Try It Out! Sample Pack Measuring Up to the OH Standards

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

Measuring Up to the OH 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:

Vocabulary in Action

Relevant real-world connections

Clearly identifi ed learning goals

Connections to prior learning

Guided Instruction and Independent Learning strengthen learning with:

Deep thinking prompts

Collaborative learning

Self-evaluation

Demonstration of problem-solving logic

Application of higher-order thinking

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

Introducing standards

Reinforcement or standards review

Intervention

Remediation

Test 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 pinpointstudent needs with customized practice.

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CH

APT

ER

2 WORDS TO KNOW

decimal

expanded form

place value

Lesson 5READ, WRITE, AND COMPARE

DECIMALS 5.NBT.A.3, 5.NBT.A.3a, 5.NBT.A.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.C.6, 4.NF.C.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. Which of these expressions is equal to 113.082? Select the three

correct answers.

Ⓐ 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

You know that three answers are

correct. Make sure you evaluate

each answer. Do not stop after

you fi nd the fi rst three correct

answers. After going through all

of the answer choices, you may

fi nd that a choice you thought was

correct is actually incorrect.




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. Use the symbols in the box to compare the decimals.

Symbols can be used more than once. Write each symbol in the

appropriate 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. Circle the symbol that correctly completes the statement.

621.071 �

�

�

621.771

6. Choose Yes or No to tell which statement is true.

a. 0.910 � 0.91 Yes No

b. 45.234 � 45.134 Yes No

c. 6.71 � 6.071 Yes No

d. 79.12 � 79.012 Yes No

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


MasteryEducation.com | 800-822-1080 | Fax: 201-712-0045

ANNOTATED

TEACHER EDITION

[ ii ]

Letter to Students vi

Letter to Parents and Families vii

What You’ll See in Measuring Up to the Ohio Learning Standards viii

5.NBT.A.1, 5.NBT.A.2

5.NBT.B.5

5.NBT.B.6

5.OA.A.1, 5.OA.A.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.A.3,

5.NBT.A.3a-b

5.NBT.A.4

Chapter 2 DECIMALS

5. Read, Write, and Compare Decimals 42

6. Round Decimals 52

OLS

OLS

LESSON

LESSON

Introduction

CONTENTS

9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb ii9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb ii 6/5/2017 7:38:28 AM6/5/2017 7:38:28 AM

[ iii ]

5.NF.A.1

5.NF.A.2

5.NF.B.3

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

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

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

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

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

5.NF.B.6, 5.NF.B.7,

5.NF.B.7c

5.MD.B.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


OLS LESSON

5.NBT.B.7

5.NBT.B.7

5.NBT.B.7

7. Add and Subtract Decimals 60

8. Multiply Decimals 70

9. Divide Decimals 80


OLS LESSON

9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb iii9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb iii 6/5/2017 7:38:33 AM6/5/2017 7:38:33 AM

[ iv ]

5.MD.A.1

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

5.MD.C.4

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

5.MD.C.5, 5.MD.C.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


OLS LESSON

5.G.B.3, 5.G.B.4

5.G.A.1

5.G.A.2

5.OA.B.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


OLS LESSON

CONTENTS

9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb iv9781609797584_OH_MUSS_Math_Gr5_SE_Book.indb iv 6/5/2017 7:38:35 AM6/5/2017 7:38:35 AM

[ v ]

Acknowledgments 282

Correlation to the Ohio Learning Standards 283

Glossary 287

Copy Masters 290

References

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[ 283 ][ 283 ]Correlation to the Ohio Learning Standards | masteryeducation.com

Correlation to the Ohio Learning Standards

This worktext is customized to the Ohio Learning Standards 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.

Ohio Learning Standards Lessons

Operations and Algebraic Thinking 5.OA

A. Write and interpret numerical expressions.

1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

4

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 � (8 + 7). Recognize that 3 � (18,932 � 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.

4

B. Analyze patterns and relationships.

3. Generate two numerical patterns using two given rules. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

27

Number and Operations in Base Ten 5.NBT

A. Understand the place value system.

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

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

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., 347.392 = 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

4. Use place value understanding to round decimals to any place. 6

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

5. Fluently multiply multi-digit whole numbers using the standard algorithm. 2

CORRELATIONS


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CORRELATIONS


6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using 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, rectangular arrays, and/or area models.

3

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

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

1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given

fractions with equivalent fractions in such a way as to produce an equivalent sum or diff erence of

fractions with like denominators. For example, 2 __ 3 + 5 __ 4 = 8 __ 12 + 15 __ 12 = 23 __ 12 . (In general, a __ b + c __ d = (ad + bc)

_______ bd .)

10

2. Solve word problems involving addition and subtraction of fractions referring to the same whole, 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

B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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

problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3 __ 4 as the result of dividing 3 by 4, noting that 3 __ 4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3 __ 4 . If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

12

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 parts of a partition of q into b equal parts; equivalently, as the

result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show ( 2 __ 3 ) × 4 = 8 __ 3 , and create a story context for this equation. Do the same with ( 2 __ 3 ) × ( 4 __ 5 ) = 8 __ 15 .

(In general, ( a __ b ) × ( c __ d ) = ac ___ bd .)

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. Multiply fractional side lengths to fi nd areas of rectangles, and represent fraction products as rectangular areas.

14

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

a. Comparing 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.

15


[ 285 ][ 285 ]Correlation to the Ohio Learning Standards | masteryeducation.com


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); explaining why multiplying a given number by a fraction less than 1 results in a product

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

(n × a) ______ (n × b) to the

eff ect of multiplying a __ b by 1.

15

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

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

A. Convert like measurement units within a given measurement system.

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

B. Represent and interpret data.

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

C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

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

4. Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft, and improvised units. 21

5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

22, 23


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CORRELATIONS


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 threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

22

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

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

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

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

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

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

4. Classify two-dimensional fi gures in a hierarchy based on properties. 24



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hund

red

ths.

Voc

abu

lary

in A

ctio

n●

Dec

imal

s ca

n b

e w

ritt

en in

wo

rds.

● W

hen y

ou w

rite

a d

eci

mal

in w

ord

s yo

u s

ay “

and

” fo

r th

e

deci

mal

po

int.

● Fo

r exa

mp

le, 34.5

6 is

thi

rty-

four

and

fi fty

-six

hun

dred

ths.

[ 43 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copy

ing

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, 3

4.5

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?

9781609797645_MUSS_OH_Math_Gr5_ATE_Book.indb 279781609797645_MUSS_OH_Math_Gr5_ATE_Book.indb 27 8/17/2018 3:13:41 PM8/17/2018 3:13:41 PM


[ 45 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copy

ing

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

Copy

ing

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

Copy

ing

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

hav

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

Copy

ing

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.

Whic

h o

f th

ese

expre

ssio

ns

is e

qual

to 1

13.0

82?

Sele

ct t

he

thre

e

corr

ect

answ

ers.

Ⓐ 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

Yo

u k

no

w t

hat

th

ree a

nsw

ers

are

corr

ect

. M

ake s

ure

yo

u e

valu

ate

eac

h a

nsw

er.

Do

no

t st

op

aft

er

you fi n

d t

he fi r

st t

hre

e c

orr

ect

answ

ers

. A

fter

goin

g th

rou

gh a

ll

of th

e a

nsw

er

cho

ices,

yo

u m

ay

fi nd

th

at a

ch

oic

e y

ou t

ho

ugh

t w

as

corr

ect

is a

ctu

ally

inco

rrect

.

Ⓑ

Ⓓ

Ⓔ



[ 49 ]

Chap

ter

2 | D

ecim

als

| m

aste

ryed

uca

tion.c

om

Copy

ing

is p

rohib

ited

.

RE

AD

, W

RIT

E, A

ND

CO

MPA

RE D

EC

IMA

LS

Less

on 5

5.

Cir

cle

the

sym

bol th

at c

orr

ectly

com

ple

tes

the

stat

emen

t.

621.0

71

� � �

621.7

71

6.

Choose

Yes

or

No t

o t

ell w

hic

h s

tate

men

t is

tru

e.

a.

0.9

10 �

0.9

1

Yes

No

b.

45.2

34 �

45.1

34

Yes

No

c.

6.7

1 �

6.0

71

Yes

No

d.

79.1

2 �

79.0

12

Yes

No

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

Copy

ing

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.

Use

the

sym

bols

in t

he

box t

o c

om

par

e th

e dec

imal

s.

Sy

mbols

can

be

use

d m

ore

than

once

. W

rite

eac

h s

ymbol in

the

appro

pri

ate

box.

�

�

�

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

wo

rds.

Ⓓ

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

Copy

ing

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

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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.


Try It Out! Sample Pack Measuring Up to the OH Standards

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