GRADE 3 ATHEMATICS CURRICULUM UIDE...Grade 3 Mathematics Nine Weeks Overview 1st rdQuarter 2nd Quarter 3 Quarter 4th Quarter Time 3.11 a, b 3.12 Temperature 3.13 Graphing 3.17 a, b,

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

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_scope_sequence/scopeseq_math3.pdf


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

http://www.learnnc.org/lp/pages/3260




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

http://illuminations.nctm.org/LessonDetail.aspx?ID=L701



http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml


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 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



http://illuminations.nctm.org/LessonDetail.aspx?id=U109




• Understand the meanings of multiplication and

division.

• Understand the models used to represent multiplying

and dividing whole numbers.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



• 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.


• 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.


• 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




• 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


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 >, <, =).


• 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.


• 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







Number of

Days

Topics, Essential Questions, and


(Students should be able to answer

essential questions.)

REQUIRED Critical

Thinking Lessons



Additional

Instructional

Resources

8 days

Patterns



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 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.


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


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







Demonstrate and explain strategies that can

be used for finding sums and difference using

fractions.


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

http://illuminations.nctm.org/LessonDetail.aspx?ID=U113




5 Days


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.


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




Additional Instructional

Resources

15 Days

Probability


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.


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.


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


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.










School Year 2011-12


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


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.


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.


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


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.


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




School Year 2011-12


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.


School Year 2011-12

3 Days

Time


Determine and explain elapsed time.


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.


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




Documents

GRADE 3 ATHEMATICS CURRICULUM UIDE...Grade 3 Mathematics Nine Weeks Overview 1st rdQuarter 2nd Quarter 3 Quarter 4th Quarter Time 3.11 a, b 3.12 Temperature 3.13 Graphing 3.17 a, b,