that rational expressions

form a system analogous to the rational





expressions.

1

Creating Equations Create equations that describe




constant

A-

CED.1



Include equations




1





constant

A-

CED.2



quantities; graph


and scales

1,3





constant

A-

CED.3






1,3

7

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equation, formula,


constant

A-

CED.4

R ODE Rearrange formulas to highlight a


reasoning as in solving

equations.

2

Reasoning with Equations and

Inequalities



reasoning.

Rational equations,

radical equations,

variable

A-

REI.2

R ODE Solve simple rational and radical




2


Inequalities


one variable



coefficient

A-

REI.3

a




1


Inequalities


one variable


REI.3

b




quadratic equation in x into an equation

of the form (x – p)^2 = q that has the

same solutions. Derive the quadratic

formula from this form.

2


Inequalities


one variable


REI.4


variable.









2

8

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Inequalities


REI.5





same solutions.

3


Inequalities


REI.6




two variables.

1,3


Inequalities

Solve systems of equations system, quadratic

equation

A-

REI.7

I ODE Solve a simple system consisting of a

linear equation and a quadratic equation

in two variables algebraically and

graphically. For example, find the points

of intersection between the line y = –3x

and the circle x2 + y2 = 3

3


Inequalities

Solve systems of equations system, matrix, linear

equation

A-

REI.8

R ODE (+) Represent a system of linear equations

as a single matrix equation in a vector

variable

3


Inequalities


system, linear

equation

A-

REI.9

R ODE (+) Find the inverse of a matrix if it exists and

use it to solve systems of linear

equations (using technology for matrices

of dimension 3x3 or greater)

3


Inequalities



graph, set of all


plane

A-

REI.1

0





line).

1

9

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Inequalities



x-coordinate, y-


A-

REI.1

1


points where the graphs of the equations

y = f(x) and y = g(x) intersect are the






and/or g(x) are linear, polynomial,

rational, absolute value, exponential, and


1


Inequalities



graph, linear

inequality, boundary,

system

A-

REI.1

2


in two variables as a half-plane

(excluding the boundary in the case of a

strict inequality), and graph the solution

set to a system of linear inequalities in

two variables as the intersection of the


3

Interpreting Functions Understand the concept of a function


domain, range, set,

function







corresponding to the input x. The graph

of f is the graph of the equation y = f(x).

1

Interpreting Functions Understand the concept of a function





terms of a context.

1

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Interpreting Functions Interpret functions that arise in




increasing,

decreasing, positive,

or negative; relative

maximums and

minimums;

symmetries; end

behavior; and

periodicity.

F-IF.4 R ODE For a function that models a relationship



the quantities, and sketch graphs

showing key features given a verbal

description of the relationship.

2






1



rate of change F-IF.6 I ODE Calculate and interpret the average rate

of change of a function (presented



change from a graph.

1

Interpreting Functions Analyze functions using different

representations

linear, quadratic,

intercepts, maxima,

minima

F-

IF.7a

R ODE Graph functions expressed




complicated cases. (a) Graph linear and

quadratic functions and show intercepts,

maxima, and minima

2

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representations


function, absolute

value

F-

IF.7b





complicated cases. b. Graph square

root, cube root, and piecewise-defined

functions, including step functions and

absolute value functions

2


representations

polynomial, zeros,

factorizations

F-

IF.7c





complicated cases. (c) Graph

polynomial functions, identifying zeros

when suitable factorizations are available,

and showing end behavior

2


representations

rational, zeros,

asymptotes

F-

IF.7d

R ODE (+) Graph functions expressed




complicated cases. (d) Graph rational

functions, identifying zeros and

asymptotes when suitable factorizations

are available, and showing end behavior.

2

12

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representations

logarithmic,

exponential,

intercepts, end

behavior, period,

midline, amplitutde

F-

IF.7e





complicated cases. (e) Graph

exponential and logarithmic functions,

showing intercepts and end behavior, and

trigonometric functions, showing period,

midline, and amplitude.

1,2


representations




function

1,2,3,4


representations





1,2,3,4

Building Functions Analyze functions using different

representations

functions, equivalent F-

BF.1

R ODE Write a function that describes a






2

Building Functions Building new functions from existing

functions

inverse function F-

BF.4a

R ODE Find inverse functions.




1

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Building Functions Building new functions from existing

functions

inverse, exponents,

logarithms

F-

BF.5

R ODE (+) Understand the inverse relationship




2

Linear and Exponential Models Construct and compare linear and


problems

linear functions,


functions

F-

LE.1a








2



problems

rate F-

LE.1b







2



problems


LE.1c




c. Recognize situations in which a

quantity grows or decays by a constant

percent rate per unit interval relative to

another.

2

14

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problems



and geometric

sequence, input,

output

F-

LE.2






table.)

2,4



problems


polynomial

F-

LE.3






2



problems

logarithm F-

LE.4

R ODE For exponential models, express as a

logarithm the solution to abct = d where

a, c, and d are numbers and the base b is

2, 10, or e; evaluate the logarithm using

technology.

2

Trigonometric Functions Extend the domain of trigonometrtic

functions using the unit circle

radian, arc length F-

TF.1

I ODE Understand radian measure of an angle

as the length of the arc on the unit circle

subtended by the angle.

1



unit circle, trigoometric

functions, traversed

F-

TF.2

I ODE Explain how the unit circle in the

coordinate plane enables the extension of

trigonometric functions to all real

numbers, interpreted as radian measures

of angles traversed counterclockwise

around the unit circle.

1

15

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special right triangles,

trionometric functions

F-

TF.3

I ODE (+) Use special triangles to determine

geometrically the values of sine, cosine,

tangent for π/3, π/4 and π/6, and use the

unit circle to express the values of sine,

cosines, and tangent for x, π + x, and 2π

– x in terms of their values for x, where x

is any real number.

1



unit circle, odd and

even symmetry

F-

TF.4

I ODE (+) Use the unit circle to explain symmetry

(odd and even) and periodicity of

trigonometric functions.

1,2

Trigonometric Functions Model periodic phenomena with

trigonometric functions

trigonmetric functions F-

TF.5

I ODE Choose trigonometric functions to model

periodic phenomena with specified

amplitude, frequency, and midline.

1



trigonmetric functions,

domain

F-

TF.6

I ODE (+) Understand that restricting a

trigonometric function to a domain on

which it is always increasing or always

decreasing allows its inverse to be

constructed.

1



inverse functions,


F-

TF.7

I ODE (+) Use inverse functions to solve

trigonometric equations that arise in

modeling contexts; evaluate the solutions

using technology, and interpret them in


1

Trigonometric Functions Prove and apply trigonometric

identities

Pythagorean Theorem F-

TF.8

I ODE Prove the Pythagorean identity sin2(θ) +

cos2(θ) = 1 and use it to find sin(θ),

cos(θ), or tan(θ) given sin(θ), cos(θ), or

tan(θ) and the quadrant of the angle.

1

16

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Trigonometric Functions Prove and apply trigonometric

identities

trigonometric identities F-

TF.9

I ODE (+) Prove the addition and subtraction

formulas for sine, cosine, and tangent

and use them to solve problems.

1

Similarity, Right Triangles, and

Trigonometry




SRT 4

R ODE Prove theorems about triangles.






1,2


Trigonometry



congruence G-

SRT 5

R,

M

ODE Use congruence and similarity criteria for



1,2


Trigonometry




angles

G-

SRT 6

R,

M

ODE Understand that by similarity, side ratios

in right triangles are properties of the

angles in the triangle, leading to

definitions of trigonometric ratios for

acute angles.

1,2


Trigonometry



sine and cosine G-

SRT 7

R,

M

ODE Explain and use the relationship between


angles

1,2


Trigonometry




SRT 8

R,

M

ODE Use trigonometric ratios and the



1,2

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Trigonometry


triangles


SRT 9





1,2


Trigonometry


triangles


cosines

G-

SRT

10

I ODE (+) Prove the Laws of Sines and Cosines

and use them to solve problems.

1,2


Trigonometry


triangles


cosines

G-

SRT

11





resultant forces).

1,2

Circles Find arc lengths and areas of sectors

of circles

arc length, area of

sector

G-C 5 R ODE Derive using similarity the fact that the






1,2

Expressing Geometric Properties with

Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 1

R ODE Derive the equation of a circle of given




equation.

3,4


Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 2

I,R ODE Derive the equation of a parabola given a

focus and directrix

4

18

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Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 3

I ODE (+) Derive the equations of ellipses and

hyperbolas given the foci, using the fact

that the sum or difference of distances

from the foci is constant.

4


Equations



parallel and

perpendicular lines

G-

GPE 5




equation of a line parallel or

perpendicular to a given line that passes

through a given point).

3


Quantiative Data

Interpret Linear Models slope, intercepts S-ID.7 M ODE Interpret the slope (rate of change) and



3


Quantiative Data

Interpret Linear Models scatter plot, linear fit S-ID.8 M ODE Compute (using technology) and interpret


3

19

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rational exponents

rational, exponent,

radical, integer

N-

RN.2

R ODE Rewrite expressions involving radicals



1


complex numbers


number

N-

CN.1

R ODE Know there is a complex number i such as



2


complex numbers


number, properties:

communative,


N-

CN.2

R ODE Use the relation i^2 = -1 and the



complex numbers.

2


complex numbers


number, conjugate

N-

CN.3

R ODE (+) Find the conjugate of a complex number;



2


complex numbers

complex numbers,

complex plane,

rectangular form, polar

form

R ODE (+) Represent complex numbers on the

complex plane in rectangular and polar

form (including real and imaginary

numbers), and explain why the

rectangular and polar forms of a given

complex number represent the same

number.

2,3



quadratic, complex


N-

CN.7

R ODE Solve quadratic equations with real


2




complex numbers

N-

CN.8

R ODE (+) Extend polynomial identities to the


x^2 + 4 as (x +2i)(x - 2i)

2

1

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polynomials,

quadratics

N-

CN.9

R ODE (+) Know the Fundamental Theorem of


polynomials

2


quantities

vector, magnitude,

direction

N-VM

1






3


quantities



N-VM

2




point

3


quantities



N-VM

3

I ODE (+) Recommended to move to the next cluster 3

Number and Quantity Vector and Matrix Quantities Perform operations on Vectors vector, magnitude,

direction

N-VM

4a


(a)Add vectors end-to-end, component-

wise, and by the parallelogram rule.

Understand that the magnitude of a sum

of two vectors is typically not the sum of

the magnitudes

1,2

Number and Quantity Vector and Matrix Quantities Perform operations on Vectors vector, magnitude,

direction

N-VM

4b


(b) Given two vectors in magnitude and

direction form, determine the magnitude

and direction of their sum

1,2

2

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4c


(c) Understand vector subtraction v – w as

v + (–w), where –w is the additive inverse

of w, with the same magnitude as w and





component-wise.

3


5a


(a) Represent scalar multiplication

graphically by scaling vectors and possibly

reversing their direction; perform scalar


3


5b


(b) Compute the magnitude of a scalar

multiple cv using ||cv|| = |c|v. Compute the

direction of cv knowing that when |c|v ≠ 0,

the direction of cv is either along v (for c >

0) or against v (for c < 0).

3


quantities


VM.7




3


quantities


VM.8

R ODE (+) Add, subtract, and multiply matrices of


3

3

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quantities


commuatitive


and distributive

property

N-

VM.9

R ODE (+) Understand that, unlike multiplications of





3


quantities




N-

VM.10

R ODE (+) Understand that the zero and identity






3


quantities

vector, matrix,

transformations

N-

VM.11





vectors.

3


quantities

transformations:



value

N-

VM.12

R ODE (+) Work with 2x2 matrices as



terms of area.

3



quantity

A-

SSE.1

b

R ODE Interpret expressions that represent a




single entity

3



quantity

A-

SSE.2

R ODE Use the structure of an expression to


3

4

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to solve problems.

expression, factor,

zeros of a function

A-

SSE.3

a







2


to solve problems.



maximum/minimum

A-

SSE.3

b








2


to solve problems.



A-

SSE.3

c







functions

2


to solve problems.


series

A-

SSE.4

R ODE Derive the formula for the sum of a finite



problems.

4




polynomials


AAPR

.1






2

5

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remainder thorem,

polynomial

A-

AAPR

.2

R ODE Know and apply the Remainder Theorem:




p(x).

2






AAPR

.3

R ODE Identify zeros of polynomials when




2




problems


AAPR

.4

R ODE Prove polynomial identities and use them


example, the polynomial identity (x2 +

y2)2 = (x2 – y2)2 + (2xy)2 can be used to

generate Pythagorean triples.

1




problems

binomial theorem A-

AAPR

.5

R ODE (+) Know and apply the Binomial Theorem for





Triangle.1

4




AAPR

.6

R ODE Rewrite simple rational expressions in







algebra system.

2

6

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AAPR

.7

R ODE Understand that rational expressions form






expressions.

1





constant

A-

CED.1



Include equations




1





constant

A-

CED.2



quantities; graph


and scales

1,3





constant

A-

CED.3






1,3



equation, formula,


constant

A-

CED.4



solving

equations.

2


Inequalities



reasoning.

Rational equations,

radical equations,

variable

A-

REI.2

R ODE Solve simple rational and radical




2


Inequalities


one variable



coefficient

A-

REI.3

a




1

7

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Inequalities


one variable


REI.3

b







from this form.

2


Inequalities


one variable


REI.4


variable.









2


Inequalities


REI.5





same solutions.

3


Inequalities


REI.6




two variables.

1,3


Inequalities

Solve systems of equations system, quadratic

equation

A-

REI.7

I ODE Solve a simple system consisting of a

linear equation and a quadratic equation

in two variables algebraically and

graphically. For example, find the points of

intersection between the line y = –3x and

the circle x2 + y2 = 3

3

8

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Inequalities

Solve systems of equations system, matrix, linear

equation

A-

REI.8

R ODE (+) Represent a system of linear equations as

a single matrix equation in a vector

variable

3


Inequalities



A-

REI.9

R ODE (+) Find the inverse of a matrix if it exists and




3


Inequalities



graph, set of all


plane

A-

REI.1

0





line).

1


Inequalities



x-coordinate, y-


A-

REI.1

1












1


Inequalities




boundary, system

A-

REI.1

2








3

9

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domain, range, set,

function









1






terms of a context.

1








minimums;

symmetries; end

behavior; and

periodicity.

F-IF.4 R ODE For a function that models a relationship





the relationship.

2






1







a graph.

1

10

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representations

linear, quadratic,

intercepts, maxima,

minima

F-

IF.7a







and minima

2


representations


function, absolute

value

F-

IF.7b








functions

2


representations

polynomial, zeros,

factorizations

F-

IF.7c








end behavior

2


representations

rational, zeros,

asymptotes

F-

IF.7d

R ODE (+) Graph functions expressed








2

11

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representations

logarithmic,



midline, amplitutde

F-

IF.7e









amplitude.

1,2



function F-

BF.1

R ODE Write a function that describes a






2



arithmetic and

geometric sequence

F-

BF.2

R ODE Write arithmetic and geometric sequences




4


functions

inverse function F-

BF.4a

R ODE Find inverse functions.




1


functions

inverse, exponents,

logarithms

F-

BF.5

R ODE (+) Understand the inverse relationship




2

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problems

linear functions,


functions

F-

LE.1a








2



problems

rate F-

LE.1b







2



problems


LE.1c







2



problems



and geometric


F-

LE.2






table.)

2,4

13

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problems


polynomial

F-

LE.3






2



problems

logarithm F-

LE.4

R ODE For exponential models, express as a




technology.

2



parameters F-

LE.5

R ODE Interpert the parameters in a linear or


2

Functions Trigonometric Functions Extend the domain of trigonometrtic


radian, arc length F-

TF.1

I ODE Understand radian measure of an angle

as the length of the arc on the unit circle

subtended by the angle.

1



unit circle, trigoometric

functions, traversed

F-

TF.2

I ODE Explain how the unit circle in the

coordinate plane enables the extension of

trigonometric functions to all real

numbers, interpreted as radian measures

of angles traversed counterclockwise

around the unit circle.

1



special right triangles,

trionometric functions

F-

TF.3

I ODE (+) Use special triangles to determine

geometrically the values of sine, cosine,

tangent for π/3, π/4 and π/6, and use the

unit circle to express the values of sine,

cosines, and tangent for x, π + x, and 2π

– x in terms of their values for x, where x

is any real number.

1

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unit circle, odd and

even symmetry

F-

TF.4

I ODE (+) Use the unit circle to explain symmetry

(odd and even) and periodicity of

trigonometric functions.

1

Functions Trigonometric Functions Model periodic phenomena with


trigonmetric functions F-

TF.5

I ODE Choose trigonometric functions to model

periodic phenomena with specified

amplitude, frequency, and midline.

1



trigonmetric functions,

domain

F-

TF.6

I ODE (+) Understand that restricting a trigonometric

function to a domain on which it is always

increasing or always decreasing allows its

inverse to be constructed.

1



inverse functions,


F-

TF.7

I ODE (+) Use inverse functions to solve

trigonometric equations that arise in

modeling contexts; evaluate the solutions

using technology, and interpret them in


1

Functions Trigonometric Functions Prove and apply trigonometric

identities

Pythagorean Theorem F-

TF.8

I ODE Prove the Pythagorean identity sin2(θ) +

cos2(θ) = 1 and use it to find sin(θ),

cos(θ), or tan(θ) given sin(θ), cos(θ), or

tan(θ) and the quadrant of the angle.

1

Functions Trigonometric Functions Prove and apply trigonometric

identities

trigonometric identities F-

TF.9

I ODE (+) Prove the addition and subtraction

formulas for sine, cosine, and tangent and


1

15

Honors Pre-Calculus

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Trigonometry




SRT 4

R ODE Prove theorems about triangles.






1,2


Trigonometry



congruence G-

SRT 5

R,

M

ODE Use congruence and similarity criteria for



1,2


Trigonometry




angles

G-

SRT 6

R,

M

ODE Understand that by similarity, side ratios in




1,2


Trigonometry



sine and cosine G-

SRT 7

R,

M

ODE Explain and use the relationship between


angles

1,2


Trigonometry




SRT 8

R,

M

ODE Use trigonometric ratios and the



1,2


Trigonometry


triangles


SRT 9





1,2


Trigonometry


triangles


cosines

G-

SRT

10



1,2

16

Honors Pre-Calculus

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Trigonometry


triangles


cosines

G-

SRT

11





resultant forces).

1,2


of circles

arc length, area of

sector

G-C 5 R ODE Derive using similarity the fact that the






1,2


Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 1

R ODE Derive the equation of a circle of given




equation.

3,4


Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 2

I,R ODE Derive the equation of a parabola given a

focus and directrix

4


Equations



conic section

circle, radius,

Pythagorean Theorem

G-

GPE 3

I ODE (+) Derive the equations of ellipses and

hyperbolas given the foci, using the fact

that the sum or difference of distances

from the foci is constant.

4


Quantiative Data

Interpret Linear Models slope, intercepts S-ID.7 M ODE Interpret the slope (rate of change) and



3

17

Honors Pre-Calculus

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Quantiative Data

Interpret Linear Models scatter plot, linear fit S-ID.8 M ODE Compute (using technology) and interpret


3


Quantiative Data

Interpret Linear Models correlation, causation S-ID.9 R ODE Distinguish between correlation and

causation.

1,2,3,4

18

AP Calculus

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solve problems

units, scale, origing N-Q 1 R ODE Use units as a way to understand





and data display

1,2,3,4


quantities

velocity, quantities N-VM

3

I ODE Solve problems involving velocity and

other quantities that can be represented

by vectors

1,2,3,4



equations, variables,

axes, quantities

A-

CED 2




axes with labels and scale

1,2,3,4






1,2,3,4


representations


function, absolute

value

F-

IF.7b








functions

4

1

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representations

polynomial, zeros,

factorizations

F-

IF.7c








end behavior

3


representations

rational, zeros,

asymptotes

F-

IF.7d

M ODE (+) Graph functions expressed








3


representations

logarithmic,



midline, amplitutde

F-

IF.7e









amplitude.

1,2,3,4


representations

functions, equivalent F-IF 8 R ODE Write a function defined by an expression



function

1,2,3,4

2

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representations

functions, equivalent F-IF.9 M ODE Compre properties of two functions each




1,2,3,4



problems


polynomial

F-

LE.3

M ODE Observe using graphs and tables that a





1,2


Equations



parallel and

perpendicular lines

G-

GPE 5






point).

1,2,3,4


Dimension



cylinder, pyramids,

cones, spheres

G-

GMD

3

R,

M



problems

1,2


Dimension



cross sections G-

GMD

4

M ODE Identify the shapes of two-dimensional





3,4

*Additionally: AP Calculus will follow all standards set forth by the College Board for Calculus A/B. See AP Calculus Curriculum Word Document.

3

AP® Calculus AB - THS Page 1

AP®

Calculus AB Tippecanoe High School

Course Overview AP calculus AB is primarily concerned with developing understanding of the concepts of calculus and providing experience with methods and applications. The course has a multirepresentational approach that includes four types of expression: graphical, numerical, analytical, and verbal. Students are encouraged to use all representations with fluency between the four types. Importance is placed on verbal explanations since that reflects a true understanding of concepts. Students are required to use widely-accepted mathematical vocabulary and notation in their explanations. Conceptual themes, rather than memorization of formulas, are emphasized throughout the course. The course is approached as a coherent body of knowledge unified by the overlapping themes of limits, derivatives, and definite and indefinite integrals. Common themes reappear throughout the year. Modeling and application are also emphasized. Technology, specifically a graphing calculator, is used regularly and appropriately, but does not take precedence over intuitive understanding of concepts. AP Calculus AB is taught as a college-level course. Students should be attempting to earn college credit or advanced placement in calculus through the AP exam, a college placement exam, or any other method employed by the college.

Goals Upon completion of this course, students should be able to:

Work with functions represented in a variety of ways: graphically, numerically, analytically, and verbally. They should understand the connections among these types of representations.

Understand the meaning of the derivative in terms of a rate of change and local linear approximation. They should be able to use derivatives to solve a variety of problems.

Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change. They should be able to use integrals to solve a variety of problems.

Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

Communicate mathematics and explain solutions to problems both verbally and in written sentences.

Model a written description of a physical situation with a function, a differential equation, or an integral.


Use technology to help solve problems, experiment, interpret results, and support conclusions.

Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

Develop an appreciation of calculus as a coherent body of knowledge and as a great human accomplishment.

Materials Textbook (provided): A Single Variable Calculus Early Transcendental textbook will be provided. Calculator (required; as needed, a limited number of calculators will be available for students for short-term or long-term loan): Texas Instruments graphing calculator (TI-83+ or higher)


AP®

Calculus AB Course Outline Topics labeled as “optional” may or may not be covered.

Functions and Models

The following topics are pre-requisites for incoming students. The schedule does not allow time for these topics to be taught in this course.

Topic Description

1. Four Ways to Represent a Function - Verbal, numeric, graphic, and symbolic representation of functions discussed - Domain and range of a function - Calculator approximations of values and functions - Piecewise functions - Using calculus to predict and to explain local and global behavior of a function

2. Mathematical Models: A Catalog of Essential Functions

- The modeling process: developing, analyzing, and interpreting a mathematical model - Classes of functions: linear, quadratic, rational, algebraic, trigonometric, exponential, and transcendental - Characteristics of each class of function

3. New Functions from Old Functions - Transformations on functions - The arithmetic of functions - Composing functions

4. Graphing Calculators - Finding roots with graphing calculators - Using graphing calculators to describe the behavior of functions - Appropriate viewing windows - Misleading or wrong answers given by graphing calculators

5. Exponential Functions - Algebraic and geometric properties of exponential functions - Translation and reflection of exponential functions - Exponential functions as models of growth and decay

6. Inverse Functions and Logarithms - Verbal, numeric, graphic, and algebraic representations of inverse functions - Algebraic and geometric properties of logarithmic functions

- The property of (-1(x)) = x


Limits and Derivatives 4 weeks

Topic Description

1. The Tangent and Velocity Problems -Average vs instantaneous velocity described numerically, graphically, and in physical terms -The tangent line as the limit of secant lines -Using the graphing calculator to zoom in on a smooth function to show local linearity -Approximating the slope of the tangent line with slopes of secant lines

2. The Limit of a Function -An intuitive understanding of the limiting process -Estimating limits from graphs or tables of data -The advantages and disadvantages of geometrically or numerically computing a limit with a graphing calculator -Optional: the delta-epsilon definition of limit

3. Calculating Limits Using the Limit Laws -Calculating limits using algebraic methods -Examples where limits do not exist

4. Continuity -An intuitive understanding of continuity -Continuity defined in terms of limits -Intermediate Value Theorem -Examples of discontinuity: removable, jump, infinite, oscillating

5. Limits Involving Infinity -Understanding asymptotes in terms of graphical behavior -Describing asymptotic behavior in terms of limits involving infinity -Comparing relative magnitudes of functions and their rates of change (relative growth of polynomials, exponential functions, and logarithmic functions)

6. Tangents, Velocities, and Other Rates of Change

-Tangent line to a curve at a point -Instantaneous rate of change as the limit of average rate of change -Approximate rates of change from graphs and tables of values

7. Derivatives -The derivative represented geometrically, numerically, and algebraically -The derivative interpreted as an instantaneous rate of change


-Derivative defined as the limit of the difference quotient -Equations involving derivatives: verbal descriptions are translated into equations involving derivatives, and vice versa

8. The Derivative as a Function -Relationship between differentiability and continuity -Slope of a curve at a point -The concept of a differentiable function, treated graphically, algebraically, and verbally,

including obtaining ’ by first considering the derivative at x, and then treating x as a variable

-Sketching the derivative of from the graph

of

9. What Does ’ Say About ? -Corresponding characteristics of the graphs of

and ’ -Relationship between increasing and

decreasing behavior of and the sign of ’ -Corresponding characteristics of the graphs of

, ’, and ’’

-Relationship between the concavity of and

the sign of ’’ -Instantaneous rate of change as the limit of average rate of change

Differentiation Rules 5 weeks

Topic Description

1. Derivatives of Polynomials -Power Rule for positive integer powers of x -Sum and Difference Rule

2. The Product and Quotient Rules -Product Rule -Quotient Rule

3. Rates of Change in the Natural and Social Sciences

-Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration -Equations involving derivatives: verbal descriptions are translated into equations involving derivatives, and vice versa

4. Derivatives of Trigonometric Functions -Derivatives of trigonometric functions

5. The Chain Rule -Chain rule

6. Implicit Differentiation -Implicit functions and implicit curves


-Implicit differentiation -Implicit differentiation to find the derivative of an inverse function -Derivatives of inverse trigonometric functions

7. Derivatives of Exponential and Logarithmic Functions

-The definition of e

-Derivatives of exponential and logarithmic functions -Logarithmic differentiation

8. Linear Approximations and Differentials

-Tangent line to a curve and local linear approximation

Optional: Taylor Polynomials -Taylor and Maclaurin polynomials

Applications of Differentiation 4 weeks

Topic Description

1. Related Rates -Modeling rates of change with related rate problems -Solution strategy for related rate problems

2. Maximum and Minimum Values of a Function

-Extreme Value Theorem: the graphical interpretation -Fermat’s Theorem -Critical values -Finding extreme values of a function on open and closed intervals

3. Derivatives and the Shapes of Curves -Corresponding characteristics of the graphs of

and ’ -Relationship between increasing and

decreasing behavior of and the sign of ’ -Mean Value Theorem and its geometric consequences -Corresponding characteristics of the graphs of

, ’, and ’’

-Relationship between the concavity of and

the sign of ’’ -Points of inflection -Analysis of curves, including the notions of monotonicity and concavity

4. Optimization Problems -Optimization, both absolute and relative extrema -Solution strategy for optimization problems -Checking results graphically with a graphing calculator


5. Applications to Business and Economics

-Concepts from economics: marginals, demand function, revenue function, average cost -The marginal as a derivative

6. Antiderivatives -Antiderivatives from derivatives of basic functions -Slope or direction fields -Initial value and boundary value problems -Position, velocity, and acceleration

Integrals 5 weeks

Topic Description

1. Areas and Distances -The area problem: the difficulty in finding area under a curve -Computation of Riemann sums using left, right, and midpoint evaluation points -Riemann sums used to model physical, social, and economic situations

2. The Definite Integral -Computation of Riemann sums using left, right, and midpoint evaluation points -The definite integral as a limit of Riemann sums over subintervals -The definite integral as the net results of accumulation of a rate of change -Basic properties of definite integrals -Use of Riemann sums to approximate definite integrals of functions represented algebraically, geometrically, and numerically -The geometric and comparison properties of definite integrals developed as statements about area

3. Evaluating Definite Integrals -The definite integral of the rate of change of a quantity over an interval interpreted as the net change of the quantity over the interval -Using the definite integral of a rate of change to give accumulated change: area of a region, distance traveled by a particle on a line -Antiderivatives of basic functions -The definite integral as the difference of the values of the antiderivative of the integrand at the limits of integration

4. The Fundamental Theorem of Calculus -The definite integral of the rate of change of


a quantity over an interval interpreted as the net change of the quantity over the interval -Use of the Fundamental Theorem to evaluate definite integrals -Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined -Indefinite integrals

5. The Substitution Rule -Substitution Rule interpreted in terms of the Chain Rule -Antiderivatives by substitution of variables -Using substitution to evaluate definite integrals

6. (optional) Integration by Parts -Integration by Parts interpreted in terms of the Product Rule -Choosing u and dv

7. Approximate Integration -Riemann sums using left, right, and midpoint evaluation points revisited -Trapezoidal Rule -Optional: Simpson’s Rule

Applications of Integration 3 weeks

Topic Description

1. More About Areas -Finding the area between curves with definite integrals -When it is advantageous to integrate with respect to y instead of with respect to x

2. Volumes -Finding the volume of a solid with known cross-sections -Finding the volume of a solid of revolution using washers

3. Average Value of a Function -Finding the average value of a function -Geometric interpretation of the Mean Value Theorem for Integrals

4. Applications to Physics and Engineering -Work -Hydrostatic pressure -Centers of mass

5. Applications to Economics and Biology -Blood flow -Cardiac output -Consumer surplus

Optional Topic: Probability -Probability density functions


-Algebraic and geometric definitions of a mean -The normal distribution

Differential Equations 4 weeks

Topic Description

1. Modeling with Differential Equations -Differential equations: verbal descriptions are translated into equations involving derivatives, and vice versa -General and particular solutions to differential equations -Initial value and boundary value problems

2. Slope fields -Interpreting slope or direction fields -Autonomous differential equations -Qualitative analysis of differential equations

3. Separable Equations -Solving separable differential equations and using them in modeling

4. Exponential Growth and Decay -The equation y’ = ky and exponential growth

5. The Logistic Equation -Logistic vs. unconstrained exponential growth -Interpreting the slope field of the logistic equation -The analytic solution of the logistic equation

Post-AP Exam 3 weeks (additional optional topics)

Topic Description

1. Partial Fractions -Using the method of partial fractions to evaluate integrals

2. Trigonometric Substitution -Using trigonometric substitution to evaluate integrals

3. Integrands with Powers of Sine and Cosine

-Integration of powers of the sine and cosine functions

4. Derivatives Project -Roller coaster development using continuity and differentiation for “smoothness”

5. Integration Project -Integrating acceleration curves from crash testing to develop appropriate velocity functions – focus on approximation techniques of integration (Riemann sums)

This schedule leaves a few weeks for flexibility if more time is required for students to better understand particular topics. It also allows time for cumulative review and to administer practice AP exams

AP Statistics

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Algebra Seeing the structure of expressions Write expressions in equivalent forms

to solve problems

geometric series A-

SSE 4

M ODE Derive the formula for the sum of a finite



problems

1,2,3,4

Statistics and

Probability


Quantitative Data





box plots

S-ID 1 M ODE Represent data with plots on the real


box plots).

1,2,3,4

Statistics and

Probability


Quantitative Data




mean, median,


standard deviation

S-ID 2 M ODE Use statistics appropriate to the shape of





1,2,3,4

Statistics and

Probability


Quantitative Data




outliers S-ID 3 M ODE Interpret differences in shape, center, and




1,2,3,4

Statistics and

Probability


Quantitative Data












1,2,3,4

1

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Statistics and

Probability


Quantitative Data











1,2,3,4

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6a









exponential models.

1,2,3,4

Statistics and

Probability


Quantitative Data




scatter plot S-ID

6b






1,2,3,4

2

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Statistics and

Probability


Quantitative Data




scatter plot S-ID

6c

M ODE Represent data on two quantitative





1,2,3,4

Statistics and

Probability


Quantitative Data

Interpret Linear Models slope, intercept S-ID 7 M ODE Interpret the slope (rate of change) and



1,2,3,4

Statistics and

Probability


Quantitative Data

Interpret Linear Models correclation coefficient S-ID 8 M ODE Compute (using technology) and interpret


1,2,3,4

Statistics and

Probability


Quantitative Data


causation


causation.

1,2,3,4

Statistics and

Probability


Conclusions



experiments


random sample





1,2,3,4

Statistics and

Probability


Conclusions



experiments







question the model?

1,2,3,4

3

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Statistics and

Probability


Conclusions




studies

sample survey,

experiments,


randomization





each.

1,2,3,4

Statistics and

Probability


Conclusions




studies

survey, mean,

proportion, margin of

error

S-IC 4 I ODE Use data from a sample survey to

estimate a population mean or proportion;

develop a margin of error through the use

of simulation models for random

sampling.

1,2,3,4

Statistics and

Probability


Conclusions




studies

parameters S-IC 5 I ODE Use data from a randomized experiment

to compare two treatments; use

simulations to decide if differences

between parameters are significant.

1,2,3,4

Statistics and

Probability


Conclusions




studies

data S-IC 6 I ODE Evaluate reports based on data. 1,2,3,4

Statistics and

Probability


of Probability



interpret data

subsets, sample

space, outcome, union,

intersection,

complements

S-CP

1






“not”).

1,2,3,4

Statistics and

Probability


of Probability



interpret data

independent S-CP

2





to determine if they are independent

1,2,3,4

4

AP Statistics

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Statistics and

Probability


of Probability



interpret data

conditional probability S-CP

3

R ODE Understand the conditional probability of A







1,2,3,4

Statistics and

Probability


of Probability



interpret data

frequency tables,

conditional probability

S-CP

4

I ODE Construct and interpret two-way

frequency tables of data when two

categories are associated with each

object being classified. Use the two-way

table as a sample space to decide if

events are independent and to

approximate conditional probabilities.

1,2,3,4

Statistics and

Probability


of Probability



interpret data


independence

S-CP

5




situations.

1,2,3,4

Statistics and

Probability


of Probability





outcomes

S-CP

6




terms of the model.

1,2,3,4

Statistics and

Probability


of Probability




addition rule S-CP

7




1,2,3,4

5

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Statistics and

Probability


of Probability





8





1,2,3,4

Statistics and

Probability


of Probability




permutations and

combinations

S-CP

9

R ODE (+) Use permutations and combinations to


and solve problems.

1,2,3,4

Statistics and

Probability



random variable, data

distributions

S-MD

1

I ODE (+) Define a random variable for a quantity of

interest by assigning a numerical value to

each event in a sample space; graph the

corresponding probability distribution

using the same graphical displays as for

data distributions.

1,2,3,4

Statistics and

Probability



expected value S-MD

2

I ODE (+) Calculate the expected value of a random

variable; interpret it as the mean of the

probability distribution.

1,2,3,4

Statistics and

Probability




3



space in which theoretical probabilities

can be calculated; find the expected value

1,2,3,4

Statistics and

Probability




4



space in which probabilities are assigned

empirically; find the expected value.

1,2,3,4

6

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Statistics and

Probability


of decisions

payoff values,

expected values

S-MD

5a




values.

a. Find the expected payoff for a game of

chance. For example, find the expected

winnings from a state lottery ticket or a

game at a fast-food restaurant.

1,2,3,4

Statistics and

Probability


of decisions

payoff values,

expected values

S-MD

5b




values.

b. Evaluate and compare strategies on the

basis of expected values. For example,

compare a high-deductible versus a low-

deductible automobile insurance policy

using various, but reasonable, chances of

having a minor or a major accident.

1,2,3,4

Statistics and

Probability


of decisions

decisions S-MD

6



number generator).

1,2,3,4

Statistics and

Probability


of decisions

probability concepts S-MD

7

I ODE (+) Analyze decisions and strategies using

probability concepts (e.g., product testing,

medical testing, pulling a hockey goalie at

the end of a game).

1,2,3,4

AP Statistics will also follow all standards set by College Board. See AP Statistics word document.

7

AP STATISTICS SYLLABUS

PRIMARY TEXTBOOK

Weiss, Neil A. Introductory Statistics. 7th

edition. New York: Pearson

Education, Inc., 2005.

OTHER SOURCES

Sternstein, Martin. How To Prepare For The AP Statistics Advanced Placement

Examination. 2nd

edition. New York: Barron’s Educational Series, Inc., 2000.

Mulekar, Madhuri S. Cracking The AP Statistics Exam. New York: Princeton Review

Publishing, L.L.C., 2004.

Discovery Channel Schools. Understanding Probability and Odds. 27-min. Bethesda,

Maryland: Discovery Communications, Inc. Videocassette 2001.

COURSE DESIGN

This fast-paced Statistics AP course is not dominated by lecture but rather by student

exploration and classroom discussion. Students are able to work in groups to complete

any multitude of tasks. Facilitating discussion and learning as it pertains to statistical

analysis is the main goal of the course. Making connections from the initial design to the

proper analysis and to the conclusion is vital. There is an emphasis on communicating,

orally and written, complete responses throughout the statistical process.

The teaching materials for the course come from textbooks, newspapers, journal writings,

videos, the internet, and some lectures. Each student is provided a formula card and set

of tables that will be needed for the entire year long course. These tables and formulas

are allowed on all activities assigned. Further each student is required to have a TI-83+

calculator to help complete assignments. Minitab is on the seven computers in the

classroom. These computers along with the media center computers, allow the students

to see the benefit in technology within the statistical field. Quick results help them avoid

many tedious calculations as they learn to interpret output from this technology of the TI-

83+, Minitab, and excel. Student assignments vary from reading text, journal responses,

statistical articles, quizzes, tests, various activities, two major projects, and general

homework.

COURSE OUTLINE

The topics are introduced by chapter from primary textbook. Activities are listed below

the topics for a given chapter. Each chapter concludes with a test and a quiz

approximately midway through the material of the chapter. These 16 chapters are

followed by approximately 2 weeks of all AP practice in class. Previously released

extended response questions from prior years are provided from AP site and multiple

choice is practiced from other sources listed above (Sternstein and Mulekar). We

practice the scoring rubric process and strategy on multiple choice. The two projects take

place during the 4th

quarter, the first being while we are preparing directly for the AP

exam and the second after the exam until the end of the year. Project description can be

found at end of course outline. Each chapter below estimates the number of days to

complete including evaluation. Further it shows what major items from the AP Topic

Outline are covered in that particular chapter. Incorporation of TI-83+ (dominant

technology used in class) is indicated, but not limited to, next to topics within course

outline by (TI).

CHAPTER 1

NATURE OF STATISTICS (8 days)

TOPICS

AP STATISTICS COURSE TOPIC

OUTLINE

- differentiating between descriptive and

inferential statistics

- acquiring information various ways;

census, sampling, or experimentation

- representative samples

- simple and systematic random sampling

- cluster sampling

- stratified sampling with proportional

allocation

- observational study

- designed experiment

- principles of experimental design

- completely randomized design and

randomized block design

Activity: Summarize and present briefly

over 3 provided articles

Activity: Designing surveys; each student

presents 1 good and 1 bad survey; class is

then evaluated on identifying each

- IIA overview of methods of data

collection #’s 1, 2, 3, 4

- IIB planning and conducting surveys

#’s 1, 2, 3, 4

- IIC planning and conducting

experiments #’s 1, 2, 3, 4, 5

- IID generalization and types of

conclusions to draw from data

collection

CHAPTER 2

ORGANIZING DATA (8 days)

TOPICS AP STATISTICS COURSE TOPIC

OUTLINE

- differentiating among qualitative and

quantitative variables/data

- differentiating between continuous and

discrete variables/data

- organizing data by single values and

grouped data tables

- organizing with histograms, dotplots, pie

charts, bar graphs, and stem and leaf plots

(TI)

- classification of distribution shapes

- symmetry

- skewness

- misleading graphs

Activity: Find and summarize article with

statistics (graphs) that are misleading

- IA constructing & interpreting

graphical displays of univariate data

#’s 1, 2, 4

- IE exploring categorical data #’s 1, 4

CHAPTER 3

DESCRIPTIVE MEASURES (7 days)


OUTLINE

- selecting the most appropriate measure of

central tendency

- measures of variation; sample standard

deviation, sample variance, and range

(TI)

- intro to Empirical Rule and Chebychev’s

Rule

- boxplots and intro into percentiles

- determining possible outliers using

interquartile range

- parameters vs. statistics

- standardizing the data; z-scores (TI)

Activity: Construct a box plot and

analyze for the 40 wealthiest people in

the world

- IB summarizing distributions of

univariate data #’s 1, 2, 3, 4

CHAPTER 4

PROBABILITY, RANDOM VARIABLES,

AND SAMPLING DISTRIBUTIONS (12 days)


OUTLINE

- definition of probability

- frequentist interpretation of probability

- sample space and events along with Venn

diagrams

- mutually excusive events

- general addition and complementation

rule

- contingency tables and conditional

probability

- independent and dependent events

- multiplication rule

- differentiate between independent and

mutually exclusive events

- Bayes’s Rule with exhaustive events

- basic counting rule and tree diagrams

- combination and permutation (TI)

Activity: Probability of winning various

lotteries across the US; where is your

best chance?

Activity: Video on probability and odds

- IE exploring categorical data #’s 2, 3

- IIIA probability #’s 1, 3

CHAPTER 5

DISCRETE RANDOM VARIABLES (7 days)


OUTLINE

- discrete random variables

- sum of the probabilities of discrete

random variable

- interpreting probability distributions

- mean (expected value) and standard

deviation of a discrete random variable

- Bernoulli Trials

- binomial distribution (TI)

- mean and standard deviation of a

binomial distribution

- geometric and hypergeometric

distributions

- Poisson distribution (TI)

- mean and standard deviation of a Poisson

- IIIA probability #’s 2, 4, 6

random variable

Activity: Simulation of rolling dice and

constructing various distribution graphs

(TI)

Activity: Finding expected values of

various casino games

CHAPTER 6

NORMAL DISTRIBUTION (8 days)


OUTLINE

- normal distribution vs. approximately

normal distributions

- standard normal curve and area tables

- finding percentiles

- using a normal probability plot to assess

normality (TI)

- intro to finding binomial probability by

using normal curve and a correction for

continuity

Activity: Are the color of Skittles

normally distributed?

- IIIC the normal distribution #’s 1, 2, 3

CHAPTER 7

SAMPLING DISTRIBUTION OF THE SAMPLE MEAN (6 days)


OUTLINE

- sampling error

- sampling distribution of the sample mean

- relationship between sampling error and

sample size

- mean of all samples of a given sample

size equals the population mean

- standard deviation of the variable sample

mean

- sampling distribution of a sample mean

for a normally distributed variable

- central limit theorem

Activity: Simulation with GRE scores;

what does all samples of a particular size

equal? (TI)

- IIID sampling distributions #’s 2, 3

CHAPTER 8

CONFIDENCE INTERVALS FOR ONE POPULATION MEAN (6 days)


OUTLINE

- using sample mean to estimate parameter,

population mean

- confidence intervals and levels

- deciding when to use one-sample z-

interval procedure

- relationship between confidence level,

interval length, and precision

- margin of error

- determining a sample size based upon

given confidence level and max error

allowed

- t-distributions and t-curves

- applying t-distributions; one sample t-

interval procedure

Activity: What does it mean to be 90%,

95%, and 99% confident?

- IIID sampling distributions # 7

- IVA estimation with point estimators

and confidence intervals #’s 1, 2, 3, 4,

and 6

CHAPTER 9

HYPOTHESIS TESTS FOR ONE POPULATION (11days)


OUTLINE

- intro to hypothesis testing (TI)

- types of error associated with hypothesis

testing

- using critical values

- finding probability of type I error

- finding probability of type II error

(provide assumed true mean)

- power of a hypothesis test

- determine the relationship between

hypothesis test and confidence intervals

- relationship between sample size and

power

- using p-values (TI)

- compare parametric methods to non-

parametric methods

- intro to first non-parametric method;

Wilcoxon Signed-Rank Test

* Activity: Response to article “Freshman

15” and possible hypothesis test to use

- IVB test of significance # 1

CHAPTER 10

INFERENCES FOR TWO POPULATION MEANS (9 days)


OUTLINE

- sampling distribution of the difference

between sample means of independent

samples

- pooled t-test and t-interval (TI)

- nonpooled t-test and nonpooled t-interval

(TI)

- non-parametric method; Mann Whitney

Test

- making inferences for two populations

given paired samples

- paired t-test and paired t-interval (TI)

- non-parametric method; Paired Wilcoxon

Signed-Rank Test


and confidence intervals # 7

- IVB tests of significance # 5

CHAPTER 11

INFERENCES FOR POPULATION STANDARD DEVIATIONS (4 days)


OUTLINE

- chi-square distributions

- hypothesis test for a population standard

deviations (TI)

- chi-square test and chi-square interval

(TI)

- f-distributions

- hypothesis test for two population

standard deviations

- f-test and f-interval


CHAPTER 12

INFERENCES FOR POPULATION PROPORTIONS (5 days)


OUTLINE

- confidence intervals for one population

proportion (TI)

- one sample z test and z interval for

population proportion (TI)

- finding sample size given constraints of

confidence level and max error

- hypothesis test for one and two

population proportions



and confidence intervals #’s 4, 5

- IVB tests of significance #’s 2, 3

CHAPTER 13

CHI-SQUARE PROCEDURES (6 days)


OUTLINE

- chi-square goodness-of-fit-test

- chi-square independence test for

univariate and bivariate data (two way

tables) (TI)

- using chi-square to check for association

between two variables

Activity: Colors of M & M’s

- IID generalization of results and

viable conclusions from data

collection


CHAPTER 14

DESCRIPTIVE METHODS IN REGRESSION AND CORRELATION (8 days)


OUTLINE

- regression equation produced from

scatter plot (TI)

- predictor variable and response variable

- extrapolation

- coefficient of determination

- regression identity

- linear correlation coefficient

- interpreting r and r-squared

Activity: Predicting ACT scores from

SAT scores

- ID exploring bivariate data #’s 1, 2, 3,

4

CHAPTER 15

INFERENTIAL METHODS IN REGRESSION AND CORRELATION (7 days)


OUTLINE

- estimating regression parameters

- analysis of residuals

- regression hypothesis t-test to check

usefulness of regression equation to make

predictions

- correlation test for normality


and confidence intervals # 8


CHAPTER 16

ANALYSIS OF VARIANCE (8 days)


OUTLINE

- analysis of variance using ANOVA

- multiple comparison method using Tukey

- non-parametric method of Kruskal-Wallis

- extra material; not applicable to AP

exam

The following is the project description/outline provided to students for both major

projects. The first project comes during the review time for the AP exam. The second

project follows after the AP exam is taken in the first week in May.

STATISTICS PROJECT

Project (125 points)

Due:

Topic: Student may pick any topic of interest for project

The project will include the following:

1. Oral Report: approximately 7-10 minutes in length describing the important

aspects of the study (25 pts)

*must have visual representation of information within study

*must involve the class

*hit all key ideas from report, Meat and Potatoes, talk statistics (vocab)

*question at hand, objective of study

*how was data collected and analyzed

*conclusion

*possible bias involved

*how could study be improved

2. Written Report: Typed with no minimum length (20 pts/section)

a. List of Data Collection

b. Description of the method of analysis with assumptions

c. Relevant graphs and/or statistics

d. Statement of conclusions

e. Reasons why the results might not be correct, along with a description of

ways in which the study could be improved, given sufficient time and

money. Incorporate research from the internet dealing with your study

that supports or does not support your data.

*Written Report must have all the information.

*Oral Report – visual representation must be seen by all

*You can collect your own data through experiments or observational studies. It is

absolutely essential to analyze the method used to collect the data, because data

carelessly collected may become completely useless. Look carefully for bias in the way

data are collected. Many procedures are based upon one working with a simple random

sample, meaning every possible sample of the same size has the same chance of being

selected. If a sample is self-selected (voluntary response), it is worthless for making

inferences about a population.

*Consider each of the following if it applies:

Center: mean and median

Variation: range and standard deviation

Distribution: a graph showing the distribution of the data

Outliers: explain if applicable

Time: is the population stable or is changing over time

*Inferences: Estimating Parameters and Hypothesis Testing. Be sure to use your

textbook when deciding which procedure to use when analyzing the data.

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