try it out! measuring up to the ga standards

Try It Out! Sample Pack | Math | Grade 5 | Lesson 5

Measuring Up to the GA Standards

The Try It Out! sample pack features:

• 1 full student lesson with complete Teacher Edition lesson • 1 full Table of Contents for your grade level • Correlation to your state standards

Developed to meet the rigor of the standards, Measuring Up employs support for using and applying critical thinking skills with direct standards instruction that elevate and engage student thinking.

Standards-based lessons feature introductions that set students up for success with:

aVocabulary in Action

aRelevant real-world connections

aClearly identified learning goals

aConnections to prior learning

Guided Instruction and Independent Learning strengthen learning with:

aDeep thinking prompts

aCollaborative learning

aSelf-evaluation

aDemonstration of problem-solving logic

aApplication of higher-order thinking

Flexible design meets the needs of whole- or small-group instruction.Use for:

aIntroducing standards

aReinforcement or standards review

aIntervention

aRemediation

aTest Preparation

Extend learning with online digital resources!Measuring Up Live 2.0 blends instructional print resources with online, dynamic assessment and practice. Meet the needs of all students for standards mastery with resources that pinpoint student needs with customized practice.

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[ 42 ] masteryeducation.com | Mathematics | Level E Copying is prohibited.

CH

APT

ER

2 WORDS TO KNOW

decimal

expanded form

place value

Lesson 5READ, WRITE, AND COMPARE

DECIMALS 5.NBT.3, 5.NBT.3a, 5.NBT.3b

INTRODUCTIONReal-World ConnectionKelly has 0.613 pound of blueberries. Hannah has sixty-four hundredths

of a pound of blueberries. Who has a greater amount of blueberries?

Let’s see who has the greater amount of blueberries at the end of

the lesson after we practice the skills in the Guided Instruction and

Independent Practice!

What I Am Going to Learn● How to read and write decimal numbers

● How to compare decimal numbers

● How to write decimal numbers in expanded form

What I May Already Know 4.NF.6, 4.NF.7

● I know how to use decimal notation for fractions with a

denominator of 10 or 100.

● I know how to compare decimals to hundredths.

Vocabulary in Action● Decimals can be written in words.

● When you write a decimal in words you say “and” for the

decimal point.

● For example, 34.56 is thirty-four and fi fty-six hundredths.

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[ 43 ]Chapter 2 | Decimals | masteryeducation.comCopying is prohibited.

READ, WRITE, AND COMPARE DECIMALS Lesson 5

● Decimals can be written in expanded form.

● When you use expanded form, each digit is multiplied by its

place value.

● For example, 34.56 is 3 � 10 � 4 � 1 � 5 � 0.1 � 6 � 0.01

● Decimals written as numbers can be compared by place value.

● 34.56 < 34.6 because they each have 34, but 34.6 is greater

than 34.5 in the tenths place.

EXAMPLE

Write the number 213.675 in words.

Step One Write the whole number part. Use “and” for the

decimal point.

two hundred thirteen and…

Step Two For the decimal part, look at the place value of the

last digit.

The last digit is 5 and is in the thousandths place, so there are

six hundred seventy-fi ve thousandths.

Step Three Write the number.

213.675 is two hundred thirteen and six hundred seventy-fi ve

thousandths.

Ones Decimals

Hundreds Tens Ones . Tenths Hundredths Thousandths

2 1 3 . 6 7 5

TURN AND TALK

Why is it important to say “and”

for the decimal point?



Lesson 5 READ, WRITE, AND COMPARE DECIMALS

EXAMPLE

Write 578.429 in expanded form.

Each digit in the number is multiplied by its place value, the same as

you would do with whole numbers. The decimal place values can be

fractions or decimals.

Step One Find the value of each digit.

Ones Decimals


5 7 8 . 4 2 9

5 is 500 � 5 � 100

7 is 70 � 7 � 10

8 is 8 � 8 � 1

4 is 0.4 � 4 � 1 __

10

2 is 0.02 � 2 � 1 ___

100

9 is 0.009 � 9 � 1 _____

1,000

Step Two Combine the values.

5 � 100 � 7 � 10 � 8 � 1 � 4 � 1 __

10 � 2 �

1 ___

100 � 9 �

1 _____

1,000

We use decimal notation for amounts of money. Pennies are

hundredths of a dollar and dimes are tenths of a dollar.

THINK ABOUT IT

When you write a decimal number

in words, you are naming the

decimal part as a fraction:

Five hundred seventy-eight

and four hundred twenty-nine

thousandths.




You can use place value to compare decimal numbers in the same way

you compare whole numbers.

EXAMPLE

Is 0.4 greater than, less than, or equal to 0.3?

Step One Write the numbers as fractions with the

same denominator.

0.4 � 4 __

10 , 0.3 �

3 __

10

Step Two Compare the numerators.

4 __

10 >

3 __

10 , so 0.4 > 0.3.

Is 0.21 greater than, less than, or equal to 0.4?

Step One Write the numbers as fractions with the

same denominator.

0.21 � 21

___

100 , 0.4 �

4 __

10 �

40 ___

100

Step Two Compare the numerators.

21 ___

100 <

40 ___

100 , so 0.21 < 0.4.

GUIDED INSTRUCTION 1. Write 86.03 in words.

Step One Write the whole number followed by “and.”

eighty-six and…

Step Two Use a place value chart to see the place value of the

last decimal digit.

Ones Decimals


0 8 6 . 0 3 0

The last decimal digit is 3 and is in the hundredths place.

Step Three Write 86.03 in words

eighty-six and hundredths

HINT, HINT

When you say a decimal number,

do not say, “86 point 03”. Say, “86

and 3 hundredths”. This will help

you to think about the place value.




2. Write 27.304 in expanded form.

Step One Arrange the digits in a place value chart.

Ones Decimals


2 7 . 3 0 4

Step Two Write the value of each digit, using decimal fractions.

2 is 20 � 2 � 10

7 is 7 � 7 � 1

3 is 0.3 � 3 � 1 __

10

4 is 0.004 � 4 � 1 _____

1,000

Step Three Write an equation showing the sum.

27.304 � 2 � � 7 � 1 � 3 � � 4 � 1 _____

1,000

3. Compare 0.056 and 0.59.

Step One Write the decimals in fraction form with the same

denominator.

0.056 � 56 _____

1,000

0.59 � 59

___

100 �

590 _____

1,000

Step Two Compare the fractions.

56 _____

1,000 <

590 _____

1,000

So, 0.056 0.59

4. Select THREE expressions that are equal to 113.082.

Ⓐ 100 � 10 � 3 � 0.8 � 0.02

Ⓑ 100 � 10 � 3 � 0.08 � 0.002

Ⓒ 100 � 10 � 3 � 8 ___

10 �

2 ____

100

Ⓓ 100 � 10 � 3 � 8 ___

100 �

2 _____

1,000

Ⓔ 1 � 100 � 1 � 10 � 3 � 1 � 8 � 1 ___

100 � 2 �

1 _____

1,000

Ⓕ 1 � 100,000 � 1 � 10,000 � 3 � 1,000 � 8 � 10 � 2 � 1

TIPS AND TRICKS

Make sure you evaluate each

answer. Do not stop after you fi nd

the fi rst correct answer.




How Am I Doing?

What questions do you have?

Imagine what the price might be of something you enjoy. Write the

price, and then write it again in expanded form.

Each place value in a decimal gets 10 times smaller. A measurement

of 6.765 inches is very precise, but probably not necessary. Can you

think of a situation where this much accuracy would be important?

Color in the traffi c signal

that shows how you are

doing with the skill.

I am stuck.

I almost have it.

I understand

the skill.

TURN AND TALK

Pretend you are going to teach

younger students about decimals.

Think about how you would teach

someone to compare decimals

to thousandths. Then, working

with a partner, create a short

demonstration. You can use grids,

pictures, place-value blocks,

technology, or any other method

other than place-value charts.

Then present your demonstration

to the class.




INDEPENDENT PRACTICEAnswer the questions.

1. What is 51.017 in word form?

Ⓐ fi fty-one thousand and seventeen

Ⓑ fi fty-one and seventeen hundredths

Ⓒ fi fty-one and seventeen tenths

Ⓓ fi fty-one and seventeen thousandths

2. Compare the decimals. Write the correct symbol in each box.

0.04 0.14 1.5 1.15 3.01 3.010

3. What is 195.438 in expanded form using decimals?

Write your answer in the box.

4. Write an expression for 105.067 in expanded form by multiplying

each digit by a decimal fraction.


HINT, HINT

When reading a number in word

form, write out each number next

to the words.

HINT, HINT

When there is a 0 in a number you

are writing in expanded form, be

sure to pay close attention to the

place values of the other digits.




5. Which statement is true?

Ⓐ 621.071 � 621.711

Ⓑ 621.071 � 621.711

Ⓒ 621.071 � 621.711

6. Which statement is true?

Ⓐ 0.910 � 0.91

Ⓑ 45.234 � 45.134

Ⓒ 6.71 � 6.071

Ⓓ 79.012 � 79.012

7. Part AGeorge’s backpack weighs 15.207 pounds. Stephen’s backpack

weighs 15.216 pounds. Whose backpack weighs more?


Part BExplain how you found your answer. Write an expression using

�, �, or � to record the results of your comparison.

TIPS AND TRICKS

Compare the digits one at a time,

using place value and starting at

the left.

WORK SPACE




WORK SPACE

8. Felix wrote an expression for the expanded form of 307.043

by multiplying each digit by a decimal fraction. His work is

shown below.

307.043 � 3 � 100 � 7 � 1 � 4 � 1 ___ 10

� 3 � 1 ____

100

Is Felix correct? If not, explain the error he made and write the

correct expression.

8.




EXIT TICKET

Now that you have mastered reading, writing, and comparing decimal numbers, let’s

solve the problem in the Real-World Connection.

Kelly has 0.613 pounds of blueberries. Hannah has sixty-fourth hundredths of a pound

of blueberries. Who has the greater amount of blueberries?

5.NBT.3, 5.NBT.3a, 5.NBT.3b


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ANNOTATED

TEACHER EDITION

[ ii ]

Letter to Students vi

Letter to Parents and Families vii

What You’ll See in Measuring Up to the Georgia Standards of Excellence viii

5.NBT.1, 5.NBT.2

5.NBT.5

5.NBT.6

5.OA.1, 5.OA.2

Chapter 1 OPERATIONS WITH WHOLE NUMBERS

1. Understand Place-Value Patterns 1

2. Multiply Whole Numbers 10

3. Divide Whole Numbers 18

4. Write and Interpret Numerical Expressions 29

Chapter 1 Practice Test 38

5.NBT.3, 5.NBT.3a-b

5.NBT.4

Chapter 2 DECIMALS

5. Read, Write, and Compare Decimals 42

6. Round Decimals 52

GSE

GSE

LESSON

LESSON

Introduction

CONTENTS

9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb ii9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb ii 6/14/2017 11:15:51 PM6/14/2017 11:15:51 PM

[ iii ]

5.NF.1

5.NF.2

5.NF.3

5.NF.4, 5.NF.4a

5.NF.4, 5.NF.4b

5.NF.5, 5.NF.5a-b

5.NF.7, 5.NF.7a

5.NF.7, 5.NF.7b

5.NF.6, 5.NF.7, 5.NF.7c

5.MD.2

Chapter 3 OPERATIONS WITH FRACTIONS

10. Add and Subtract Fractions 94

11. Solve Word Problems Involving Fraction 104Addition and Subtraction

12. Divide Whole Numbers with Fraction Quotients 114

13. Multiply Whole Numbers by Fractions 124

14. Multiply Fractions by Fractions 134

15. Compare Factors and Products 144

16. Divide Unit Fractions by Whole Numbers 153

17. Divide Whole Numbers by Unit Fractions 162

18. Solve Word Problems Involving Fraction 171Multiplication and Division

19. Make and Use Line Plots 181


GSE LESSON

5.NBT.7

5.NBT.7

5.NBT.7

7. Add and Subtract Decimals 60

8. Multiply Decimals 70

9. Divide Decimals 80


GSE LESSON

9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb iii9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb iii 6/14/2017 11:15:53 PM6/14/2017 11:15:53 PM

[ iv ]

5.MD.1

5.MD.3, 5.MD.3a-b,

5.MD.4

5.MD.5, 5.MD.5a-b

5.MD.5, 5.MD.5c

Chapter 4 MEASUREMENT

20. Convert Measurement Units 195

21. Understand Volume 204

22. Find Volume of Rectangular Prisms 214

23. Find Volume of Solids 223


GSE LESSON

5.G.3, 5.G.4

5.G.1

5.G.2

5.OA.3

Chapter 5 GEOMETRY

24. Classify Two-Dimensional Figures 239

25. Understand the Coordinate Plane 248

26. Graph Points to Represent Problems 257

27. Use Pattern Rules 267


GSE LESSON

CONTENTS

9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb iv9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb iv 6/14/2017 11:15:54 PM6/14/2017 11:15:54 PM

[ v ]

Acknowledgments 282

Correlation to the Georgia Standards of Excellence 283

Glossary 287

Copy Masters 290

References

9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb v9781609797348_GA_MUSS_Math_Gr5_SE_Book.indb v 6/14/2017 11:15:56 PM6/14/2017 11:15:56 PM

[ 283 ][ 283 ]Correlation to the Georgia Standards of Excellence | masteryeducation.com

Correlation to the Georgia Standards of Excellence

This worktext is customized to the TGeorgia Standards of Excellence for Mathematics. Most lessons focus on one content standard for in-depth review. Mathematical Practices are interwoven throughout each lesson to connect practices to content at point-of-use and promote depth of understanding.

Georgia Standards of Excellence Lessons

Operations and Algebraic Thinking 5.OA

Write and interpret numerical expressions.

MGSE5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions

with these symbols.

4

MGSE5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical

expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply

by 2” as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without

having to calculate the indicated sum or product.

4

Analyze patterns and relationships.

MGSE5.OA.3 Generate two numerical patterns using a given rule. Identify apparent relationships

between corresponding terms. Form ordered pairs consisting of corresponding terms from the two

patterns, and graph the ordered pairs on a coordinate plane.

27

Number and Operations in Base Ten 5.NBT

Understand the place value system.

MGSE5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as

it represents in the place to its right and 1 __ 10 of what it represents in the place to its left.

1

MGSE5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by

powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied

or divided by a power of 10. Use whole-number exponents to denote powers of 10.

1

MGSE5.NBT.3 Read, write, and compare decimals to thousandths. 5

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded

form, e.g., the expanded form of 347.392 is written as 3 × 100 + 4 × 10 + 7 × 1 + 3 × ( 1 __ 10 ) +

9 × ( 1 ___ 100 ) + 2 × (

1 _____ 1,000 ).

5

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =,

and < symbols to record the results of comparisons.

5

MGSE5.NBT.4 Use place value understanding to round decimals to the hundredths place. 6

Perform operations with multi-digit whole numbers and with decimals to hundredths.

MGSE5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm (or other

strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.

2

CORRELATIONS


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CORRELATIONS


MGSE5.NBT.6 Fluently divide up to 4-digit dividends and 2-digit divisors by using at least one of the

following methods: strategies based on place value, the properties of operations, and/or the relationship

between multiplication and division. Illustrate and explain the calculation by using equations or concrete

models.(e.g., rectangular arrays, area models).

3

MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or

drawings and strategies based on place value, properties of operations, and/or the relationship between

addition and subtraction; relate the strategy to a written method and explain the reasoning used.

7, 8, 9

Number and Operations-Fractions 5.NF

Use equivalent fractions as a strategy to add and subtract fractions.

MGSE5.NF.1 Add and subtract fractions with unlike denominators by fi nding a common denominator

and equivalent fractions to produce like denominators.

10

MGSE5.NF.2 Solve word problems involving addition and subtraction of fractions, including cases of

unlike denominators (e.g., by using visual fraction models or equations to represent the problem).

Use benchmark fractions and number sense of fractions to estimate mentally and assess the

reasonableness of answers. For example, recognize an incorrect result 2 __ 5 + 1 __ 2 = 3 __ 7 , by observing that 3 __ 7 < 1 __ 2 .

11

Apply and extend previous understandings of multiplication and division to multiply and divide

fractions.

MGSE5.NF.3 Interpret a fraction as division of the numerator by the denominator ( a __ b = a ÷ b). Solve

contextual problems involving division of whole numbers leading to answers in the form of fractions or

mixed numbers by using visual fraction models or equations to represent the problem.

12

MGSE5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole

number by a fraction.

13, 14

a. Interpret the product ( a __ b ) × q as a × q ÷ b (partition the quantity q into b equal parts and then

multiply by a). Interpret the product ( a __ b ) × q as (a x q) ÷ b (multiply a times the quantity q and then

partition the product into b equal parts).

13

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the

appropriate unit fraction side lengths, and show that the area is the same as would be found

by multiplying the side lengths.

14

MGSE5.NF.5 Interpret multiplication as scaling (resizing), by: 15

a. Compare the size of a product to the size of one factor on the basis of the size of the other factor,

without performing the indicated multiplication. Example: 4 x 10 is twice as large as 2 x 10.15

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater

than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar

case); explain why multiplying a given number by a fraction less than 1 results in a product smaller

than the given number; and relate the principle of fraction equivalence a __ b =

(n × a) ______ (n × b) to the eff ect of

multiplying a __ b by 1.

15

MGSE5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by

using visual fraction models or equations to represent the problem.

18


[ 285 ][ 285 ]Correlation to the Georgia Standards of Excellence | masteryeducation.com


MGSE5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole

numbers and whole numbers by unit fractions.

16, 17, 18

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

For example, create a story context for ( 1 __ 3 ) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that ( 1 __ 3 ) ÷ 4 = 1 __ 12 because ( 1 __ 12 ) × 4 = 1 __ 3 .

16

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ ( 1 __ 5 ), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ ( 1 __ 5 ) = 20 because 20 × ( 1 __ 5 ) = 4.

17

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and

division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to

represent the problem. For example, how much chocolate will each person get if 3 people share 1 __ 2 lb of chocolate equally? How many 1 __ 3 -cup servings are in 2 cups of raisins?

18

Measurement and Data 5.MD

Convert like measurement units within a given measurement system.

MGSE5.MD.1 Convert among diff erent-sized standard measurement units within a given measurement

system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world

problems.

20

Represent and interpret data.

MGSE5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit ( 1 __ 2 ,

1 __ 4 ,

1 __ 8 ). Use

operations on fractions for this grade to solve problems involving information presented in line plots.

For example, given diff erent measurements of liquid in identical beakers, fi nd the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

19

Geometric measurement: understand concepts of volume and relate volume to multiplication and to

addition.

MGSE5.MD.3 Recognize volume as an attribute of solid fi gures and understand concepts of

volume measurement.

21

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and

can be used to measure volume.

21

b. A solid fi gure which can be packed without gaps or overlaps using n unit cubes is said to have a

volume of n cubic units.

21

MGSE5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft, and

improvised units.

21

MGSE5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and

mathematical problems involving volume.

22, 23

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with

unit cubes and show that the volume is the same as would be found by multiplying the edge

lengths, equivalently by multiplying the height by the area of the base. Represent whole-number

products of three factors as volumes (e.g., to represent the associative property of multiplication).

22


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CORRELATIONS


b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to fi nd volumes of right

rectangular prisms with whole-number edge lengths in the context of solving real world and

mathematical problems.

22

c. Recognize volume as additive. Find volumes of solid fi gures composed of two non-overlapping right

rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to

solve real world problems.

23

Geometry 5.G

Graph points on the coordinate plane to solve real-world and mathematical problems.

MGSE5.G.1 Use a pair of perpendicular number lines, called axes, to defi ne a coordinate system, with

the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point

in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the

fi rst number indicates how far to travel from the origin in the direction of one axis, and the second

number indicates how far to travel in the direction of the second axis, with the convention that the

names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and

y-coordinate).

25

MGSE5.G.2 Represent real world and mathematical problems by graphing points in the fi rst quadrant of

the coordinate plane, and interpret coordinate values of points in the context of the situation.

26

Classify two-dimensional fi gures into categories based on their properties.

MGSE5.G.3 Understand that attributes belonging to a category of two-dimensional fi gures also belong

to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

24

MGSE5.G.4 Classify two-dimensional fi gures in a hierarchy based on properties (polygons, triangles,

and quadrilaterals).

24



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6 is

thi

rty-

four

and

fi fty

-six

hun

dre

dth

s.

[ 43 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copyi

ng

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

● D

eci

mal

s ca

n b

e w

ritt

en in

expan

ded

form

.

● W

hen y

ou u

se e

xpan

ded

fo

rm, eac

h d

igit

is m

ult

iplie

d b

y it

s

pla

ce v

alue.

● Fo

r ex

amp

le, 34.5

6 is

3 �

10 �

4 �

1 �

5 �

0.1

� 6

� 0

.01

● D

eci

mal

s w

ritt

en a

s num

bers

can

be c

om

par

ed

by

pla

ce v

alue.

● 34.5

6 <

34.6

beca

use

they

eac

h h

ave 3

4, b

ut

34.6

is g

reat

er

than

34.5

in t

he t

enth

s p

lace

.

EX

AM

PLE

Wri

te t

he n

um

ber

213.6

75 in

wo

rds.

Step

One

Wri

te t

he w

ho

le n

um

ber

par

t. U

se “

and

” fo

r th

e

deci

mal

po

int.

two

hund

red

thir

teen a

nd

…

Step

Tw

o Fo

r th

e d

eci

mal

par

t, lo

ok

at t

he p

lace

val

ue o

f th

e

last

dig

it.

The la

st d

igit

is 5

and

is in

the t

ho

usa

nd

ths

pla

ce, so

there

are

six

hund

red

seve

nty

-fi v

e t

ho

usa

nd

ths.

Step

Thre

e W

rite

the n

um

ber.

213.6

75 is

tw

o h

und

red

thir

teen a

nd

six

hund

red

seve

nty

-fi v

e

tho

usa

nd

ths. O

ne

sD

ecim

als

Hund

red

s Tens

Ones

.Tenth

sH

und

red

ths

Tho

usa

nd

ths

21

3.

67

5

TU

RN

AN

D T

ALK

Why

is it

imp

ort

ant

to s

ay “

and

”

for

the d

eci

mal

po

int?

9781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 279781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 27 1/31/2019 5:15:03 PM1/31/2019 5:15:03 PM


[ 45 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copyi

ng

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

Yo

u c

an u

se p

lace

val

ue t

o c

om

par

e d

eci

mal

num

bers

in t

he s

ame w

ay

you c

om

par

e w

ho

le n

um

bers

.

EX

AM

PLE

Is 0

.4 g

reat

er

than

, le

ss t

han

, o

r eq

ual

to

0.3

?

Step

One

Wri

te t

he n

um

bers

as

frac

tio

ns

wit

h t

he

sam

e d

eno

min

ato

r.

0.4

�

4

__

10 ,

0.3

�

3

__

10

Step

Tw

o C

om

par

e t

he n

um

era

tors

.

4

__

10 >

3

__

10 ,

so

0.4

> 0

.3.

Is 0

.21 g

reat

er

than

, le

ss t

han

, o

r eq

ual

to

0.4

?

Step

One

Wri

te t

he n

um

bers

as

frac

tio

ns

wit

h t

he

sam

e d

eno

min

ato

r.

0.2

1 �

21

__

_

100 ,

0.4

�

4

__

10 �

40

__

_

100

Step

Tw

o C

om

par

e t

he n

um

era

tors

.

21

__

_

100 <

40

__

_

100 ,

so

0.2

1 <

0.4

.

GU

IDED

INST

RUCT

ION

1.

Wri

te 8

6.0

3 in w

ord

s.

Step

One

Wri

te t

he w

ho

le n

um

ber

follo

wed

by

“and

.”

eig

hty

-six

and

…

Step

Tw

o U

se a

pla

ce v

alue c

har

t to

see t

he p

lace

val

ue o

f th

e

last

deci

mal

dig

it.

On

es

Decim

als

Hund

red

s Tens

Ones

.Tenth

sH

und

red

ths

Tho

usa

nd

ths

08

6.

03

0

The la

st d

eci

mal

dig

it is

3 a

nd

is in

the h

und

red

ths

pla

ce.

Step

Thre

e W

rite

86.0

3 in

wo

rds

eig

hty

-six

and

th

ree

hund

red

ths

HIN

T, H

INT

Wh

en y

ou s

ay a

deci

mal

nu

mb

er,

do

no

t sa

y, “

86 p

oin

t 03”.

Say

, “8

6

and

3 h

un

dre

dth

s”. T

his

will

help

you t

o t

hin

k ab

ou

t th

e p

lace

val

ue.

[ 44 ]

mas

tery

educa

tion.c

om

| M

athem

atic

s | Lev

el E

Copyi

ng

is p

rohib

ited

.

Less

on 5

R

EA

D, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

EX

AM

PLE

Wri

te 5

78.4

29 in

exp

and

ed

fo

rm.

Eac

h d

igit

in t

he n

um

ber

is m

ult

iplie

d b

y it

s p

lace

val

ue, th

e s

ame a

s

you w

ould

do

wit

h w

ho

le n

um

bers

. T

he d

eci

mal

pla

ce v

alues

can b

e

frac

tio

ns

or

deci

mal

s.

Step

One

Find

the v

alue o

f eac

h d

igit

.

On

es

Decim

als

Hund

red

s Tens

Ones

.Tenth

sH

und

red

ths

Tho

usa

nd

ths

57

8.

42

9

5 is

500 �

5 �

100

7 is

70 �

7 �

10

8 is

8 �

8 �

1

4 is

0.4

� 4

�

1

__

10

2 is

0.0

2 �

2 �

1

__

_

100

9 is

0.0

09 �

9 �

1

__

__

_

1,0

00

Step

Tw

o C

om

bin

e t

he v

alues.

5 �

100 �

7 �

10 �

8 �

1 �

4 �

1

__

10 �

2 �

1

__

_

100 �

9 �

1

__

__

_

1,0

00

We u

se d

eci

mal

no

tati

on f

or

amo

unts

of

mo

ney

. Pe

nnie

s ar

e

hund

red

ths

of

a d

olla

r an

d d

imes

are t

enth

s o

f a

do

llar.

TH

INK

AB

OU

T IT

Wh

en y

ou w

rite

a d

eci

mal

nu

mb

er

in w

ord

s, y

ou a

re n

amin

g th

e

deci

mal

par

t as

a f

ract

ion:

Five

hu

nd

red

seve

nty

-eig

ht

and

fo

ur

hu

nd

red

tw

enty

-nin

e

tho

usa

nd

ths.



[ 47 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copyi

ng

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

How

Am

I D

oin

g?

What

ques

tions

do y

ou h

ave?

Imag

ine

what

the

pri

ce m

ight

be

of so

met

hin

g yo

u e

njo

y. W

rite

the

pri

ce, an

d t

hen

wri

te it

agai

n in e

xpan

ded

form

.

Eac

h p

lace

val

ue

in a

dec

imal

get

s 10 t

imes

sm

alle

r. A

mea

sure

men

t

of 6.7

65 inch

es is

very

pre

cise

, but

pro

bab

ly n

ot

nec

essa

ry. C

an y

ou

thin

k of a

situ

atio

n w

her

e th

is m

uch

acc

ura

cy w

ould

be

import

ant?

Colo

r in

the

traffi

c

sign

al

that

show

s how

you a

re

doin

g w

ith t

he

skill

.

I am

stu

ck.

I al

most

ha v

e it

.

I under

stan

d

the

skill

.

TU

RN

AN

D T

ALK

Pre

ten

d y

ou a

re g

oin

g to

teac

h

you

nge

r st

ud

ents

ab

ou

t d

eci

mal

s.

Th

ink

abo

ut

ho

w y

ou w

ou

ld t

eac

h

som

eo

ne t

o c

om

par

e d

eci

mal

s

to t

ho

usa

nd

ths.

Th

en

, w

ork

ing

wit

h a

par

tner,

cre

ate a

sh

ort

dem

on

stra

tio

n. Y

ou c

an u

se g

rid

s,

pic

ture

s, p

lace

-val

ue b

lock

s,

tech

no

logy

, o

r an

y o

ther

meth

od

oth

er

than

pla

ce-v

alu

e c

har

ts.

Th

en p

rese

nt

you

r d

em

on

stra

tio

n

to t

he c

lass

.

[ 46 ]

mas

tery

educa

tion.c

om

| M

athem

atic

s | Lev

el E

Copyi

ng

is p

rohib

ited

.

Less

on 5

R

EA

D, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

2.

Wri

te 2

7.3

04 in e

xpan

ded

form

.

Step

One

Arr

ange

the d

igit

s in

a p

lace

val

ue c

har

t.

On

es

Decim

als

Hund

red

s Tens

Ones

.Tenth

sH

und

red

ths

Tho

usa

nd

ths

27

.3

04

Step

Tw

o W

rite

the v

alue o

f eac

h d

igit

, usi

ng

deci

mal

fra

ctio

ns.

2 is

20 �

2 �

10

7 is

7 �

7 �

1

3 is

0.3

� 3

�

1

__

10

4 is

0.0

04 �

4 �

1

__

__

_

1,0

00

Step

Thre

e W

rite

an e

quat

ion s

ho

win

g th

e s

um

.

27.3

04 �

2 �

10

� 7

� 1

� 3

�

1 __

10

�

4 �

1

_____

1,0

00

3.

Com

par

e 0.0

56 a

nd 0

.59.

Step

One

Wri

te t

he d

eci

mal

s in

fra

ctio

n f

orm

wit

h t

he s

ame

deno

min

ato

r.

0.0

56 �

56

__

__

_

1,0

00

0.5

9 �

59

__

_

100 �

590

__

__

_

1,0

00

Step

Tw

o C

om

par

e t

he fra

ctio

ns.

56

__

__

_

1,0

00 <

590

__

__

_

1,0

00

So, 0.0

56

< 0

.59

4.

Sele

ct T

HR

EE e

xpre

ssio

ns

that

are

equal

to 1

13.0

82.

Ⓐ 10

0 �

10 �

3 �

0.8

� 0

.02

Ⓑ 10

0 �

10 �

3 �

0.0

8 �

0.0

02

Ⓒ 10

0 �

10 �

3 �

8

___

10 �

2

____

100

Ⓓ 10

0 �

10 �

3 �

8

__

_

100 �

2

__

__

_

1,0

00

Ⓔ

1 �

100 �

1 �

10 �

3 �

1 �

8 �

1

__

_

100 �

2 �

1

__

__

_

1,0

00

Ⓕ

1 �

100,0

00 �

1 �

10,0

00 �

3 �

1,0

00 �

8 �

10 �

2 �

1

TIP

S A

ND

TR

ICK

S

Mak

e s

ure

yo

u e

valu

ate e

ach

answ

er.

Do

no

t st

op

aft

er

you fi n

d

the fi r

st c

orr

ect

an

swer.

Ⓑ

Ⓓ

Ⓔ



[ 49 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copyi

ng

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

5.

Whic

h s

tate

men

t is

tru

e?

Ⓐ

621.0

71 �

621.7

11

Ⓑ

621.0

71 �

621.7

11

Ⓒ

621.0

71 �

621.7

11

6.

Whic

h s

tate

men

t is

tru

e?

Ⓐ

0.9

10 �

0.9

1

Ⓑ

45.2

34 �

45.1

34

Ⓒ

6.7

1 �

6.0

71

Ⓓ

79.0

12 �

79.0

12

7.

Par

t A

Geo

rge’

s bac

kpac

k w

eigh

s 15.2

07 p

ounds.

Ste

phen

’s b

ackp

ack

wei

ghs

15.2

16 p

ounds.

Whose

bac

kpac

k w

eigh

s m

ore

?

W

rite

your

answ

er in t

he

box.

Ste

phen

’s

Par

t B

Expla

in h

ow

you found y

our

answ

er. W

rite

an e

xpre

ssio

n u

sing

�, �

, or

� t

o r

ecord

the

resu

lts

of yo

ur

com

par

ison.

Sam

ple

answ

er: B

oth

wei

ghts

sta

rt w

ith th

e sa

me

who

le n

umbe

r, so

I ch

ange

d th

e de

cim

als

tofra

ctio

ns to

com

pare

them

. 15.

207

� 1

5 20

7 __

__

1,00

0 an

d

15.2

16 �

15

216

____

1,00

0 . 1

5 20

7 __

__

1,00

0 �

15

216

____

1,00

0 ,

so 1

5.20

7 �

15.

216.

Ⓒ

TIP

S A

ND

TR

ICK

S

Co

mp

are t

he d

igit

s o

ne a

t a

tim

e,

usi

ng

pla

ce v

alu

e a

nd

sta

rtin

g at

the le

ft.

Ⓑ

WO

RK

SPA

CE

[ 48 ]

mas

tery

educa

tion.c

om

| M

athem

atic

s | Lev

el E

Copyi

ng

is p

rohib

ited

.

Less

on 5

R

EA

D, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

IND

EPEN

DEN

T PR

ACTI

CEA

nsw

er

the q

uest

ions.

1.

What

is

51.0

17 in w

ord

form

?

Ⓐ

fi fty

-one t

ho

usa

nd

and

seve

nte

en

Ⓑ

fi fty

-one a

nd

seve

nte

en h

und

red

ths

Ⓒ

fi fty

-one a

nd

seve

nte

en t

enth

s

Ⓓ

fi fty

-one a

nd

seve

nte

en t

ho

usa

nd

ths

2.

Com

par

e th

e dec

imal

s. W

rite

the

corr

ect

sym

bol in

eac

h b

ox.

0.0

4

� 0.1

4

1.5

�

1.1

5

3.0

1

� 3.0

10

3.

What

is

195.4

38 in e

xpan

ded

form

usi

ng

dec

imal

s?

W

rite

your

answ

er in t

he

box.

100

� 9

0 �

5 �

0.4

� 0

.03

� 0

.008

4.

Wri

te a

n e

xpre

ssio

n for

105.0

67 in e

xpan

ded

form

by

mult

iply

ing

each

dig

it b

y a

dec

imal

fra

ctio

n.

W

rite

your

answ

er in t

he

box.

1

� 1

00 �

5 �

1 �

6 �

1 ___

100 �

7 �

1

____

_ 1,

000

HIN

T, H

INT

Wh

en r

ead

ing

a n

um

ber

in w

ord

form

, w

rite

ou

t eac

h n

um

ber

next

to t

he w

ord

s.

Ⓓ

HIN

T, H

INT

Wh

en t

here

is a

0 in

a n

um

ber

you

are w

riti

ng

in e

xp

and

ed

fo

rm, b

e

sure

to

pay

clo

se a

ttenti

on t

o t

he

pla

ce v

alu

es

of th

e o

ther

dig

its.



[ 51 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copyi

ng

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

EXIT

TIC

KET

Now

that

you h

ave

mas

tere

d r

eadin

g, w

riti

ng,

and c

om

par

ing

dec

imal

num

ber

s, let

’s

solv

e th

e pro

ble

m in t

he

Rea

l-W

orl

d C

onnec

tion.

Kel

ly h

as 0

.613 p

ounds

of blu

eber

ries

. H

annah

has

six

ty-f

ourt

h h

undre

dth

s of a

pound

of blu

eber

ries

. W

ho h

as t

he

grea

ter

amount

of blu

eber

ries

?

Han

nah

has

a gr

eate

r am

ount

of b

lueb

errie

s th

an K

elly.

0.61

3 �

61

3 __

___

1,00

0 si

xty-

four

hun

dred

ths

� 64

__

_ 10

0 �

640

____

_ 1,

000

613

____

_ 1,

000 �

64

0 __

___

1,00

0 S

o, H

anna

h ha

s a

grea

ter a

mou

nt o

f blu

eber

ries

than

Kel

ly.

5.N

BT.

3, 5

.NB

T.3a

, 5.N

BT.

3b

[ 50 ]

mas

tery

educa

tion.c

om

| M

athem

atic

s | Lev

el E

Copyi

ng

is p

rohib

ited

.

Less

on 5

R

EA

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8.




TEACHER NOTESREAL-WORLD GOALS FOR STUDENTS

• Students will understand how to read decimal numbers.

• Students will understand how to write decimal numbers in words and expanded form.

• Students will compare decimal numbers.

TIPS FOR THE STRUGGLING LEARNER

• Students may struggle with decimals with a zero digit: 0.304, 0.340, 0.034. In all three cases,

students need to say the number and the place value of the last digit. Although a number

such as 0.340 is 34 hundredths, if the zero is shown, it is a signifi cant digit. It is better for

students to say three hundred forty thousandths than to worry about whether the zero is

a placeholder or not.

• If students struggle with reading the values of decimals, provide them with place value

charts. Students can write the decimals in the chart to help them understand the value of

each number.

• To reinforce place value, encourage struggling learners to say the value of the decimal

rather than using a phrase similar to “point 34.”

TIPS FOR THE ENGLISH LANGUAGE LEARNER

• English learners may confuse the words for whole-number place values, such as thousand,

and their decimal equivalents, such as thousandth. Focus students’ attention on the letters

th and point out that they indicate a decimal place value in words such as tenth, hundredth,

and thousandth.

ACTIVITIES FOR THE ADVANCED LEARNER

• Given a set of decimals that are close in value, have students compare which decimal is

greater and by how much. For example, 4.1 is 1 thousandth more than 4.099.

• Have students name and write decimal numbers to further place values, up to millionths.


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