GRADE 4 ATHEMATICS CURRICULUM UIDE

GRADE 4 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 4 Mathematics Nine Weeks Overview

1st Quarter 2

nd Quarter 3

rd Quarter 4

th Quarter

Place value 4.1

Add and subtract

whole numbers 4.4 a, b, d

Functions 4.15

Equality 4.16

Multiplication and division

of whole numbers 4.4

Probability 4.13

Graphing 4.14

Fractions 4.5 a, b, d

4.2

Decimals 4.3

4.5 c

Measurement 4.7

4.6

4.8

Geometry 4.10

4.11

4.12

Elapsed time 4.9

Grade 4 Quarter 1 School Year 2011-12

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

ESS: VDOE Enhanced Scope and Sequence

25 days

Working with Whole Numbers 4.1 Essential Questions • Demonstrate and explain the relationship

between each place in a number. • Demonstrate and explain how the place value

system can be used to name and compare large numbers.

• Compare and contrast the appropriateness of using estimation and finding the exact value.

4.1 Essential Understandings • Understand the relationships in the place

value system in which the value of each place is ten times the value of the place to its right.

• Use the patterns in the place value system to read and write numbers.

• Understand that reading place value correctly is essential when comparing numbers.

• Understand that rounding gives a close number to use when exact numbers are not needed for the situation at hand.

• Develop strategies for rounding.

INV: Mathematical Thinking at Grade 4 Investigation 1: “How Many Hundreds”, Sessions 1 – 4 Investigation 3: “Using Number Patterns”, Sessions 1 - 5 INV: Landmarks in the Thousands Investigation 1: “Working with 100”, Sessions 1 – 3 Investigation 2: “Exploring Multiples of 100”, Sessions 1 – 5 Investigation 3: “How Much is 1000”, Sessions 1 – 5 Investigation 4: “Making a 10,000 Chart”, Sessions 1 - 3

SOL 4.1 The student will a) identify orally and in writing the place value for each digit in a whole number expressed through millions; b) compare two whole numbers expressed through millions using symbols (>, <, or =); and c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. 4.1 Essential Knowledge and Skills • Identify and communicate, both orally and

in written form, the placed value for each digit in whole numbers expressed through the one millions place.

• Read whole numbers through the one millions place that are presented in standard format, and select the matching number in written format.

• Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format.

• Identify and use the symbols for greater than, less than, and equal to.

• Compare two whole numbers expressed through the one millions, using symbols >, <, or =.

• Round whole numbers expressed through

ESS: • Location, Location,

Location • Estimation Game • Modeling Addition and

Subtraction • Multiplying and

Trading • Balance Beams • Weighty Problems

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_scope_sequence/scopeseq_math4.pdf

~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4.4 Essential Questions • Demonstrate and explain finding a sum, a

difference. • Demonstrate and explain inverse operations.

4.4 Essential Understandings • Develop and use strategies to estimate whole

number sums and differences and to judge the reasonableness of such results.

• Understand that addition and subtraction are inverse operations.

• Understand how to solve single-step and multistep problems using whole number operations.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.15 Essential Questions • Create and justify numerical patterns using

words, tables, graphs, and/or symbols. • Analyze and extend numerical patterns using

various methods. 4.15 Essential Understandings Understand that patterns and functions can be

represented in many ways and described using words, tables, graphs, and symbols.

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

the one millions place to the nearest thousand, ten thousand, and hundred-thousand place.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.4 The student will a) estimate sums, differences, …; b) add, subtract, and multiply whole numbers; d) solve single-step and multistep addition, subtractions, …problems with whole numbers. 4.4 Essential Knowledge and Skills • Estimate whole number sums, differences. • Refine estimates by adjusting the final

amount, using terms such as closer to, between, and a little more than.

• Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, using paper and pencil, and using a calculator.

• Solve single-step and multistep problems using whole number operations.

• Verify the reasonableness of sums, differences … of whole numbers using estimation.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.15 The student will recognize, create, and extend numerical and geometric patterns. 4.15 Essential Knowledge and Skills • Describe geometric and numerical

patterns, using tables, symbols, or words. • Create geometric and numerical patterns,

using concrete materials, number lines, tables, and words.

• Extend geometric and numerical patterns, using concrete materials, number lines, tables, and words.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.16 The student will

~~~~~~~~~~~~~~~~~~~~ Grade 4 ESS: • This Fruit is a Mass! • Kiddy Pool Grade 5 ESS: • Measurement Mania

Smart Measurement Site http://smartmeasurement.wikispaces.com/ ~~~~~~~~~~~~~~~~~~ Exploration of a Balance

http://smartmeasurement.wikispaces.com/

http://smartmeasurement.wikispaces.com/

20 days

4.16 Essential Questions • What is an equation? • Demonstrate and explain the associative

property. • How are the associative properties for

addition and multiplication alike? • Demonstrate and explain the commutative

property. • How are the commutative properties for

addition and multiplication alike? • Compare and contrast the associative

properties for addition and multiplication. 4.16 Essential Understandings • Understand that mathematical relationships

can be expressed using equations. • Understand that quantities on both sides of an

equation must be equal. • Understand that the associative property for

addition means you can change the groupings of three or more addends without changing the sum.

• Understand that the associative property for multiplication means you can change the groupings of three or more factors without changing the product.

a) recognize and demonstrate the meaning of equality in an equation; and b) investigate and describe the associative property for addition and multiplication. 4.16 Essential Knowledge and Skills • Recognize and demonstrate that the equals

sign (=) relates equivalent quantities in an equation.

• Write an equation to represent equivalent mathematical relationships (e.g., 4 × 3 = 2 × 6).

• Recognize and demonstrate appropriate use of the equals sign in an equation.

• Investigate and describe the associative property for addition as (6 + 2) + 3= 6 + (2 + 3).

• Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4).

(Lesson 2)

3 days Enrichment, Assessment, and Remediation


Page 1

Number

of Days

Topics, Essential Questions, and

Essential Understandings

(Students should be able to answer

essential questions.)

REQUIRED

Critical

Thinking

Lessons

Standards of Learning

Essential Knowledge and Skills

Additional

Instructional

Resources

ESS: VDOE

Enhanced Scope

and Sequence

Lessons

20 days

Working with Whole Numbers

4.4 Essential Questions

There are many methods for

determining a product. What are the

criteria considered when choosing a

strategy?

What are inverse relationships?

What does it mean to divide?

What does multiplication mean?

What effect does multiplication have

on a number?

What does the divisor represent in a

real life application? Dividend?

Quotient? How are each of these

represented using the three division

models?

What is the similarity between

multiplication and addition?

What is the similarity between

division and subtraction?

4.4 Essential Understandings

All students should:

Develop and use strategies to

estimate whole number sums and

Packages and

Groups

Investigation 2:

Double Digit

Multiplication,

Sessions 1 – 3

Investigation 3:

Multiplication

and Division

Choices,

Sessions 1 - 10

SOL 4.4 The student will

a) a) estimate … products, and quotients

of whole numbers;

b) …multiply whole numbers;

c) c) divide whole numbers, finding

quotients with and without remainders;

and

d) d) solve single-step and multistep …

multiplication problems with whole

numbers.

4.4 Essential Knowledge and Skills

Estimate whole number …

products, and quotients.

Refine estimates by adjusting the

final amount, using terms such as

closer to, between, and a little more

than.

Estimate and find the products of

two whole numbers ….

Estimate and find the quotient of

two whole numbers….

Solve single-step and multipstep

problems using whole number

operations.

Verify the reasonableness of sums,

ESS:

http://www.doe.vir

ginia.gov/testing/s

ol/standards_docs/

mathematics/index

.shtml

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






Page 2

differences and to judge the

reasonableness of such results.

Understand that addition and

subtraction are inverse operations.

Understand that division is the

operation of making equal groups or

equal shares. When the original

amount and the number of shares are

known, divide to find the size of each

share. When the original amount and

the size of each share are known,

divide to find the number of shares.

Understand that multiplication and

division are inverse operations.

Understand various representations of

division and the terms used in

division are dividend, divisor, and

quotient.

dividend divisor = quotient

quotient divisor dividend

Understand how to solve single-step

and multistep problems using whole

number operations.

differences, products, and quotients

of whole numbers using estimation.

5 days

Outcomes and Data


Between what 2 numbers do probability

values lie? Why?

Explain how the outcome of a simple


a) predict the likelihood of an outcome of

a simple event; and

b) represent probability as a number

between 0 and 1, inclusive.


Page 3

event relates to the numbers of 0 and 1.

Identify the likelihood of an event

occurring and relate it to its rational

representation.

Provide a real life example of something

that has a probability of 1. 0. ½ and

others in between.

Represent the probability of an event as a

common fraction.


Understand and apply basic concepts of

probability.

Describe events as likely or unlikely and

discuss the degree of likelihood, using

the terms certain, likely, equally likely,

unlikely, and impossible.

Predict the likelihood of an outcome of

a simple event and test the prediction.

Understand that the measure of the

probability of an event can be

represented by a number between 0 and

1, inclusive.


Model and determine all possible

outcomes of a given simple event

where there are no more than 24

possible outcomes, using a variety of

manipulatives, such as coins, number

cubes, and spinners.

Write the probability of a given

simple event as a fraction, where the

total number of possible outcomes is

24 or fewer.

Identify the likelihood of an event

occurring and relate it to its fractional

representation (e.g., impossible/0;

equally likely/1

2 ; certain/1).

Determine the outcome of an event

that is least likely to occur (less than

half) or most likely to occur (greater

than half) when the number of

possible outcomes is 24 or less.

Represent probability as a point

between 0 and 1, inclusively, on a

number line.

10 days


Collect, organize, display, and interpret data

from a variety of graphs.

Compare and contrast line, bar, picture,

circle graphs, and line plots.


Understand the difference between

representing categorical data and

representing numerical data.

Understand that line graphs show

INV: The Shape of

Data

Investigation 1:

Introduction to

Data Analysis,

Sessions 1 – 3

Investigation 2:

Landmarks in the

Data, Sessions 1 –

7

SOL 4.14 The student will collect,

organize, display, and interpret data from a

variety of graphs.


Collect data, using, for example,

observations, measurement, surveys,

scientific experiments, polls, or

questionnaires.

Organize data into a chart or table.

Construct and display data in bar

ESS

http://www.doe.virg

inia.gov/testing/sol/s

tandards_docs/math

ematics/index.shtml

Lucky Sums?

Looking for a Pet!

How Certain Are

You?

Sandwich Data






Page 4

change over time (numerical data).

Understand that bar graphs should be

used to compare counts of different

categories (categorical data).

Understand how data displayed in bar

and line graphs can be interpreted so

that informed decisions can be made.

Understand that the title and labels of the

graph provide the foundation for

interpreting the data.

graphs, labeling one axis with equal

whole number increments of 1 or

more (numerical data) (e.g., 2, 5, 10,

or 100) and the other axis with

categories related to the title of the

graph (categorical data) (e.g.,

swimming, fishing, boating, and water

skiing as the categories of “Favorite

Summer Sports”).

Construct and display data in line

graphs, labeling the vertical axis with

equal whole number increments of 1

or more and the horizontal axis with

continuous data commonly related to

time (e.g., hours, days, months, years,

and age). Line graphs will have no

more than 10 identified points along a

continuum for continuous data. For

example, growth charts showing age

versus height place age on the

horizontal axis (e.g., 1 month, 2

months, 3 months, and 4 months).

Title or identify the title in a given

graph and label or identify the axes.

Interpret data from simple line and bar

graphs by describing the

characteristics of the data and the data

as a whole (e.g., the category with the

greatest/least, categories with the

same number of responses,

similarities and differences, the total

number). Data points will be limited

to 30 and categories to 8.

Interpret the data to answer the

question posed, and compare the

answer to the prediction (e.g., “The

Say, “Here!”

Spinning Colors


Page 5

summer sport preferred by most is

swimming, which is what I predicted

before collecting the data.”).

Write at least one sentence to describe

the analysis and interpretation of the

data, identifying parts of the data that

have special characteristics, including

categories with the greatest, the least,

or the same.

6 days Assessment, Enrichment, and

Remediation


Page 1

Number

of Days



(Students should be able to answer

essential questions.)

REQUIRED

Critical

Thinking

Lessons

Standards of Learning


Additional

Instructional

Resources

ESS: VDOE

Enhanced Scope

and Sequence

Lessons

22 days

Working with Rational Numbers

Fractions

4.5 a, b, d Essential Questions

Compare and contrast whole number

operations with fraction operations.

Explain why least common multiples

and least common denominators are

used when computing the sums and

differences of fractions.

Give an example of a practical

problem using fractions.

Give an example of a practical

problem using decimals.

4.5 a, b, d Essential Understandings Understand and use common multiples

and common factors for simplifying

fractions.

Develop and use strategies to estimate

addition and subtraction involving

fractions ….

Use visual models to add and subtract

with fractions and decimals.

INV: Different

Shapes, Equal

Pieces

Investigation 3:

Ordering

Fractions,

Sessions 1 – 9

INV: Three Out

of Four Like

Spaghetti

Investigation 1:

Using Fractions

to Describe Data,

Sessions 1 – 4

SOL 4.5 a, b, d The student will a) determine common multiples and

factors, including least common multiple

and greatest common factor;

b) add and subtract fractions having like

and unlike denominators that are limited to

2, 3, 4, 5, 6, 8, 10, and 12, and simplify the

resulting fractions, using common

multiples and factors;

4.5 a, b, d Essential Knowledge and

Skills Find common multiples and common

factors of numbers.

Determine the least common multiple

and greatest common factor of

numbers.

Use least common multiple and/or

greatest common factor to find a

common denominator for fractions.

Add and subtract with fractions

having like denominators whose

denominators are limited to 2, 3, 4, 5,

6, 8, 10, and 12, and simplify the

resulting fraction using common

multiples and factors.

Add and subtract with fractions having

ESS

http://www.doe.vir

ginia.gov/testing/s

ol/standards_docs/

mathematics/index

.shtml

Fraction Grids

Register Tape

Fractions

Circle Fractions

Fraction Strips

Egg Carton

Fractions

Pattern Block

Fractions

Build the Whole

Pattern Block

Fraction Game

Comparing

Fractions

Which is Closer?

Fraction Strip

Addition

Fraction Riddles

Fraction Bar Kit







Page 2

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

4.2 a, b, c Essential Questions

Demonstrate and explain patterns

within equivalent fractions.

Given more than one fraction,

how do you determine which

fraction is smallest?

Identify the division statement

that represents a fraction.

Explain the strategy of using

landmark ¼, ½, ¾ help you in

comparing and ordering fractions.

Explain how a fraction can

represent a relationship as well as

a division operation.

Justify how a fractional number

describes part of a set.

Explain how to determine a

fraction is in simplest form.

Demonstrate and explain that

multiple representations of

unlike denominators whose





Solve problems that involve adding

and subtracting with fractions having

like and unlike denominators whose





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

SOL 4.2 a, b, c The student will

a) compare and order fractions and mixed

numbers;

b) represent equivalent fractions; and

c) identify the division statement that

represents a fraction.

4.2 Essential Knowledge and Skills Compare and order fractions having

denominators of 12 or less, using

manipulative models and drawings,

such as

region/area models.

Compare and order fractions with like

denominators by comparing number

of parts (numerators) (e.g., 1

5 <

3

5 ).

Compare and order fractions with like

numerators and unlike denominators

by comparing the size of the parts

INV: Different

Shapes, Equal

Pieces

Investigation 1:

Parts of Squares:

Halves, Fourths,

and Eighths,

Sessions 1 – 5

Investigation 2:

Parts of

Rectangles:

Thirds, Sixths, and

Twelfths,

Sessions 1 – 4


Page 3

answers are equivalent. (For

example, ½ and 2/4 are the same.)

Explain equivalent fractions through

multiple representations.

4.2 a, b, c Essential Understandings

Two fractions are equivalent

(represent the same number) when both

fractions correspond to the same point on

the number line.

Recognize and generate

equivalent fractions with denominators of

2, 3, 4, and 6 (e.g., ½ =2/4, 4/6=2/3), and

explain the reasoning.

Fractions apply to situations

where a whole is decomposed into equal

parts; use fractions to describe parts of

wholes. For example, to show 1/3 of a

length, decompose the length into 3 equal

parts and show one of the parts

Develop an understanding of fractions

as parts of unit wholes, as parts of a

collection, and as locations on a number

line. Understand that a mixed number is a

fraction that has two parts: a whole

number and a proper fraction. The

mixed number is the sum of these two

parts.

Use models, benchmarks, and

equivalent forms to judge the size of

fractions.

(e.g., 3

9 <

3

5 ).

Compare and order fractions having

unlike denominators of 12 or less by

comparing the fractions to

benchmarks

(e.g., 0, 1

2 or 1) to determine their

relationships to the benchmarks or by

finding a common denominator.

Compare and order mixed numbers

having denominators of 12 or less.

Use the symbols >, <, and = to

compare the numerical value of

fractions and mixed numbers having

denominators of 12 or less.

Represent equivalent fractions

through twelfths, using region/area

models, set models, and measurement

models.

Identify the division statement that

represents a fraction (e.g., 3

5 means

the same as 3 divided by 5).


Page 4

~~~~~~~~

22 days

Recognize that a whole divided into

nine equal parts has smaller parts than if

the whole had been divided into five

equal parts.

Recognize and generate equivalent

forms of commonly used fractions and

decimals.

Understand the division statement that

represents a fraction.

Understand that the more parts the

whole is divided into, the smaller the

parts (e.g.,

1

5 <

1

3 ).

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

Decimals

4.3 a, b, c, d Essential Questions

Prove how a fraction and a decimal can

represent the same value.

Explain the difference between reading a

number with a decimal compared to

reading a number without a decimal.

Describe the differences between saying,

reading, and/or writing one hundred and

one hundredths? (also do tens vs. tenths.

. . and thousands vs. thousandths)

Explain how the place value system is

used to name and compare decimal

numbers smaller than 1.

Justify how the magnitude of a base-10

model represents decimals.

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

SOL 4.3 The student will a) read, write, represent, and identify

decimals expressed through thousandths;

b) round decimals to the nearest whole

number, tenth, and hundredth;

c) compare and order decimals; and

d) given a model, write the decimal and

fraction equivalents.

4.3 Essential Knowledge and Skills Investigate the ten-to-one place value

relationship for decimals through

thousandths, using Base-10

manipulatives (e.g., place value

mats/charts, decimal squares, Base-10

blocks, money).

Represent and identify decimals

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

ESS

http://www.doe.vir

ginia.gov/testing/s

ol/standards_docs/

mathematics/index

.shtml

Comparing

Decimals

Rounding

Decimals

Decimal Rings

Reading and

Writing Decimals







Page 5

Demonstrate and prove fraction and

decimal equivalents.

Compare and prove decimal values using

>, <. =.

Explain when it would be appropriate to

round a number to a whole number,

tenths, or hundredths.

4.3 a, b, c, d Essential Understandings Understand the place value structure of

decimals and use this structure to read,

write, and compare decimals.

Understand that decimal numbers can

be rounded to an estimate when exact

numbers are not needed for the situation

at hand.

Understand that decimals are rounded in

a way that is similar to the way whole

numbers are rounded.

Understand that decimals and fractions

represent the same relationship;

however, they are presented in two

different formats.

Understand that models are used to

show decimal and fraction equivalents.

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

4.5 c Essential Questions

Compare and contrast adding and

subtracting fractions and decimals.

Compare and contrast whole number

operations with decimal operations.

4.5 c Essential Understandings Develop and use strategies to estimate

expressed through thousandths, using

Base-10 manipulatives, pictorial

representations, and numerical

symbols (e.g., relate the appropriate

drawing to 0.05).

Identify and communicate, both orally

and in written form, the position and

value of a decimal through

thousandths. For example, in 0.385,

the 8 is in the hundredths place and

has a value of 0.08.

Read and write decimals expressed

through thousandths, using Base-10

manipulatives, drawings, and

numerical symbols.

Round decimals to the nearest whole

number, tenth, and hundredth.

Compare decimals, using the symbols

>, <, =.

Order a set of decimals from least to

greatest or greatest to least.

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

SOL 4.5 c The student will c) add and subtract with decimals; and….

4.5 c Essential Knowledge and Skills Find common multiples and common

factors of numbers.

Determine the least common multiple

and greatest common factor of


Page 6

addition and subtraction involving

fractions ….

Use visual models to add and subtract

with …decimals.

numbers.

Use least common multiple and/or

greatest common factor to find a

common denominator for fractions.


having like denominators whose






having unlike denominators whose





Solve problems that involve adding

and subtracting with fractions having

like and unlike denominators whose





.

4 days Enrichment, Assessment, and

Remediation

Grade 4 Quarter 4

School Year 2011-12

Number

of Days



(Students should be able to answer essential

questions.)

REQUIRED

Critical Thinking

Lessons

Standard(s) of Learning


Additional Instructional

Resources

ESS: VDOE Enhanced

Scope and Sequence

15 days

Measurement


Length/Distance

Give a real life example of what you would

measure in inches, feet, yards, miles,

millimeters, centimeters, meters, and

kilometers.

Why are there two different units of

measurement?

What is an appropriate tool to measure in

inches, feet, yards, millimeters, centimeters,

meters, and kilometers?



Use benchmarks to estimate and measure

length.

Understand how to convert units of length

between the U.S. Customary and metric

systems, using ballpark comparisons.

Understand the relationship between U.S.

Customary units and the relationship between

metric units.

Measurement

Benchmarks

(from 5th grade

Investigations)

Investigation 1:

Measures of Length

and Distance,

Sessions 1 – 6

Investigation 2:

Measures of Weight

and Liquid Volume,

Sessions 1 - 6


a) estimate and measure length, and describe

the result in both metric and U.S.

Customary units; and

b) identify equivalent measurements between

units within the U.S. Customary system

(inches and feet; feet and yards; inches and

yards; yards and miles) and between units

within the metric system (millimeters and

centimeters; centimeters and meters; and

millimeters and meters).


Determine an appropriate unit of measure

(e.g., inch, foot, yard, mile, millimeter,

centimeter, and meter) to use when

measuring everyday objects in both metric

and U.S. Customary units.

Estimate the length of everyday objects

(e.g., books, windows, tables) in both

metric and U.S. Customary units of

measure.

Measure the length of objects in both

metric and U.S. Customary units,

measuring to the nearest inch (1

2 ,

1

4 ,

1

8 ),

foot, yard, mile, millimeter, centimeter, or

meter, and record the length including the

appropriate unit of measure (e.g., 24

inches).

http://illuminations.nctm.or

g/LessonDetail.aspx?id=L1

84

How Long? How Tall?

How Wide? How Deep?

http://illuminations.nctm.or

g/LessonDetail.aspx?id=L6

35

http://illuminations.nctm.org/LessonDetail.aspx?id=L184






Grade 4 Quarter 4

School Year 2011-12

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


Weight/Mass

What is the difference between weight and mass?


measure in ounces, pounds, tons, grams, and

kilograms.



weight/mass.

Identify equivalent measures between units

within the U.S. Customary and between units

within the metric measurements.

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


Liquid Volume

Compare estimates of the length of

objects with the actual measurement of

the length of objects.

Identify equivalent measures of length

between units within the U.S. Customary

measurements and between units within

the metric measurements.

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


a) a) estimate and measure weight/mass and

describe the results in U.S. Customary and

metric units as appropriate; and

b) b) identify equivalent measurements between

units within the U.S. Customary system

(ounces, pounds, and tons) and between units

within the metric system (grams and

kilograms).



(e.g., ounce, pound, ton, gram, kilogram)

to use when measuring everyday objects

in both metric and U.S. Customary units.

Measure objects in both metric and U.S.

Customary units (e.g., ounce, pound, ton,

gram, or kilogram) to the nearest

appropriate measure, using a variety of

measuring instruments.

Record the mass of an object including the

appropriate unit of measure (e.g., 24

grams).

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


a) estimate and measure liquid volume and

describe the results in U.S. Customary units;

Grade 4 Quarter 4

School Year 2011-12


measure in cups, pints, quarts, and gallons.




volume.

Identify equivalent measurements between

units within the U.S. Customary system.

and

b) identify equivalent measurements between

units within the U.S. Customary system (cups,

pints, quarts, and gallons).


The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations to


(cups, pints, quarts, gallons) to use when

measuring liquid volume in U.S.

Customary units.

Estimate the liquid volume of containers

in U.S. Customary units of measure to the

nearest cup, pint, quart, and gallon.

Measure the liquid volume of everyday

objects in U.S. Customary units, including

cups, pints, quarts, and gallons, and record

the volume including the appropriate unit

of measure (e.g., 24 gallons).

Identify equivalent measures of volume

between units within the U.S. Customary

system.

20 days

Geometry

Plane Figures


Compare and contrast a line, line segment,

angle and ray.

Create and identify a line, line segment, angle,

and ray.

What is the relationship between a line

segment and an angle?

Explain the relationship between a ray and an

angle.


a) identify and describe representations of

points, lines, line segments, rays, and angles,

including endpoints and vertices; and

b) identify representations of lines that

illustrate intersection, parallelism,

perpendicularity


Grade 4 ESS Lessons:

Simple Pictures

Geometry Review

Geometric Figures

Congruent Figures

Coordinate Points

Toothpick, Door and

Staircase Patterns

Investigations:

Mathematical Thinking in

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_scope_sequence/scopeseq_math4.pdf

Grade 4 Quarter 4

School Year 2011-12

Identify and justify real life examples of

parallel lines.

Identify and justify real life examples

perpendicular lines.

Compare and contrast characteristics of

intersecting lines and perpendicular lines.


Understand that points, lines, line segments,

rays, and angles, including endpoints and

vertices are fundamental components of

noncircular geometric figures.

Understand that the shortest distance between

two points on a flat surface is a line segment.

Understand that lines in a plane either

intersect or are parallel. Perpendicularity is a

special case of intersection.

Identify practical situations that illustrate

parallel, intersecting, and perpendicular lines.

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


Compare and contrast geometric

transformations.

Demonstrate and explain congruency of a

plane figure after a reflection, translation,

and/or rotation.

Demonstrate and justify various strategies for

rotation, reflection, and translation of an

image.

What are real life models of reflection,

translation, and rotation?

Prove the image of a plane figure is congruent

to the original image after a transformation.

Explain what understandings are important

when determining if two figures are

congruent.

Identify and describe representations of

points, lines, line segments, rays, and

angles, including endpoints and vertices.

Understand that lines in a plane can

intersect or are parallel. Perpendicularity

is a special case of intersection.

Identify practical situations that illustrate

parallel, intersecting, and perpendicular

lines.

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


a) investigate congruence of plane figures

after geometric transformations, such as

reflection, translation, and rotation, using

mirrors, paper folding, and tracing; and

b) recognize the images of figures resulting

from geometric transformations, such as

translation, reflection, and rotation.


Recognize the congruence of plane figures

resulting from geometric transformations such

as translation, reflection, and rotation, using

mirrors, paper folding and tracing.

Grade 4

Investigation 4: “Making

Geometric Patterns”,

Sessions 1 – 6

Grade 4 Quarter 4

School Year 2011-12


Understand the meaning of the term

congruent.

Understand how to identify congruent

figures.

Understand that the orientation of figures

does not affect congruency or

noncongruency.

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


What is a polygon?

Create and identify polygons with ten or

fewer sides.


Identify polygons with 10 or fewer sides in

everyday situations.

Identify polygons with 10 or fewer sides in

multiple orientations (rotations, reflections,

and translations of the polygons)

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


a) define polygon; and

b) identify polygons with ten or fewer sides.


Define and identify properties of polygons

with 10 or fewer sides.

Identify polygons by name with 10 or

fewer sides in multiple orientations

(rotations, reflections, and translations of

the polygons)

5 days

Elapsed Time


What is elapsed time?

How do you determine elapsed time?

Determine elapsed time given between 2

given hours and additional minutes.

Given a beginning and ending time of an

event, use at least two different strategies to

calculate elapsed time.

Provided an ending time and an elapsed time,

determine the start time of the event.


Understand the “counting on” strategy for

determining elapsed time in hour and minute

SOL 4.9 The student will determine elapsed

time in hours and minutes within a 12-hour

period.


The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations to

Determine the elapsed time in hours and

minutes within a 12-hour period (times

can cross between a.m. and p.m.).

Solve practical problems in relation to

time that has elapsed

Grade 4 Quarter 4

School Year 2011-12

increments over a 12-hour period from a.m.

to a.m. or p.m. to p.m.

3 days Enrichment, Assessment, and Remediation

GRADE 4 ATHEMATICS CURRICULUM UIDE

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