1.4 Compare and Order Decimals - District / Homepage Mifflin Harcourt Publishing Company? Math How can you use place value to compare and order decimals? 1 • 4 • • Soar to Success

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e

Texas Essential Knowledge and Skills

Number and Operations—5.2.B Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, =MATHEMATICAL PROCESSES5.1.A Apply mathematics to problems5.1.E Create and use representations

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 1.4 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

1.4 Compare and Order Decimals How can you use place value to compare and order decimals? Essential Question?

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about comparing numbers.

Write the signs > and < on the board. Ask: What does each symbol mean when comparing two numbers? (> means “is greater than,”; < means “is less than”) Add the equals sign to the two inequality signs on the board and ask: What does this symbol mean when comparing two numbers? (It shows that the numbers on either side have the same value.) How can you use the > symbol to compare 25 and 73? (73 > 25) How can you use the < symbol to compare 25 and 73? (25 < 73)

Using the Digital LessonEmphasize that when reading a decimal number, the decimal point is indicated by the word and. Review with students the place values to the right of the decimal point.

Learning TaskWhat is the problem the students are trying to solve? Connect the story to the problem.

• What are the widths of the spider webs? (0.457 meters and 0.409 meters)

• How many digits are there to the right of the decimal point in each width? (3 digits)

• What is Jed comparing? (the widths of the two spider webs)

Literacy and MathematicsView the lesson opener with the students. Then, choose one or more of the following activities.

• Ask students to write the decimals 0.457 and 0.419 in word form. Discuss whether word form helps tell which number has the greater value or lesser value.

• Have students research and write one paragraph about spider webs. The paragraph should include information on what they are made of and how the spider uses them.

How can you use place value to compare and

order decimals?

Lesson 1.4 23A

Unlock the ProblemUnlock the Problem

Essential Question?

Mathematical ProcessesMath Talk

Explain why it is important to line up the decimal

points when comparing decimals.

Name Number and Operations—5.2.B

MATHEMATICAL PROCESSES5.1.A, 5.1.E

How can you use place value to compare and order decimals?

Compare and Order Decimals1.4

The table lists some of the mountains in the United States

that are over two miles high. How does the height of Cloud

Peak in Wyoming compare to the height of Boundary

Peak in Nevada?

One Way Use place value.

Line up the decimal points. Start at the left. Compare the

digits in each place-value position until the digits are different.

STEP 1 Compare the ones.

2.495

2.488

STEP 2 Compare the tenths.

2.495

2.488

STEP 3 Compare the hundredths.

2.495

2.488

Since 9 ● 8, then 2.495 ● 2.488, and 2.488 ● 2.495.

So, the height of Cloud Peak is ___

the height of Boundary Peak.

Another Way Use a place-value chart to compare.

Compare the height of Cloud Peak to Wheeler Peak.

Mountain Heights

Mountain and State Height (in miles)

Boundary Peak, Nevada 2.488

Cloud Peak, Wyoming 2.495

Grand Teton Peak, Wyoming 2.607

Wheeler Peak, New Mexico 2.493

↓ 9 ● 8↓ 4 ● 4↓ 2 = 2

Ones Tenths Hundredths Thousandths

2 4 9 5

2 4 9 3

2 = 2 4 = _ 9 = _ 5 > _

.

.

.

Since 5 ● 3, then 2.495 ● 2.493, and 2.493 ● 2.495.

So, the height of Cloud Peak is ___

the height of Wheeler Peak.

greater than

Possible explanation: You need to line up the decimal points to make sure that you are comparing digits in the same place-value position.4 9 3

greater than

= >

>

>

>

>

<

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Language SupportELL

English Language Learners

ELPS 1.B.1, 3.E, 3.H.3

Leveled Activities ELPS

Beginning: Activity 2 2.I.4, 3.C.4, 3.G.2

Intermediate: Activity 24 3.D.1, 3.F.2, 4.F.9

Advanced: Activity 34 2.C.4, 2.I.5, 4.F.8

Advanced High: Activity 18 4.C.4, 4.E, 4.F.7,

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Interpersonal / Social Partners

Strategy: Creative Grouping• Partner advanced English learners or students who are fluent in English

with beginning and intermediate students.• Have students practice comparing decimals. Have the advanced English

learners explain the process of comparing decimals first.• Then have the beginning and intermediate students explain the process

either verbally or in drawings.

Unlock the ProblemRead and discuss the problem.

• What are you comparing? the height of Cloud Peak, 2.495 miles, and the height of Boundary Peak, 2.488 miles

One WayDiscuss how to line up place values and compare the digits from left to right.

• What happens if you do not line up the decimal points? Possible answer: I may not compare the digits in the same place-value position correctly.

• Why do you compare the digits from left to right? Possible answer: I need to start with the greatest place-value position; the number with the greater digit in the greatest place-value position is greater.

• What do you do if the digits in the greatest place-value position are the same? Possible answer: I move to the next lesser place-value position and compare the digits.

Another WayDiscuss how to compare two numbers using a place-value chart.

• How can you use a place-value chart to compare decimals? Possible answer: Write the digits in the correct place-value positions, and then compare the digits in each place-value position, starting from the greatest place value.

• What is another way to state the answer? Possible answer: The height of Wheeler Peak is less than the height of Cloud Peak.

Math Talk Use Math Talk to focus on students’ understanding of the importance of lining up decimal points when comparing decimals.

Mathematical Processes

23 Module 1

Example

Share and ShowShare and Show

Mathematical ProcessesMath Talk

Explain why you do not have to compare the digits in the thousandths place to order the heights of

the 3 mountains.

Mount Whitney in California is 2.745 miles high, Mount Rainier in Washington

is 2.729 miles high, and Mount Harvard in Colorado is 2.731 miles high. Order

the heights of these mountains from least to greatest. Which mountain has the

least height? Which mountain has the greatest height?

STEP 1

Line up the decimal points. There are the same number of ones. Circle the tenths and compare.

2.745 Whitney

2.729 Rainier

2.731 Harvard

There are the same number of tenths.

STEP 2

Underline the hundredths and compare. Order from least to greatest.

2.745 Whitney

2.729 Rainier

2.731 Harvard

Since ● < ● < ●, the heights in order from least to

greatest are __ , __ , __.

So, _____ has the least height and

_____ has the greatest height.

1. Use the place-value chart to compare the two

numbers. What is the greatest place-value

position where the digits differ?

Compare. Write <, >, or =.

2. 4.563 ● 4.536 3. 5.640 ● 5.64 4. 8.673 ● 8.637

Name the greatest place-value position where the digits differ. Name the greater number.


3 4 7 2

3 4 4 5

.

.

Order Decimals You can use place value to order decimal numbers.

5. 3.579; 3.564

____

____

6. 9.572; 9.637

____

____

7. 4.159; 4.152

____

____

2 3 4

2.729 2.731 2.745

Mount Rainier

Mount Whitney

Possible explanation: Since the digits are all different in the hundredths place, you can order the decimals without comparing the digits in the thousandths place.

hundredths; 3.472 > 3.445 or 3.445 < 3.472

> = >

hundredths tenths thousandths

3.579 9.637 4.159

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Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

0.782 0.669

VisualPartners

Materials: index cards

• Give each student 10 index cards, and have them write a decimal up to thousandths on each card.

• Have partners combine their cards, shuffle them, and then divide them into two equal piles. Each student takes a pile and keeps the cards facedown.

• Partners turn over their top cards at the same time and compare the decimals. The student with the greater decimal keeps the cards.

• Play continues until one student has all the cards and is declared the winner.

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a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 3

ExampleRead and discuss how to order the heights from least to greatest.

• In Step 1, why do you move to the tenths and compare the digits? The digits in the ones place are all the same.

• In Step 2, why are you comparing the digits in the hundredths place? The digits in the tenths place are all the same.

• How do you know that 2.729 is the least? Possible answer: When I compare the digits in the hundredths place, the 2 is the least digit. 2 hundredths is less than 3 hundredths and 4 hundredths.

• How do you know which decimal is the greatest? Possible answer: When comparing the hundredths, the digit with the greatest value is the greatest number. 4 is the greatest digit in the hundredths place, so 2.745 is the greatest number.

Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

Math Talk Use Math Talk to focus on students’ understanding of ordering decimals.


COMMON ERRORSError Students may use digits that do not have the same place value to compare and order decimals.

Example 6.76 < 6.759 because 6 < 7

Springboard to Learning Have students write the numbers in a place-value chart to help them compare the digits in the correct place-value positions.

CE

Lesson 1.4 24

Problem SolvingProblem Solving


Name

Order from greatest to least.

8. 2.007; 2.714; 2.09; 2.97

______

9. 0.386; 0.3; 0.683; 0.836

______

Mountains Over Three Miles High

Mountain and Location Height (in miles)

Blackburn, Alaska 3.104

Bona, Alaska 3.134

Steele, Yukon 3.152

Algebra Find the unknown digit to make each statement true.

10. 3.59 > 3.5 1 > 3.572 11. 6.837 > 6.83 > 6.835 12. 2.45 < 2. 6 < 2.461

13. Dawn keeps track of her softball batting average each year. The first

year, her batting average is .783. The second year, her batting average

is .81. In which year did she have the greater batting average?

Use the table for 14–16.

14. Use Math Language How does the height of Steele

Mountain compare to the height of Blackburn Mountain?

Compare the heights using words.

15. Write MathWrite Math Explain how to order the height of the mountains

from greatest to least.

16. Multi-Step What if the height of Blackburn Mountain

were 0.05 mile greater. Would it then be the mountain with the

greatest height? Explain.

2.97; 2.714; 2.09; 2.007

the second year

0.836; 0.683; 0.386; 0.3

8 6 4

Steele Mountain has a height that is greater

than the height of Blackburn Mountain.

Compare the place values from left to right. The ones and

tenths are the same. Comparing the hundredths, 5 > 3 > 0.

From greatest to least height: Steele, Bona, and Blackburn

Yes; Possible explanation: It would have the same digits as

Steele in the ones, tenths, and hundredths places, but a

greater digit in the thousandths place.

Possible explanation:

Possible answer:

Module 1 • Lesson 4 25

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© Houghton Mifflin Harcourt Publishing Company

Name

E4Enrich

Enrich 4

Order Your Own Decimals

Solve each problem. In each row, use each digit exactly once.

1. Place the digits 0, 2, 5, 8 in each row of the table to create four decimals that are in order from least to greatest.


2 8 5 05 8 0 28 2 0 58 5 2 0

2. Place the digits 1, 3, 6, 9 in each row of the table to create four decimals that are in order from greatest to least.


9 6 3 16 9 1 33 9 6 11 9 6 3

3. Place the digits 0, 1, 4, 7, 8 in each row of the table to create four decimals that are in order from least to greatest.

Tens Ones Tenths Hundredths Thousandths

1 0 4 7 84 1 8 0 77 1 8 0 48 7 4 1 0

4. Place the digits 2, 3, 6, 8, 9 in each row of the table to create four decimals that are in order from greatest to least.

Tens Ones Tenths Hundredths Thousandths

9 8 6 3 28 9 3 2 63 6 2 8 92 3 9 6 8

Possible answers are given.

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Name

You can use a place-value chart to compare decimals.


4.375 4.382

Write both numbers in a place-value chart. Then compare the digits, starting with the highest place value. Stop when the digits are different and compare.

The digits are different in the hundredths place.

Since 7 hundredths < 8 hundredths, 4.375 4.382.

1. Use the place-value chart to compare the two numbers. What is the greatest place-value position where the digits differ?

Compare. Write < , > or = .

2. 5.37 5.370 3. 9.425 9.417 4. 7.684 7.689

Order from least to greatest.

5. 5.04; 5.4; 5.406; 5.064

6. 2.614; 2.146; 2.46; 2.164

Compare and Order DecimalsOBJECTIVE Compare and order decimals to thousandths using place value.

LESSON 3

The ones digits

are the same.

The tenths digits

are the same.

The hundredths

digits are different.

<


4 3 7 5

4 3 8 2


2 8 6 5

2 8 6 1

thousandths; 2.865 > 2.861

5.04; 5.064; 5.4; 5.406 2.146; 2.164; 2.46; 2.614

= > <

Number and Operations 5

Enrich 4RtI Tier 1 Lesson 3

Problem SolvingProblems

In Problems 10–12, students must find an unknown digit that makes a true statement with two comparisons.

• What strategy can you use to find the unknown digit? Possible answer: I can guess a digit and then check to see if each comparison is true. If it isn’t, then I can revise my guess and check again.

Problem 16 requires students to first add 0.05 to the height of Blackburn Mountain and then compare the sum with the other heights in the table.

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

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25 Module 1


Daily Assessment TaskDaily Assessment Task

TEXAS Test Prep20. Mount Logan in the Yukon is 3.702 miles high. Mount McKinley in

Alaska is 3.848 miles high and Pico de Orizaba in Mexico is 3.571 miles

high. Order these mountains by height from greatest to least.

A Logan, McKinley, Pico de Orizaba

B McKinley, Logan, Pico de Orizaba

C Pico de Orizaba, Logan, McKinley

D Logan, Pico de Orizaba, McKinley

Fill in the bubble completely to show your answer.

17. The length of a piece of plastic for a science kit needs to be greater

than 22.4 inches and less than 22.5 inches. Which length of plastic

can be used?

A 22.35 in C 22.47 in.

B 22.51 in D 22.40 in.

18. Louis is comparing the numbers 8.402 and 8.451. What is the least place

value he needs to compare to decide which number is greater?

A ones

B tenths

C hundredths

D thousandths

19. Multi-Step Melinda compares four numbers. Which shows the

numbers from least to greatest?

A 3.04; 3.10; 3.529; 3.685

B 3.10; 3.04; 3.529; 3.685

C 3.10; 3.04; 3.685; 3.529

D 3.04; 3.685; 3.529; 3.10

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Games

Differentiated Centers Kit

ActivitiesDo We Decimal?Students complete orange Activity Card 4 by drawing models of decimals and representing the models as decimals and as fractions.

LiteratureDewey and His DecimalsStudents read about the Dewey Decimal system used to order books in the library.

GamesDecimal ChallengeStudents name a decimal greater than, less than, or equal to the given decimal.

TEXAS Test Prep CoachIn the Test Prep exercise, if students selected:

A or D They did not compare place values correctly.

C They ordered from least to greatest instead of from greatest to least.

Essential Question? WriteMathWriteMath

How can you use place value to compare and order decimals? Possible answer: Line up the decimal points of the numbers to be compared or ordered or use a place-value chart. Compare the digits in each place-value position, starting from the greatest place-value position. The digit that is greatest is the greatest number. If the digits are the same, move to the next lesser place-value position and compare the digits.

THENIF

YES

NO

Daily Assessment Task 1

2

3

• Enrich 4

• Homework and Practice Lesson 1.4

• Soar to Success MathWarm-Up 8.44

Can students compare and order decimals?

Lesson 1.4 26

TEXAS Test PrepLesson CheckLesson Check

Fill in the bubble completely to show your answer.

16. Which number has the greatest value?

A 9.382

B 9.47

C 9.09

D 9.7

17. Kerry is comparing the numbers 9.207 and

9.210. What is the least place value she

needs to compare to decide which

number is greater?

A ones

B thousandths

C hundredths

D tenths

18. Which number has the least value?

A 7.034

B 7.304

C 7.403

D 7.003

19. In 5.820, what is the place-value position

of the 0?

A thousandths

B tenths

C hundredths

D ones

20. Multi-Step Jenna compares the lengths of

her pet fish. The table shows the lengths of the

fish. Which shows the lengths in order from

greatest to least?

Name Length

Oscar 4.32 inches

Gus 4.055 inches

Gem 4.21 inches

Spots 4.7 inches

A Spots, Oscar, Gus, Gem

B Oscar, Spots, Gem, Gus

C Gus, Oscar, Gem, Spots

D Spots, Oscar, Gem, Gus

21. Multi-Step Look at the table in Question 20.

What if Gem grew 0.5 inches. Which would

then show the lengths in order from

greatest to least?

A Gem, Spots, Gus, Oscar

B Gus, Oscar, Gem, Spots

C Gem, Spots, Oscar, Gus

D Spots, Oscar, Gem, Gus

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Homeworkand Practice

Name

1.4 Compare and Order Decimals

Number and Operations—5.2.BMATHEMATICAL PROCESSES 5.1.A, 5.1.E


1. 9.23 ● 9.32 2. 7.20 ● 7.2 3. 1.994 ● 1.493

4. 4.44 ● 4.044 5. 3.61 ● 3.87 6. 5.4 ● 5.400

Order from greatest to least.

7. 7.081; 7.81; 7.002; 7.14

8. 1.001; 1.1; 1.403; 1.078

9. 0.04; 0.5; 0.021; 0.133

10. 4; 4.022; 4.002; 4.221

14. Jack travels 2.45 miles to school. Wanda travels

2.31 miles to school. Compare the distances

using words.

15. In a jumping contest, Marcus jumped

1.02 meters, Gustavo jumped 1.29 meters, and

Loreena jumped 1.202 meters. Who won the

jumping contest?

11. 5.345 > 5.34 > 5.343 12. 8.25 < 8. 6 < 8.361 13. 6.48 > 6.4 1 > 6.470

Find the unknown digit to make each statement true.

7.81; 7.14; 7.081; 7.002

Possible answer: Jack travels a greater

Gustavodistance to school than Wanda travels.

1.403; 1.1; 1.078; 1.001

4.221; 4.022; 4.002; 40.5; 0.133; 0.04; 0.021

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Module 1 • Lesson 4 27

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Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

27-28 Module 1

Documents

1.4 Compare and Order Decimals - District / Homepage Mifflin Harcourt Publishing Company? Math How can you use place value to compare and order decimals? 1 • 4 • • Soar to Success