grade 3 athematics curriculum uide...grade 3 mathematics nine weeks overview 1st rdquarter 2nd...
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GRADE 3 MATHEMATICS
CURRICULUM GUIDE
Loudoun County Public Schools
2011-2012 Complete scope, sequence, pacing and resources are available on the LCPS Intranet.
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun
County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other
statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers
concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the
lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively unchanged
over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can
combine them with the GUIDE for ease in lesson planning.
Mathematics Internet Safety Procedures
1. Teachers should review all Internet sites and links prior to using it in the classroom.
During this review, teachers need to ensure the appropriateness of the content on the site,
checking for broken links, and paying attention to any
inappropriate pop-ups or solicitation of information.
2. Teachers should circulate throughout the classroom while students are on the
internet checking to make sure the students are on the appropriate site and
are not minimizing other inappropriate sites.
Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
3. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
4. Teachers should assure that the use of websites correlate with the objectives
of the lesson and provide students with the appropriate challenge.
Grade 3 Mathematics Nine Weeks Overview
1st Quarter 2
nd Quarter 3
rd Quarter 4
th Quarter
Time 3.11 a, b
3.12
Temperature 3.13
Graphing 3.17 a, b, c
Place Value 3.1 a, b, c
Addition and
Subtraction 3.2
3.4
3.20
Multiplication & Division 3.5
3.6
3.19
3.20
Money 3.8
Addition & Subtraction 3.4
3.2
3.20
Patterns 3.19
Geometry 3.14
3.15
3.16
Fractions 3.3 a, b, c
Probability 3.18
Measurement 3.9 a, b, c
Perimeter & Area 3.10 a, b, c
Time 3.11
Quarter 1 2011-2012 Third Grade Mathematics
Daily Classroom Routines are built on life skills and should be used all year. The content identified to be taught during the first three days of school is either a review or extension of previous knowledge and should be addressed in scaffolded assessments throughout the year. Teachers are encouraged to use the first three days of school to introduce telling time on a clock, elapsed time in one-hour increments, determine the value of a set of coins and bills, and read thermometers to tell temperature to the nearest degree.
Number of Days
Topic, Essential Questions, and Essential Understandings
(Students should be able to answer essential questions.)
REQUIRED Critical
Thinking Lessons
Standard(s) of Learning Essential Knowledge and Skills
Additional Instructional
Resources
3 days (then ongoing during the year)
Daily Classroom Routines Based on Life Skills During the first 3 days, review time, calendar, money, and temperature from previous grades. Students should be able to answer essential questions by the end of the year. (Time and money SOL are revisited during the school year.) Time 3.11 Essential Questions • Compare and contrast analog and digital
clocks. • Explain and justify how to determine time on
an analog clock. • Explain and justify how to determine elapsed
time. • How is a calendar organized to measure time? • Describe the relationships that exist among
periods of time within a calendar year. • When and why do we have a leap year? 3.11 Essential Understandings • Apply appropriate techniques to determine time to the nearest minute, using analog and digital clocks. • Understand how to determine elapsed time in one
SOL 3.11 The student will a) tell time to the nearest minute, using analog and digital clocks; and b) determine elapsed time in one-hour increments over a 12-hour period. 3.11 Essential Knowledge and Skills • Tell time to the nearest minute, using analog and digital clocks. • Match the times shown on analog and digital clocks to written times and to each other. • When given the beginning time and ending time, determine the elapsed time in one-hour increments within a 12-hour period (times do not cross between a.m. and p.m.). • Solve practical problems in relation to time that has elapsed.
Grade 3 ESS Lessons: • It’s About
Time • Was the
Groundhog Correct?
Investigations: Mathematical Thinking at Grade 3 “Ten Minute Math”, pages 87-90
hour increments over a 12-hour period. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3.12 Essential Questions 3.12 Essential Understanding Understand the relationship that exists among periods of time, using calendars, and clocks. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Temperature 3.13 Essential Questions • What the purpose of a thermometer? • How is temperature related to everyday
activities? Explain how to read temperatures which fall between the decade numbers on a thermometer. 3.13 Essential Understanding Understand how to measure temperature in Celsius and Fahrenheit with a thermometer.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 3.12: The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours. 3.12 Essential Knowledge and Skills • Identify equivalent relationships observed in a calendar, including the number of days in a given month, the number of days in a week, the number of days in a year, and the number of months in a year. • Identify the number of minutes in an hour and the number of hours in a day. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 3.13: The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used. SOL 3.13 Essential Knowledge and Skills Read temperature to the nearest degree from real Celsius and Fahrenheit thermometers and from physical models (including pictorial representations) of such thermometers.
Telling Time ~~~~~~~~~~ ~~~~~~~~~~~~ Temperature Graphs School weather station located in the library and on your school’s web page.
10 days
Graphing: Working with Data 3.17 Essential Questions • Explain strategies that can be used to collect,
organize, and represent data. • How does the type of data and the questions to
be answered influence the choice of graph? • Compare and contrast the key elements needed
when constructing line plots and graphs. • Collect, organize, display, and interpret data to
SOL 3.17: The student will a) collect and organize data, using observations, measurements, surveys, or experiments; b) construct a line plot, a picture graph, or a bar graph to represent the data; and c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.
ESS: • Statistics
Through the Years
• Data ManiaInvestigations: Mathematical
provide different kinds of information. • Explain how you know which interpretation of
a graph is correct and the remaining interpretations are incorrect.
SOL 3.17 Essential Understandings • Understand how data can be collected and organized. • Understand that data can be displayed in different types of graphs depending on the data. • Understand how to construct a line plot, picture graph, or bar graph. • Understand that data sets can be interpreted and analyzed to draw conclusions.
3.17 Essential Knowledge and Skills • Formulate questions to investigate. • Design data investigations to answer formulated questions. • Collect data, using surveys, polls, questionnaires, scientific experiments, and observations. • Organize data and construct a bar graph on grid paper. • Construct a line plot. • Read, interpret and analyze information from line plots by writing at least one statement. • Label each axis on a bar graph and give the bar graph a title. • Read the information presented on a simple bar or picture graph (e.g., the title, the categories, the description of the two axes). • Analyze and interpret information from picture and bar graphs by writing at least one sentence. • Describe the categories of data and the data as a whole (e.g., data were collected on four ways to cook or prepare eggs — scrambled, fried, hard boiled, and egg salad — eaten by students). • Identify parts of the data that have special characteristics, including categories with the greatest, the least, or the same (e.g., most students prefer scrambled eggs). • Select a correct interpretation of a graph from a set of interpretations of the graph, where one is correct and the remaining are incorrect. For example, a bar graph containing data on four ways to cook or prepare eggs — eaten by students show that more students prefer scrambled eggs. A correct answer response, if given, would be that more students prefer scrambled eggs than any other way to cook or prepare eggs.
Thinking in Grade 3 Investigation 3: “Data and Handfuls”, Sessions 1 – 4 Illuminations:As People Get Older, They Get Taller
Place Value: Relationships in Number 3.1 Essential Questions
SOL 3.1: The student will
ESS http://www.doe.virginia.gov/testi
11 days
• Explain the relationship in the place value system using a six-digit numeral.
• Compare and contrast written formats for whole numbers (standard, written, and expanded notation).
• Explain the relative magnitude of each 4 in the number 4,444?
• Explain strategies for comparing two whole numbers.
• Explain the use of an inequality symbol in an equation.
• Why are numbers rounded? • Demonstrate and explain how to round a four-
digit number using a variety of strategies. SOL 3.1 Essential Understandings • Understand that knowledge of place value is essential when comparing numbers. • Understand the relationships in the place value system, where each place is ten times the value of the place to its right. • Understand that rounding gives an estimate to use when exact numbers are not needed for the situation. • Understand the relative magnitude of numbers by comparing numbers.
a) read and write six-digit numerals and identify the place value and value of each digit; b) round whole numbers, to the nearest ten, hundred, and thousand; and c) compare two whole numbers using symbols (>, <, or =) and words(greater than, less than, or equal to). SOL 3.1 Essential Knowledge and Skills • Investigate and identify the place and value for each digit in a six-digit numeral, using Base-10 manipulatives (e.g., Base-10 blocks). • Use the patterns in the place value system to read and write numbers. • Read six-digit numerals orally. • Write six-digit numerals that are stated verbally or written in words. • Round a given whole number to the nearest ten, hundred, and thousand. • Solve problems, using rounding of numbers to the nearest ten, hundred, and thousand. • Determine which of two whole numbers is greater. • Determine which of two whole numbers is less. • Compare two whole numbers using the symbols >, <, or =. • Use the terms greater than, less than, and equal to when comparing two whole numbers.
ng/sol/standards_docs/mathematics/index.shtml Build the Bigger Number p. Digi-blocks Base 10 Blocks www.learnnc.org/lp/pages/3420 Anthill Number Round Off www.learnnc.org/lp/pages/3075 Rounding Ball
20 Days
Computing with Whole Numbers 3.2 Essential Questions • Explain how are the operations of addition and
subtraction related? • What strategies can help find the missing part
in a number sentence? • Explain the identity property of addition. • Explain the commutative property of addition. • Explain strategies that can be used for finding
sums and differences. 3.2 Essential Understanding
INV: Combining and Comparing Investigation 1: Comparisons with Record Numbers, Sessions 1 – 3
SOL 3.2: The student will recognize and use the inverse relationships between addition/subtraction and multiplication/ division to complete basic fact sentences. The student will use these relationships to solve problems. 3.2 Essential Knowledge and Skills • Use the inverse relationships between addition/subtraction and multiplication/division to solve related basic fact sentences. For example, 5 + 3 = 8 and 8 – 3 = 5.
ESS http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml Domino Addition
Understand how addition and subtraction are related. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3.4 Essential Questions 3.4 Essential Understandings • Understand that estimation skills are valuable, timesaving tools particularly in practical situations when exact answers are not required or needed. • Understand that estimation skills are also valuable in determining the reasonableness of the sum or difference when solving for the exact answer is needed. • Develop and use strategies to estimate whole number sums and differences to determine the reasonableness of an exact answer. • Develop flexible methods of adding whole numbers by combining numbers in a variety of ways, most depending on place values. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3.20 Essential Questions 3.20 Essential Understandings • Understand that mathematical relationships can be expressed using number sentences. • Understand the identity property for addition. • Understand the commutative property of addition.• Understand that quantities on both sides of an equals sign must be equal.
~~~~~~~~~~INV: Combining and Comparing Investigation 3: Adding with Money, Inches, and Time, Sessions 1 – 3 INV: Combining and Comparing Investigation 4: Working with Hundreds Sessions 1-4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3.4: The student will estimate solutions to and solve single-step and multi-step problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping. 3.4 Essential Knowledge and Skills • Determine whether an estimate or an exact answer is an appropriate solution for practical addition and subtraction problems situations involving single step and multistep problems. • Determine whether to add or subtract in practical problem situations. • Estimate the sum or difference of two whole numbers when an exact answer is not required. • Add or subtract two whole numbers. • Solve practical problems involving the sum of two whole numbers, using calculators, paper and pencil, or mental computation in practical problem situations. • Solve practical problems involving the difference of two whole numbers, using calculators, paper and pencil, or mental computation in practical problem situations. • Solve single-step and multistep problems involving the sum or difference of two whole numbers. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 3.20: The student will a) investigate the identity and the commutative properties for addition. b) identify examples of the identity and commutative properties for addition. 3.20 Essential Knowledge and Skills • Investigate the identity property for addition and determine that when the number zero is added to another number or another number is added to the
Summary: In the first quarter, classroom routines are established to practice the life skills of time, money, and temperature. Students will continue to practice these skills throughout the year. Collecting, displaying, describing, and interpreting data and graphs is a critical skill for third grade. Numbers and number relationships are explored through place value and magnitude. Students compare and contrast written formats and estimation of whole numbers. Landmark numbers, multiples of 10 and 100, are used to compare quantities. Vocabulary: Time: Analog, digital, leap year, elapsed time Money: greater than, less than, equal to, value, purchase price, change, Temperature: Celsius, Fahrenheit, symbol of degrees for Celsius and Fahrenheit, Data: data, title, axis, key, survey, line plot, bar graph, picture graph, analyze, Relationships in Number: written form, periods, expanded form, digit, standard form, greater than, less than, and inequality symbols, estimate, round
• Understand that quantities on both sides of the not equal sign are not equal.
number zero, that number remains unchanged. Examples of the identity property for addition are0 + 2 = 2; 5 + 0 = 5. • Recognize that the commutative property for addition is an order property. Changing the order of the addends does not change the sum (5 + 4 = 9 and 4 + 5 = 9). • Write number sentences to represent equivalent mathematical relationships (e.g., 4 x 3 = 14 - 2). • Identify examples of the identity and commutative properties for addition.
4 days
Enrichment, Assessment, and Remediation
Computing with Whole Numbers: Inverse operations, fact families, addend, sum, minuend, subtrahend, difference, estimate
Grade 3 Quarter 2 School Year 2011-2012
Number of
Days
Topic, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
REQUIRED
Critical
Thinking
Lessons
Standard(s) of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
30 days
Multiplication and Division
3.5 Essential Questions
Explain how:
addition and multiplication are related.
subtraction and division related.
multiplication and skip counting are related.
multiplication and division are related.
Demonstrate strategies used to recall addition,
subtraction, multiplication, and/or division facts.
What strategies can be used to find the missing part
in an equation?
Demonstrate multiple ways to represent
multiplication.
Explain the identity and commutative properties of
multiplication.
3.5 Essential Understanding
Develop fluency with number combinations
for multiplication and division.
• Understand that multiplication is repeated addition.
• Understand that division is the inverse of
multiplication.
• Understand that patterns and relationships exist in the
facts.
• Understand that number relationships can be used to
learn and retain the facts.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3.6 Essential Questions
3.6 Essential Understandings
INV: Things
That Come In
Groups
Investigation 4:
The Language
of
Multiplication
and
Division/Sessio
ns 1-4
INV: Things
That Come In
Groups
Investigation 5:
Problems with
Larger
Numbers,
Sessions
1-4
SOL 3.5: The student will recall multiplication facts
through the twelves table, and the corresponding
division facts.
3.5 Essential Knowledge and Skills
• Recall and state the multiplication and division facts
through the twelves table.
• Recall and write the multiplication and division
facts through the twelves table.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 3.6: The student will represent multiplication
and division, using area, set, and number line models,
and create and solve problems that involve
ESS Multiplication
Baseball
INV: Things That
Come In Groups
Investigation 1:
Things that Come in
Groups
Sessions 1-4
Investigation 2: Skip
Counting and 100
Charts
Sessions 1-6
Investigation 3:
Arrays and Skip
Counting
Sessions 1-5
INV Landmarks in
the Hundreds
Investigation 1:
Finding Factors,
Sessions 1 – 7
Investigation 2:
Using Landmarks to
Solve Problems,
Sessions 1 – 6
http://illuminations.n
ctm.org/LessonDetai
l.aspx?id=U109
All About
Multiplication
Grade 3 Quarter 2 School Year 2011-2012
• Understand the meanings of multiplication and
division.
• Understand the models used to represent multiplying
and dividing whole numbers.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3.19 Essential Questions
3.19 Essential Understandings
• Understand that numeric and geometric patterns can
be expressed in words or symbols.
• Understand the structure of a pattern and how it
grows or changes.
• Understand that mathematical relationships exist in
patterns.
• Understand that patterns can be translated from one
representation to another.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 3.20 Essential Understandings
• Understand that mathematical relationships can be
expressed using number sentences.
• Understand the identity property for multiplication.
multiplication of two whole numbers, one factor 99 or
less and the second factor 5 or less.
3.6 Essential Knowledge and Skills
• Model multiplication, using area, set, and number
line models.
• Model division, using area, set, and number line
models.
• Solve multiplication problems, using the
multiplication algorithm, where one factor is 99 or
less and the second factor is 5 or less.
• Create and solve word problems involving
multiplication, where one factor is 99 or less and the
second factor is 5 or less.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 3.19: The student will recognize and describe a
variety of patterns formed using numbers, tables, and
pictures, and extend the patterns, using the same or
different forms.
3.19 Essential Knowledge and Skills
• Recognize repeating and growing numeric and
geometric patterns (e.g., skip counting, addition
tables, and multiplication tables).
• Describe repeating and growing numeric and
geometric patterns formed using numbers, tables,
and/or pictures, using the same or different forms.
• Extend repeating and growing patterns of numbers
or figures using concrete objects, numbers, tables,
and/or pictures.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 3.20: The student will
a) investigate the identity and the commutative
properties for addition and multiplication; and
b) identify examples of the identity and
commutative properties for addition and
www.learnnc.org/lp/
pages/3017 M&M
Math
Grade 3 Quarter 2 School Year 2011-2012
• Understand the commutative property of
multiplication.
• Understand that quantities on both sides of an equals
sign must be equal.
• Understand that quantities on both sides of the not
equal sign are not equal.
multiplication.
SOL 3.20 Essential Knowledge and Skills
• Investigate the identity property for multiplication
and determine that when the number one is multiplied
by another number or another number is multiplied
by the number one, that number remains unchanged.
Examples of the identity property for multiplication
are 1 x 3 = 3; 6 x 1 = 6.
• Recognize that the commutative property for
multiplication is an order property. Changing the
order of the factors does not change the product (2 ×
3 = 3 × 2).
• Write number sentences to represent equivalent
mathematical relationships (e.g., 4 x 3 = 14 - 2).
• Identify examples of the identity and commutative
properties for addition and multiplication.
7 days
Money
3.8 Essential Questions
Demonstrate and explain strategies for determining
change.
Demonstrate and explain strategies for determining
the value of a set of coins and bills.
Explain and justify how the value of two sets of coins
can be compared,
(using >, <, =).
3.8 Essential Understandings
• Understand that a collection of coins and bills has a
value that can be counted.
• Understand how to make change from $5.00 or less.
SOL 3.8: The student will determine, by counting,
the value of a collection of bills and coins whose total
value is $5.00 or less, compare the value of the bills
and coins, and make change.
3.8 Essential Knowledge and Skills
• Count the value of collections of coins and bills up
to $5.00.
• Compare the values of two sets of coins or bills, up
to $5.00, using the terms greater than, less than, and
equal to.
• Make change from $5.00 or less.
www.learnnc.org/lp/
pages/3166
Money and More
Money
www.learnnc.org/lp/
pages/3554
Shopping Spree
3 days
Enrichment, Assessment, and Remediation
Grade 3 Quarter 3 School Year 2011-2012
Number of
Days
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
REQUIRED Critical
Thinking Lessons
Standard(s) of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
8 days
Patterns
3.19 Essential Questions
3.19 Essential Understandings
Understand that numeric and geometric
patterns can be expressed in words or
symbols.
Understand the structure of a pattern and
how it grows or changes.
Understand that mathematical relationships
exist in patterns.
Understand that patterns can be translated
from one representation to another.
SOL 3.19 The student will recognize
and describe a variety of patterns formed
using numbers, tables, and pictures, and
extend the patterns, using the same or
different forms.
3.19 Essential Knowledge and Skills Recognize repeating and growing
numeric and geometric patterns (e.g.,
skip counting, addition tables, and
multiplication tables).
Describe repeating and growing
numeric and geometric patterns
formed using numbers, tables, and/or
pictures, using the same or different
forms.
Extend repeating and growing patterns
of numbers or figures using concrete
objects, numbers, tables, and/or
pictures.
Geometry
3.14 Essential Questions
3.14 Essential Understandings Understand how to identify and describe
plane and solid geometric figures by using
relevant characteristics.
Understand the similarities and differences
between plane and solid figures.
SOL 3.14 The student will identify,
describe, compare, and contrast
characteristics of plane and solid geometric
figures (circle, square, rectangle,
triangle, cube, rectangular prism, square
pyramid, sphere, cone, and cylinder) by
identifying relevant characteristics,
including the number of angles, vertices,
and edges, and the number and shape of
faces, using concrete models.
Grade 3 Quarter 3 School Year 2011-2012
14 days
3.14 Essential Knowledge and Skills Identify models and pictures of plane
geometric figures (circle, square,
rectangle, and triangle) and solid
geometric figures (cube, rectangular
prism, square pyramid, sphere, cone,
and cylinder) by name.
Identify and describe plane geometric
figures by counting the number of
sides and angles.
Identify and describe solid geometric
figures by counting the number of
angles, vertices, edges, and by the
number and shape of faces.
Compare and contrast characteristics
of plane and solid geometric figures
(e.g., circle/sphere, square/cube,
triangle/square pyramid, and
rectangle/rectangular prism), by
counting the number of sides, angles,
vertices, edges, and the number and
shape of faces.
Compare and contrast characteristics of
solid geometric figures (i.e., cube,
rectangular prism, square pyramid, sphere,
cylinder, and cone) to similar objects in
everyday life (e.g., a party
18 days
Fractions
3.3 Essential Questions
What is a fraction?
Name and represent a fraction using a region,
measurement, and set models (including
mixed numbers).
Compare and justify the values of two unit
fractions.
INV: Fair Shares
Investigation 2: Pattern
Block Cookies,
Sessions 1 – 7
INV: Fair Shares
Investigation 3: Other
SOL 3.3 The student will
a) name and write fractions (including
mixed numbers) represented by a model;
b) model fractions (including mixed
numbers) and write the fractions’ names;
and
c) compare fractions having like and
ESS
http://www.doe.vir
ginia.gov/testing/so
l/standards_docs/m
athematics/index.s
html
Grade 3 Quarter 3 School Year 2011-2012
Demonstrate and explain strategies that can
be used for finding sums and difference using
fractions.
3.3 Essential Understandings
Understand that the whole must be defined.
Understand that the denominator tells the
number of equal parts that represent a
whole.
Understand that the numerator is a counting
number that tells how many equal size parts
are being considered.
Understand that the value of a fraction is
dependent on both the number of parts in a
whole (denominator) and the number of
those parts being considered (numerator).
Understand that a proper fraction is a
fraction whose numerator is smaller than its
denominator.
Understand that an improper fraction is a
fraction whose numerator is greater than or
equal to the denominator and is one or
greater than one.
Understand that an improper fraction can be
expressed as a whole number or a mixed
number.
Understand that a mixed number is written
as a whole number and a proper fraction.
Things to Share,
Sessions 1 – 3
unlike denominators, using words and
symbols (>, <, or =).
3.3 Essential Knowledge and Skills Name and write fractions (including
mixed numbers) represented by a
model to include halves, thirds,
fourths, eighths, tenths, and twelfths.
Use concrete materials and pictures to
model at least halves, thirds, fourths,
eighths, tenths, and twelfths.
Compare fractions using the terms
greater than, less than, or equal to and
the symbols ( <, >, and =).
Comparisons are made between
fractions with both like and unlike
denominators, using models, concrete
materials and pictures.
Fractions are built from unit fractions. For
example, 5/4 represents the point on a
number line obtained by marking off five
lengths of ¼ to the right of zero.
Fractions apply to situations where a whole is decomposed into equal parts; use
fractions to describe parts of wholes.
Compare and order fractional quantities
with equal numerators or equal
denominators, using the fractions
themselves, tape diagrams, number line
representations, benchmark fractions, and
area models. Use > and < symbols to
record the results of comparisons.
Creating Fraction
Strips
Something’s Fishy
Fraction Strip
Addition
Four in a Row
Fraction Strip
Subtraction
Meter Strip
Which Is Closer?
The In-Between
Game
Fun with Fractions
– Developing the
Region Model http://illuminations.n
ctm.org/LessonDetai
l.aspx?ID=U113
Grade 3 Quarter 3 School Year 2011-2012
5 Days
3.7 Essential Questions
3.7 Essential Understandings Understand that a proper fraction is a
fraction whose numerator is smaller than its
denominator.
Understand that an improper fraction is a
fraction whose numerator is greater than or
equal to the denominator and is one or
greater than one.
Understand that an improper fraction can be
expressed as a whole number or a mixed
number.
Understand that a mixed number is written
as a whole number and a proper fraction. A
mixed number is the sum of a whole
number and the proper fraction.
Understand that computation with fractions
uses the same strategies as whole number
computation.
SOL 3.7 The student will add and subtract
proper fractions having like
denominators of 12 or less.
3.7 Essential Knowledge and Skills
Demonstrate a fractional part of a
whole, using
– region/area models (e.g., pie
pieces, pattern blocks,
geoboards, drawings);
– set models (e.g., chips, counters,
cubes, drawings); and
– length/measurement models (e.g.,
nonstandard units such as rods,
connecting cubes, and
drawings).
Name and write fractions and mixed
numbers represented by drawings or
concrete materials.
Represent a given fraction or mixed
number, using concrete materials,
pictures, and symbols. For example,
write the symbol for one-fourth and
represent it with concrete materials
and/or pictures.
Add and subtract with proper fractions
having like denominators using
concrete materials and pictorial
models representing area/regions
(circles, squares, and rectangles),
length/measurements (fraction bars
and strips), and sets (counters).
3 days Enrichment, Assessment, and
Remediation
Quarter 4 Grade 3 Mathematics
School Year 2011-12
Number of
Days
Topic and Essential Questions
(Students should be able to answer essential
questions.)
REQUIRED
Critical Thinking
Lessons
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
Additional Instructional
Resources
15 Days
Probability
3.18 Essential Questions
What is probability?
Justify the number of possible outcomes for a
given situation.
Identify and explain outcomes of an event using
informal terms.
Explain and justify how the probability of an
event occurring is represented by the ratio
between 0 and 1, with 0 being impossible and 1
being certain.
3.18 Essential Understandings
Investigate, understand, and apply basic
concepts of probability.
Understand that probability is the chance of
an event happening.
SOL 3.18 The student will investigate and
describe the concept of probability as
chance and list possible results of a given
situation.
3.18 Essential Knowledge and Skills
Define probability as the chance that
an event will happen.
List all possible outcomes for a given
situation (e.g., heads and tails are the
two possible outcomes of flipping a
coin).
ESS
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml Two-Color Counter Toss
15 Days
Measurement
3.9 Essential Questions
Explain the purpose of benchmarks in
measurement.
Explain and justify a unit of length, liquid
volume, and weight/mass.
Demonstrate and explain how to
determine the actual measure of length,
liquid volume, and weight/mass.
INV: From Paces to
Feet
Investigation 4:
Balobbyland,
Sessions 1 – 3
INV: Up and Down
the Number Line
Investigation 1: Net
SOL 3.9 The student will estimate and use
U.S. Customary and metric units to measure
a) length to the nearest 1
2 inch, inch, foot,
yard, centimeter, and meter;
b) liquid volume in cups, pints, quarts,
gallons, and liters;
c) weight/mass in ounces, pounds, grams,
and kilograms; ….
ESS
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml Meter Strip p.
Getting to Know You p.
How Much Does It Hold?
p.
How Heavy Is It? p.
Quarter 4 Grade 3 Mathematics
School Year 2011-12
3.9 Essential Understandings
Understand how to estimate measures of
length, liquid volume, weight/mass, area and
perimeter.
Understand how to determine the actual
measure of length, liquid volume,
weight/mass, area and perimeter.
Understand that perimeter is a measure of the
distance around a polygon.
Understand that area is a measure of square
units needed to cover a surface.
Change,
Sessions 1 – 8
3.9 Essential Knowledge and Skills
Estimate and use U.S. Customary and
metric units to measure lengths of
objects to the nearest 1
2 of an inch,
inch, foot, yard, centimeter, and meter.
Determine the actual measure of length
using U.S. Customary and metric units
to measure objects to the nearest 1
2 of
an inch, foot, yard, centimeter, and
meter.
Estimate and use U.S. Customary and
metric units to measure liquid volume
to the nearest cup, pint, quart, gallon,
and liter.
Determine the actual measure of liquid
volume using U.S. Customary and
metric units to measure to the nearest
cup, pint, quart, gallon, and liter.
Estimate and use U.S. Customary and
metric units to measure the
weight/mass of objects to the nearest
ounce, pound, gram, and kilogram.
http://smartmeasurement.wikispaces.com/
Smart Measurement
8 Days
Perimeter and Area
3.10 Essential Questions
Solve problems involving perimeters of
polygon.
Add given side lengths, and multiply for the
case of equal sides.
Find an unknown length of a side in a polygon
given the perimeter and all other side lengths.
Exhibit rectangles with the same perimeter
and different area, and with the same area and
different perimeter.
SOL 3.10 The student will
a) measure the distance around a polygon
in order to determine perimeter; and
b) count the number of square units needed
to cover a given surface in order to
determine area.
3.10 Essential Knowledge and Skills
Measure each side of a variety of
polygons and add the measures of the
sides to determine the perimeter of
INV: Flips Turns, and
Area
Investigation 2: Finding
Area, Sessions 1 – 5
Quarter 4 Grade 3 Mathematics
School Year 2011-12
3.10 Essential Understandings
Understand the meaning of a polygon as a
closed figure with at least three sides. None
of the sides are curved and there are no
intersecting lines.
Understand that perimeter is a measure of the
distance around a polygon.
Understand how to determine the perimeter
by counting the number of units around a
polygon.
Understand that area is a measure of square
units needed to cover a surface.
Understand how to determine the area by
counting the number of square units.
Compare and contrast area and perimeter.
Represent and explain the area and perimeter
of a figure.
each polygon.
Determine the area of a given surface
by estimating and then counting the
number of square units needed to cover
the surface.
~Understand and use the concepts of area
measurement:
~A square with side length 1 unit called “a
unit square” is said to have one square unit
of area.
~A plane figure which can be covered
without gaps or overlaps by n unit squares
has an area of n square units. Areas of some
other figures can be measured with by using
fractions of unit squares or using figures
whose areas have been found by
decomposing other figures.
Determine and compare areas by counting
square units. Use cm2, m
2, in
2, ft
2, and
improvised units.
Multiplication of whole numbers can be
represented by area models; a rectangular
region that is a length units (where a and b
are whole numbers) and tiled with unit
squares illustrates why the rectangle
encloses an area of a x b square units.
Quarter 4 Grade 3 Mathematics
School Year 2011-12
3 Days
Time
3.11 Essential Questions
Determine and explain elapsed time.
3.11 Essential Understandings
Understand how to determine elapsed time in
one-hour increments over a 12-hour period.
SOL 3.11 The student will …
b) determine elapsed time in one-hour
increments over a 12-hour period.
3.11 Essential Knowledge and Skills
When given the beginning time and
ending time, determine the elapsed
time in one-hour increments
within a 12-hour period.
Solve practical problems in relation to
time that has elapsed.
www.learnnc.org/lp/pages/3503
Disney World Timelines
2 Days
Enrichment, Assessment, and Remediation