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e

Texas Essential Knowledge and Skills

Number and Operations—5.2.C Round decimals to tenths or hundredths

MATHEMATICAL PROCESSES5.1.A Apply mathematics to problems5.1.E Create and use representations

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 1.5 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

1.5 Round Decimals How can you use place value to round decimals to a given place?

Essential Question?

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about decimals. Ask the following questions:

What is the relationship between the decimal places in a place-value chart? (Moving from left to right after the decimal point, each place is 1 __ 10 of the place value to its left. Moving from right to left, each place is 10 times as much as the place value to its right.) How do you represent the number 1.186 in expanded form? (1 + 0.1 + 0.08 + 0.006) What is the value of the decimal digits in the number 1.186? (The digit 1 has a value of 1 __ 10 ; the digit 8 has a value of 8 ___ 100 , and the value of the digit 6 is 6 ____ 1,000 )

Using the Digital LessonHave students look at a ruler and discuss why rounding a number like 1.186 to the hundredths place might make sense. (Possible answer: our rulers don’t measure to so many decimal places.

Learning TaskConnect the story to the problem. Ask students the following questions.

• What are you being asked to do? (round a number in the thousandths place to the hundredths place)

• What is a number in thousandths between 1.180 and 1.190 that is less than 1.186? (Possible answers: 1.181, 1.182, 1.183, 1.184, and 1.185) That is greater than 1.186? (Possible answers: 1.187, 1.188, and 1.189)

Literacy and Mathematics• Why might it be unreasonable to round 1.186 to the ones place? (Possible answer:

when rounded to the ones place, 1.186 becomes 1.0. That value is an underestimate of the actual length, which misrepresents the actual size of the spider.)

How can you use place value to round decimals to

a given place?

Lesson 1.5 29A

Essential Question?

Unlock the ProblemUnlock the Problem

Name

How can you use place value to round decimals to a given place?

1.5 Round Decimals

Number and Operations—5.2.C

MATHEMATICAL PROCESSES5.1.A, 5.1.E

Ones Tenths Hundredths Thousandths

0 3 8 6•Think: Does the digit in the rounding place stay the same or increase by 1?

The Gold Frog of South America is one of the smallest

frogs in the world. It is 0.386 of an inch long. What is this

length rounded to the nearest hundredth of an inch?

• Underline the length of the Gold Frog.

• Is the frog’s length about the same as the length or the width of a large paper clip?

One Way Use a place-value chart.

• Write the number in a place-value chart and circle the

digit in the place value to which you want to round.

• In the place-value chart, underline the digit to the

right of the place to which you are rounding.

• If the digit to the right is less than 5, the digit in the

place value to which you are rounding stays the same.

If the digit to the right is 5 or greater, the digit in the

rounding place increases by 1.

• Drop the digits after the place to which you are rounding.

So, to the nearest hundredth of an inch, a Gold Frog is

about __ of an inch long.

Another Way Use place value.

The Little Grass Frog is the smallest frog in North America.

It is 0.437 of an inch long.

A What is the length of the frog to the nearest hundredth of an inch?

0.437

0.44

So, to the nearest hundredth of an inch, the frog is

about __ of an inch long.

7 > 5 3 < 5

↓ ↓

B What is the length of the frog to the nearest tenth of an inch?

0.437

0.4

So, to the nearest tenth of an inch, the frog is about

__ of an inch long.

the width of a large paper clip

0.44

0.39

0.4

Module 1 29

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Language SupportELL

English Language Learners

ELPS 2.C.2, 3.C.4, 3.D.2

Leveled Activities ELPS

Beginning: Activity 38 1.B.1, 2.D.1, 3.B.3

Intermediate: Activity 22 1.A.1, 3.G.1, 4.C.1

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

Advanced High: Activity 60 2.I.3, 4.F.7, 4.G.3

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

Strategy: Define• Students can define words by using them in context with their

definitions. The word round has different meanings. In math, it means to replace a number with one that is simpler and is approximately the same size as the original number.

• Remind students that when they round, they are finding a close approximation.

• Model the sentences, “1.25 rounded to the nearest tenth is 1.3. 1.25 is about 1.3. 1.25 is close to 1.3.” Have students repeat the sentences.

• Then have students round several decimals to the nearest tenth, repeating the same sentence pattern each time.

Verbal / LinguisticSmall Group

Unlock the ProblemRead and discuss the problem about the length of the smallest frog in the world.

• What number are you rounding? 0.386

• To what place are you rounding? hundredth

One WayDiscuss how to use a place-value chart to round decimals.

• Why do you circle the 8? Possible answer: This is the digit in the place to which I want to round.

• Why do you underline the 6? Possible answer: This digit will tell me whether to increase the circled digit by 1 or keep it the same. If it is greater than or equal to 5, then I increase the digit in the rounding place by 1. If it less than 5, then I keep the digit in the rounding place the same.

• How does a place-value chart help you round? Possible answer: I can easily find the digit in the rounding place and the digit to its right that tells me whether to increase the digit in the rounding place or keep it the same.

Another WayDiscuss how to round using place value.

• In Part A, which digit is in the place to which you are rounding? 3

• How will you decide whether to increase the digit in the rounding place or keep it the same? Possible answer: I will look at the digit to the right of the 3. It’s a 7, which is greater than 5. So, I will increase 3 by 1 and drop the digits to its right.

• In Part B, which digit is in the place to which you are rounding? 4

• How will you decide whether to increase the digit in the rounding place or keep it the same? Possible answer: I will look at the digit to the right of the 4. It’s a 3, which is less than 5. So, I will keep the 4 the same and drop the digits to its right.

29 Module 1

Share and ShowShare and Show

Problem SolvingProblem Solving

Write the place value of the underlined digit. Round eachnumber to the place of the underlined digit.

1. 0.673

___

___

2. 4.282

___

___

3. 12.917

___

___

Name the place value to which each number was rounded.

4. 0.982 to 0.98

___

5. 3.695 to 4

___

6. 7.486 to 7.5

___

Write the place value of the underlined digit. Round eachnumber to the place of the underlined digit.

7. 0.592

___

___

8. 6.518

___

___

9. 0.809

___

___

Round 16.748 to the place named.

10. tenths __ 11. hundredths __ 12. ones __

13. Write MathWrite Math Explain why any number less than 12.5 and greater

than or equal to 11.5 would round to 12 when rounded to the nearest

whole number.

14. Write MathWrite Math Explain what happens when you round 4.999 to the

nearest tenth.

hundredths tenths ones

0.67 4.3 13

hundredths ones tenths

tenths ones hundredths

0.6 7 0.81

16.7 16.75 17

Possible explanation: Since there is a 9 in the hundredths place, the number in the tenths

place will increase by 1. Since 9 + 1 = 10, a 0 will go in the tenths place and the 1 will be

added to the 4 in the ones place making the answer 5.0.

Possible explanation: With any digit less than 5 in the tenths place, the digit in the ones

place remains unchanged. With any digit greater than or equal to 5 in the tenths place, the

digit in the ones place increases by 1.

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

Enrich

• Write the following problem on the board:

• Have students find the answer, checking it with a partner. C• Then have students write similar problems for their partners to solve.

Encourage students to write problems involving decimals that round to ones, tenths, and hundredths.

Logical / MathematicalIndividual / Partners

Share and ShowThe first problems connect to the learning model.

Use the checked exercises for Quick Check.

Problem SolvingIn Problem 14, students must explain what happens when rounding when there is a 9 in the place to which they are rounding.

• How would you round to the nearest hundredth? Possible answer: I would look at the digit in the thousandths place, 9. Since 9 is greater than 5, I would increase the digit in the hundredths place by 1. 9 + 1 = 10. That would add a 1 to the tenths place. 9 + 1 = 10. This adds a 1 to the ones place. 4 + 1 = 5. So, I get 5.00.

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 4

COMMON ERRORSError Students may round to the wrong place value.

Example 5.683 rounded to the nearest hundredth is 5.7.

Springboard to Learning Encourage students to circle the digit in the place they are rounding to and then look at the digit to its right.

CE

______ rounded to the nearest tenth is 6.5.

A 6.43 C 6.53

B 6.44 D 6.59

Lesson 1.5 30

Problem SolvingProblem Solving

Dragonfly

Horsefly

Bumblebee

Honeybee

Housefly

6.974

3.934

2.861

2.548

1.967

Insect Speeds (meters per second)

Insect Speed

Write MathWrite Math Show Your Work

Name

Use the table for 15–18.

15. The speeds of two insects when rounded

to the nearest whole number are the same.

Which two insects are they?

16. What is the speed of the housefly rounded to

the nearest hundredth?

17. The speed of an insect is about 3.9 meters per

second. Which insect could it be?

18. What’s the Error? Mark said

that the speed of a dragonfly rounded to the

nearest tenth was 6.9 meters per second. Is he

correct? If not, what is his error?

19. Multi-Step A rounded number for the speed

of an insect is 5.67 meters per second. What are the fastest

and slowest speeds to the thousandths that could round to

5.67? Explain.

bumblebee and honeybee

horsefl y

1.97 meters per second

Mark is not correct. He should have

written a 0 in the tenths place and

rounded the ones to 7.

The fastest speed is 5.674. The slowest speed is

5.665. Possible explanation: Any number greater

than 5.674 would round to 5.68. Any number less

than 5.665 would round to 5.66.

Module 1 • Lesson 5 31

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E5Enrich

Enrich 5

Decimal Round Up

1. In circle A, write 9 decimals, with three decimal places, that when rounded to the nearest hundredth, round to 4.56.

2. In circle B, write 9 decimals, with one decimal place, that when rounded to the nearest one, round to 7.

3. In circle C, write 9 decimals, with two decimal places, that when rounded to the nearest tenth, round to 8.7.

4. In circle D, write 9 decimals, with three decimal places, that when rounded to the nearest tenth, round to 1.3.

5. In which circle are more than 9 decimals possible? Explain.

4.555, 4.556,

4.557, 4.558,

4.559, 4.561,

4.562, 4.563,

4.564

6.5, 6.6, 6.7,

6.8, 6.9, 7.1,

7.2, 7.3, 7.4

8.65, 8.66,

8.67, 8.68,

8.69, 8.71,

8.72, 8.73,

8.74

1.254,1.259,

1.267, 1.269,

1.273, 1.275,

1.284, 1.286,

1.295

Circle D. Possible explanation: when you round a

decimal to the tenths place, you only look at the

digit in the hundredths place. Any digit can be in the

thousandths place without affecting the rounded value.

Possible answers are given.1

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Rounding decimals is similar to rounding whole numbers.

Round 4.682 to the nearest tenth.

Step 1 Write 4.682 in a place-value chart.

Step 2 Find the digit in the place to which you want to round.

Circle that digit. The digit is in the tenths place.

Step 3 Underline the digit to the right of the circled digit.

The digit is to the right of the circled digit.

Step 4 If the underlined digit is less than 5, the circled digit stays the same. If the underlined digit is 5 or greater, the circled digit increases by 1.

> 5, so round 6 up to 7.

Step 5 After you round the circled digit, drop the digits to the right of the circled digit.

So, 4.682 rounded to the nearest tenth is .

Write the place value of the underlined digit. Round each number to the place of the underlined digit.

1. 0.392

2. 5.714

3. 16.908

Name the place value to which each number was rounded.

4. 0.825 to 0.83

5. 3.815 to 3.82

6. 1.546 to 1.5

Round DecimalsOBJECTIVE Round decimals to any place.

LESSON 4

6

8

8

4.7

Ones Tenths Hundredths Thousandths

4 6 8 2

hundredths 0.39

hundredths hundredths tenths

tenths 5.7

tenths 16.9

Number and Operations 7

In Exercises 15–18, students use information from a table to solve problems involving rounding decimals.

In Exercise 19, students need to find the least and greatest numbers that would round to 5.67.

Enrich 5RtI Tier 1 Lesson 4

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.

1

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31 Module 1

Mathematical Processes

Daily Assessment TaskDaily Assessment Task

Fill in the bubble completely to show your answer.

20. Chef Round uses 1.257 kilograms of meat for his famous meatballs.

There are four packages at the market. Which amount is closest to

1.257 kilograms?

A 1.26 kg

B 1.2 kg

C 1.3 kg

D 1.35 kg

21. Representations The table shows the neck lengths for four giraffes in

the Long-Necked Friends Sanctuary. Which two giraffes have necks that

are the same length when rounded to the nearest tenth?

A Spot and Stretch

B Mittens and Spot

C Mittens and Stretch

D Spot and Zippy

22. Multi-Step Janis sells friendship bracelets at a fair. She has three

bracelets that are 16.53 cm, 16.755 cm, and 16.55 cm long. She

wants to label the lengths to the nearest tenth of a centimeter.

In order, how should she label the bracelets?

A 16.5 cm, 16.76 cm, 16.6 cm

B 16.6 cm, 16.7 cm, 16.5 cm

C 16.5 cm, 16.8 cm, 16.6 cm

D 16.3 cm, 16.5 cm, 16.5 cm

TEXAS Test Prep23. To which place value is the number rounded?

6.706 to 6.71

A ones C hundredths

B tenths D thousandths

Giraffe’s Name Neck Length (feet)

Mittens 5.632

Spot 5.725

Stretch 5.405

Zippy 5.657

32

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Games

Differentiated Centers Kit

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.

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

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

A, B, or D They identified the wrong place value.

Essential Question? WriteMathWriteMath

How can you use place value to round decimals to a given place? Possible answer: Find the digit in the place to which you are rounding. Then look at the digit to its right. If that digit is greater than or equal to 5, increase the digit in the place to which you are rounding by 1 and drop the digits to its right. If the digit to the right is less than 5, keep the digit in the place value you are rounding to the same and drop the digits to its right.

THENIF

YES

NO

Daily Assessment Task 1

2

3

• Enrich 5

• Homework and Practice Lesson 1.5

• Soar to Success MathWarm-Up 25.23

Can students use place value to round decimals?

Lesson 1.5 32

TEXAS Test PrepLesson CheckLesson Check

Fill in the bubble completely to show your answer.

15. To which place value is the number rounded?

8.293 to 8.29

A ones

B tenths

C hundredths

D thousandths

16. To which place value is the number rounded?

0.799 to 0.8

A ones

B tenths

C hundredths

D thousandths

17. Which number is 5.389 rounded to the nearest

hundredth?

A 5.4

B 5.38

C 5.39

D 5.399

18. Which number is 7.323 rounded to the nearest

tenth?

A 7.3

B 7.4

C 7.32

D 7.33

19. A baker uses 2.327 kilograms of blueberries for muffins. There are four

packages at the fruit market. Which amount is closest to 2.327 kilograms?

A 2.3 kg

B 2.42 kg

C 2.33 kg

D 2.4 kg

20. Multi-Step The chart shows the length of each

student’s pencil. Which person has a pencil

length that can be rounded up to the nearest

tenth of an inch?

A Lori

B Ping

C Jason

D Annie

Student Pencil Length (inches)

Lori 6.61

Ping 5.055

Jason 4.91

Annie 6.5

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34

Problem SolvingProblem Solving

Homeworkand Practice

Name

1.5 Round DecimalsWrite the place value of the underlined digit. Round each number to the place of the underlined digit.

1. 0.782

2. 4.071

3. 21.939

4. 8.155

5. 34.09

6. 4.276

Round 8.293 to the place named.

7. hundredths _ 8. tenths _ 9. ones _

Round 12.462 to the place named.

10. tenths _ 11. hundredths _ 12. ones _

13. What is Anita’s speed rounded to the

nearest hundredth?

14. The speeds of two runners when rounded to the

nearest tenth are the same. Which two runners

are they?

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

Runner Speeds (meters per second)

Runner Speed

Luke 0.178

Margola 0.169

Anita 0.277

Shateel 0.289

tenths

0.28 meter per second

Luke and Margola

tenths

hundredths

tens

ones

hundredths

0.8

8.2

8.29

12.5

8.3

12.46

8

12

4.07

30

22

4.28

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Module 1 • Lesson 5 33

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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.

33-34 Module 1