mathematics curriculum subject area: honors algebra … 2013/honors... · cell phone service for a...

Mathematics Curriculum

CCSS

ClusterCommon Core Standard

(D)=District Standard

Show Me

StandardsDOK

Instructional Strategies

Student Activities/ResourcesAssessment

The students will:

Pe

rfo

rm a

rith

me

tic o

pera

tio

ns w

ith

co

mp

lex

nu

mb

ers

1. know there is a complex number i

such that i² = –1, and every complex

number has the form a + bi with a

and b real.

2. use the relation i² = –1 and the

commutative, associative, and

distributive properties to add,

subtract, and multiply complex

numbers

MA 5

3.4

Str

ate

gic

Thin

kin

g

1. Introduce the complex number system and imaginary

numbers stressing √-1= i

2. Applying i2 = -1, commutative, associative and

distributive properties students will add, subtract and

multiply complex numbers.

1. DESE: Polynomial Expressions

and Functions Unit for Algebra II

2. Simplify (2+3i)(2-4i)

(SMP 2,6,7,8)

Subject Area: Honors Algebra II 10-12

CCSS Conceptual Category: Number and Quantity

CCSS Domain: The Complex Number System (N-CN)

Show-Me Standards

1 2/28/2013 Cape Girardeau Public Schools 2013

http://www.capetigers.com/Portals/0/Curriculum/Documents/Curriculum Development/Show Me Standards.pdf


CCSS



Show Me

StandardsDOK



The students will:


CCSS Conceptual Category: Number and Quantity

CCSS Domain: The Complex Number System (N-CN)

Show-Me Standards

Use

co

mp

lex

nu

mb

ers

in

po

lyn

om

ial

ide

nti

tie

s a

nd

eq

uati

on

s

7. solve quadratic equations with

real coefficients that have complex

solutions.

8. (+) extend polynomial identities to

the complex numbers.

9. (+) know the Fundamental

Theorem of Algebra; show that it is

true for quadratic polynomials.

MA 5

3.4

Str

ate

gic

Thin

kin

g

7. Solve quadratic equations including those with complex

solutions.

8. Factor polynomials involving complex numbers.

9. Apply the Fundamental Theorem of Algebra to quadratic

polynomials.

7. Solve x2- x + 1 = 0

8. Rewrite x2 + 4 as (x + 2i)(x –

2i).

9. Explain why the Fundamental

Theorem of Algebra holds for 3x2 -

18x - 24

(SMP 1,7)




CCSS



Show Me

StandardsDOK



The students will:

Inte

rpre

t th

e s

tru

ctu

re o

f e

xp

res

sio

ns

1. interpret expressions that

represent a quantity in terms of its

context.★

a. interpret parts of an expression,

such as terms, factors, and

coefficients.

b. interpret complicated expressions

by viewing one or more of their

parts as a single entity.

2. use the structure of an

expression to identify ways to

rewrite it.

MA 1, 5

3.1, 1.6

Skill

/Concept

1a. Examine expressions to explain terms, factors and

coefficients.

1b. Decompose expressions by expressing the meanings

of individual parts.

2. Rewrite algebraic expressions in different equivalent

forms.

1a. Analyze the expression .40s

+12.95 which gives the cost of

cell phone service for a month.

1b. Interpret P(1+r)n as the

product of P and a factor not

depending on P.

2. Rewrite x4 – y

4 as (x

2)2 – (y

2)2,

thus recognizing it as a difference

of squares that can be factored

as (x2 – y

2)(x

2 + y

2)

(SMP 2,5)


CCSS Conceptual Category: Algebra

CCSS Domain: Seeing Structure in Expressions (A-SSE)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:



CCSS Domain: Seeing Structure in Expressions (A-SSE)

Show-Me Standards

Wri

te e

xp

res

sio

ns

in

eq

uiv

ale

nt

form

s t

o s

olv

e p

rob

lem

s

4. 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. ★

Arithmetic with Polynomials and

Rational Expressions

MA 5

1.6

Str

ate

gic

Thin

kin

g

4. For the sum Sn, why is the last term of the series a1rn-1

and not a1rn?

4. In January the Smith family

starts saving for a trip to Hawaii.

In August, the Smiths expect the

vacation to cost $5,375. They

start with $525 and each month

plan to deposit 20% more than

the previous month. Will they

have enough money for the trip?

In your solution show the

derivation and use the formula.

(SMP 4,7,8)




CCSS



Show Me

StandardsDOK



The students will:

Pe

rfo

rm a

rith

me

tic o

pera

tio

ns o

n p

oly

no

mia

ls

1. 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.

MA 1, 5

3.4

Skill

/Concept

1. Expand and simplify (x-3)(x2+3x+9)

1. Simplify (3x2+5x+2) + (2x

2+6x-

1) - (4x2+2x+4).

(SMP 2,7)



CCSS Domain: Arithmetic with Polynomials and Rational Expressions (A-APR)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

Un

de

rsta

nd

th

e r

ela

tio

nsh

ip b

etw

ee

n z

ero

s

an

d f

ac

tors

of

po

lyn

om

ials

2. 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. 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.

MA 4

1.6

Str

ate

gic

Thin

kin

g/ S

kill

Concept 2. Divide 4x

2-5x-20 by x-4 using synthetic division. What is

the remainder?

3. Let f(x)=(x-1)2(x+2)(x-4). Find the zeros and use sign

graphs to sketch a rough graph of the function.

2. When determining P(-4), what

factor are you dividing by?

3. Given a polynomial function,

find the zeros and create a rough

graph.

(SMP 1,2,4,5,8)




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

Use

po

lyn

om

ial

ide

nti

tie

s t

o s

olv

e p

rob

lem

s

4. prove polynomial identities and

use them to describe numerical

relationships.

MA 4

3.4

Skill

/Concept

4. Expand (x+2y)2

4. Given a variety of powers of

polynomials use Pascal's

Triangle or memorized patterns

to expand.

(SMP 7,8)




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

Rew

rite

ra

tio

nal

ex

pre

ss

ion

s

6. 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.

7. (+) 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.

MA 4

3.4

Skill

/Concept

6. Divide using synthetic or long division.

7. Simplify

6. Given various polynomials be

able to perform long or synthetic

division.

7. Given various rational

expressions be able to add,

subtract, multiply and divide.

(SMP 2,5,7,8)

𝟔𝒙𝟐 + 𝟏𝟒𝒙 + 𝟕

𝟐𝒙 + 𝟑

𝟐𝒙 + 𝟏𝟐

𝟑𝒙 − 𝟗×𝟔 − 𝟐𝒙

𝟑𝒙 + 𝟖




CCSS



Show Me

StandardsDOK



The students will:

Cre

ate

eq

uati

on

s t

hat

de

sc

rib

e n

um

be

rs o

f re

lati

on

sh

ips

1. create equations and inequalities

in one variable and use them to

solve problems. Include equations

arising from linear and quadratic

functions, and simple rational and

exponential functions.

2. create equations in two or more

variables to represent relationships

between quantities; graph equations

on coordinate axes with labels and

scales.

3. represent constraints by

equations or inequalities, and by

systems of equations and/or

inequalities, and interpret solutions

as viable or nonviable

options in a modeling context.

4. rearrange formulas to highlight a

quantity of interest, using the same

reasoning as in solving equations.

MA 1, 5

1.6, 1.10

Skill

/Concept

1. A rental car agency charges $25 a day and $0.35 per

mile. You have allowed $300 for transportation. How many

miles can you travel?

2. A library ordered 48 fiction and non fiction books. A

fiction book cost $15 and a non fiction book cost $20. The

total cost of the order was $900. How many non fiction

books were ordered?

3. A club is selling t-shirts and sweatshirts as a fundraiser.

The budget is $1500 and they want to order at least 250

items. They must buy at least as many t-shirts as

sweatshirts. A t-shirt cost $6 and a sweatshirt cost $10.

What is the maximum number of sweatshirts they can

buy?

4. Solve p=2l+2w for w.

1. Water shoots from a geyser in

a parabolic path. The height, h in

t seconds is given by

f(t)=-16t2+64t+936. After how

many seconds does it reach a

maximum height of 750 ft?

2. Given real world situations

involving 2 or more quantities

write and solve a system of two

equations.

3. Represent inequalities

describing nutritional and cost

constraints on combinations of

different foods.

4. Rearrange Ohm’s law V = IR to

highlight resistance R.

(SMP 1,2,4,5)



CCSS Domain: Creating Equations (A-CED)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:

Un

de

rsta

nd

so

lvin

g e

qu

ati

on

s a

s a

pro

ce

ss

of

rea

so

nin

g a

nd

ex

pla

in t

he

re

as

on

ing

2. solve simple rational and radical

equations in one variable, and give

examples showing how extraneous

solutions may arise.

MA 1, 5

3.4

Skill

/Concept

2. Solve and check √2x-1 +7=-2

2. Given a variety of radical

equations, isolate the radical,

clear the radical and check.

(SMP 1,2,3,7)



CCSS Domain: Reasoning with Equations and Inequalities (A-REI)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:



CCSS Domain: Reasoning with Equations and Inequalities (A-REI)

Show-Me Standards

Rep

res

en

t a

nd

so

lve

eq

uati

on

s a

nd

in

eq

uali

tie

s g

rap

hic

all

y

11. 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.★

MA 3

1.5, 1.8

Skill

/Concept

11. Solve the system:

7x-y=6

-7x+y=-6

11. Solve linear, polynomial,

rational, absolute value,

exponential and logarithmic

systems of equations graphically

and algebraically.

(SMP 2,4,5,6)




CCSS



Show Me

StandardsDOK



The students will:

Inte

rpre

t fu

ncti

on

s t

hat

ari

se

in

ap

plic

ati

on

s

in t

erm

s o

f th

e c

on

tex

t

4. for a function that models a

relationship between two quantities,

interpret key features of graphs and

tables in terms of the quantities, and

sketch graphs showing key features

given a verbal description of the

relationship. Key features include:

intercepts; intervals where the

function is increasing, decreasing,

positive, or negative; relative

maximums and minimums;

symmetries; end behavior; and

periodicity.★

5. relate the domain of a function to

its graph and, where applicable, to

the quantitative relationship it

describes.★

6. 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.★

MA 1, 4

1.6

Skill

/Concept

4. A cannon is shot from 180 ft above the ground at time

t=0. The function that models this situation is given by

h=-16t2+96t+180 where t is measured in seconds and h is

height above the ground in feet. What is the height of the

cannon ball 2 seconds after it is launched? What is the

maximum height of the cannon ball? When is the cannon

ball 100 feet above the ground? When does the cannon

ball hit the ground.

5. Refer to number 4. Find the domain and interpret it

within the real world context of the problem.

6. Refer to number 4. Find two points on the function and

then find the average rate of change.

4. Given real world examples

modeled by quadratics or higher

degrees, find the maximum or

minimum value, intercepts,

intervals of increase or decrease

and describe end behavior.

5. If the function h(n) gives the

number of person-hours it takes

to assemble n engines in a

factory, then the positive integers

would be an appropriate domain

for the function.

6. Calculate average rate of

change for a given function of

degree two or higher.

(SMP 2,4,5,6,7,8)


CCSS Conceptual Category: Functions

CCSS Domain: Interpreting Functions (F-IF)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

An

aly

ze

fu

ncti

on

s u

sin

g d

iffe

ren

t re

pre

se

nta

tio

ns

7. graph functions expressed

symbolically and show key features

of the graph, by hand in simple

cases and using technology for

more complicated cases.★

b. graph square root, cube root, and

piecewise-defined functions,

including step functions and

absolute value functions.

c. graph polynomial functions,

identifying zeros when suitable

factorizations are available, and

showing end behavior.

e. graph exponential and logarithmic

functions, showing intercepts and

end behavior, and trigonometric

functions, showing period, midline,

and amplitude.

MA 1, 5

1.4, 1.8

Skill

/Concept 7b. Graph y=√x+2

7c. Graph y=(x-1)(x+2)(x-3)

7e. Graph y=2x

7b. Distinguish between square

root and absolute value functions,

then graph.

7c. Graph polynomial functions

using zeros and a sign graph.

7e. Identify percent rate of

change in functions such as y =

(1.02)t, y = (0.97)

t, y = (1.01)

12t, y

= (1.2)t/10

, and classify them as

representing exponential growth

or decay.

(SMP 5,6)




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

An

aly

ze

fu

ncti

on

s u

sin

g d

iffe

ren

t re

pre

se

nta

tio

ns

8. write a function defined by an

expression in different but

equivalent forms to reveal and

explain different properties of the

function.

a. use the process of factoring and

completing the square in a

quadratic function to show zeros,

extreme values, and symmetry

of the graph, and interpret these in

terms of a context.

b. use the properties of exponents

to interpret expressions for

exponential functions.

9. compare properties of two

functions each represented in a

different way (algebraically,

graphically, numerically in tables, or

by verbal descriptions).

MA 1, 5

1.4, 1.8

Skill

/Concept

8a. Change f(x)=x2-3x+2 to vertex ready form.

8b. Compare y=3x to y=(1/3)

x and identify as growth or

decay.

9. Given the graph of y=4x2-3x+1 and the equation

y=2x2+5x-1. Find the maximum or minimum value of each.

8a. Change standard form to

vertex ready form for parabolas.

8b. Identify functions as either

exponential growth or decay or

rate of change.

9. Given a graph of one quadratic

function and

an algebraic expression for

another, say which has the larger

maximum.

(SMP 6,7)




CCSS



Show Me

StandardsDOK



The students will:

Bu

ild

a f

un

cti

on

th

at

mo

dels

a r

ela

tio

nsh

ip b

etw

ee

n

two

qu

an

titi

es

1. write a function that describes a

relationship between two

quantities.★

b. combine standard function types

using arithmetic operations.

MA 1, 4

1.6, 1.8

Skill

/Concept 1b. A cup of tea begins with the temperature of 90°F. The

difference between its temperature and the room

temperature of 70°F decreases by 10% each minute. Write

a function telling the temperature of the coffee as a

function of time.

1b. Build a function that models

the temperature of a cooling body

by adding a constant function to a

decaying exponential, and relate

these functions to the model.

(SMP 1,2,3,4,5,6,7,8)



CCSS Domain: Building Functions (F-BF)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:



CCSS Domain: Building Functions (F-BF)

Show-Me Standards

Bu

ild

ne

w f

un

cti

on

s f

rom

ex

isti

ng

fu

ncti

on

s 3. identify the effect on the graph of

replacing f(x) by f(x) + k, k f(x),

f(kx), and f(x + k) for specific values

of k (both positive and negative);

find the value of k given the graphs.

Experiment with cases and

illustrate an explanation of the

effects on the graph using

technology. Include recognizing

even and odd functions from their

graphs and

algebraic expressions for them.

4. 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.

MA 4, MA 5

1.6

Skill

/Concept

3. Graph y=x2, y=(x-3)

2, y=x

2+4 on the same set of axes

and describe the transformations.

4. Rewrite f(x)=x+1 as an inverse function.

3. Graph y=x3, y=(x-4)

3, y=x

3-3

4. Rewrite f(x) =2x3 or f(x) =

(x+1)/(x–1) for x ≠ 1 as inverse

functions.

(SMP 4,5,7)




CCSS



Show Me

StandardsDOK



The students will:

Co

ns

tru

ct

an

d c

om

pa

re l

ine

ar,

qu

ad

rati

c,

an

d e

xp

on

en

tia

l

mo

de

ls a

nd

so

lve

pro

ble

ms

4. 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.

MA 1, 4

1.6, 1.8

Skill

/Concept

4. Solve 200e0.04t

=450 for t.

4. Solve a variety of exponential

equations by rewriting

logarithmically.

(SMP 3,4,5,7,8)



CCSS Domain: Linear, Quadratic, and Exponential Models (F-LE)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:

Ex

ten

d t

he

do

ma

in o

f tr

igo

no

me

tric

fu

ncti

on

s

usin

g t

he

un

it c

irc

le

1. understand radian measure of an

angle as the length of the arc on the

unit circle subtended by the angle.

2. 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.

MA 2

3.4

Skill

/Concept

1. What is the measure of the arc formed by the slice of

pie with a radius of 6 inches and central angle of 30°?

State your answer in radians.

2. Sketch a unit circle and find the sine of 120°.

1. Given various radii and central

angles on provided diagrams,

convert to radian measures and

solve.

2. Use the unit circle to evaluate

trigonometric functions at various

angles.

(SMP 2,3,6)



CCSS Domain: Trigonometric Function (F-TF)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

Mo

del

pe

rio

dic

ph

en

om

en

a w

ith

tri

go

no

me

tric

fu

ncti

on

s

5. choose trigonometric functions to

model periodic phenomena with

specified amplitude, frequency, and

midline.★

MA 4

1.8

Skill

/Concept

5. The soundwave can be modeled by this function

y=0.001sin1320πx. Find the amplitude, period, frequency

and midline.

5. Know how to find amplitude,

frequency, period and midline of

the various trigonometric

functions.

(SMP 4,5,7)




CCSS



Show Me

StandardsDOK



The students will:




Show-Me Standards

Pro

ve

an

d a

pp

ly t

rig

on

om

etr

ic i

den

titi

es

8. 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.

MA 2

1.6, 3.4

Skill

/Concept

8. Using the unit circle find sine and cosine ratios and

prove the Pythagorean Identity. Use this to find cosx given

sinx=3/5.

8. Using the Pythagorean

Theorem, develop the

Pythagorean Identity involving

sines and cosines.

(SMP 3,7,8)




CCSS



Show Me

StandardsDOK



The students will:

Su

mm

ari

ze

, re

pre

se

nt,

an

d in

terp

ret

data

on

a s

ing

le c

ou

nt

or

me

as

ure

me

nt

va

ria

ble 4. 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.

MA 3

1.8

Skill

/Concept

4. What is the mean, variance and standard deviation for

3.7, 4.5, 6.8, 5.4, 4.4?

4. Given a set of data, find the

mean, variance and standard

deviation. Note outliers to

determine if such a procedure is

appropriate.

(SMP 1,2,3,4,5,7)


CCSS Conceptual Category: Statistics and Probability

CCSS Domain: Interpreting Categorical and Quantitative Data (S-ID)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:

Un

de

rsta

nd

an

d e

va

lua

te r

an

do

m p

roc

es

se

s

un

derl

yin

g s

tati

sti

ca

l e

xp

eri

me

nts

1. understand statistics as a

process for making inferences

about population parameters based

on a random sample from that

population.

2. decide if a specified model is

consistent with results from a given

data-generating process, e.g., using

simulation.

MA 3

1.8

Skill

/Concept

1. For a class problem, students in math class ask every

12th student entering the school if they eat breakfast in the

morning.

2. 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?

1. Take a random sample and

draw inferences from the data

using statistical processes.

2. After generating data, analyze

your results to determine if they fit

a specified model.

(SMP 1,2,3,4,5,6,7,8)



CCSS Domain: Making Inferences and Justifying Conclusions (S-IC)

Show-Me Standards




CCSS



Show Me

StandardsDOK



The students will:



CCSS Domain: Making Inferences and Justifying Conclusions (S-IC)

Show-Me Standards

Ma

ke

in

fere

nce

s a

nd

ju

sti

fy c

on

clu

sio

ns f

rom

sa

mp

le

su

rve

ys

, e

xp

eri

me

nts

, a

nd

ob

se

rva

tio

nal

stu

die

s

3. recognize the purposes of and

differences among sample surveys,

experiments, and observational

studies; explain how randomization

relates to each.

4. 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.

5. use data from a randomized

experiment to compare two

treatments; use simulations to

decide if differences between

parameters are significant.

6. evaluate reports based on data.

MA 3

1.8

Str

ate

gic

Thin

kin

g

3. Students in a high school math class decide that their

term project would be a study of the strictness of the

parents or guardians of students in the school. Their goal

was to estimate the proportion of students in the school

who thought of their parents or guardians as "strict". They

do not have time to interview all 1000 students so they

plan to obtain data from a sample of students.

4. In a survey of 530 randomly selected high school

students, 250 prefer watching baseball to watching

football. Find a. sample proportion b. margin of error

5. Using a completely randomized design, 20 students

counted the number of times they blinked their eyes and

the number of breaths they took in one minute.

6. Cite a media source, include the data and evaluate the

validity of the report.

3. Identify situations as sample

survey, experiments or

observational studies and

determine which is appropriate.

4. Given a real world scenario

find the sample proportion and

the margin of error.

5. Find data from a random

experiment. Compare and

determine if the differences

between parameters are

significant.

6. Using statistical concepts,

evaluate the validity of various

reports.

(SMP 1,2,3,4,5,6,7,8)

