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Texas Essential Knowledge and Skills

Number and Operations—5.2.A Represent the value of the digit in decimals through the thousandths using expanded notation and numerals

Also 5.2.B

MATHEMATICAL PROCESSES5.1.D Communicate mathematical ideas and reasoning

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 1.3 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

1.3 Place Value of Decimals How do you read, write, and represent decimals through thousandths?

Essential Question?

Lesson OpenerMaking ConnectionsInvite students to talk about owls.

Ask students to describe what owls look like. (They have small, sharp beaks and wide faces.) Tell students that owls do not make their nests like other birds. They make their nests in holes in trees that other animals like squirrels make.

Using the Digital LessonWork with the whole class to review how to use a place-value chart to compare the value of the digits in a two place decimal. Remind students of the relationship between adjacent numbers in a place-value chart: the value of the digit to the immediate left of a digit in the chart is 10 times as much, and the value of a digit to the immediate right of a number is 1 __ 10 of the decimal place.

Learning TaskConnect the story to the problem.

• Emphasize that when reading a decimal number, the decimal point is represented by the word and.

• Review with students that the expanded form of a number is the sum of the values of each digit in the number. The addends that represent the digits to the left of the decimal point are written in order, starting with the greatest value, say hundreds, followed by tens, and then ones. The addends that represent the digits to the right of the decimal point are also listed in order starting with the greatest value of tenths, then hundredths, then thousandths, and so on.

Literacy and Mathematics• Ask students to find the lengths of eggs from other owl species and write those

decimal lengths in standard, word, and expanded forms.

• Have students analyze the story and evaluate which parts are needed in order to answer the math question.

How do you read, write, and represent decimals through thousandths?

Lesson 1.3 17A

Essential Question?

Unlock the ProblemUnlock the Problem

Mathematical ProcessesMath Talk

Name Number and Operations—5.2.A Also 5.2.B

MATHEMATICAL PROCESSES5.1.D

How do you read, write, and represent decimals through thousandths?

Place Value of Decimals1.3

The Brooklyn Battery Tunnel in New York City is 1.726 miles

long. It is the longest underwater tunnel for vehicles in

the United States. To understand this distance, you need

to understand the place value of each digit in 1.726.

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

Whole numbers are to the left of the decimal point. Decimals

are to the right of the decimal point. The thousandths place

is to the right of the hundredths place.

The place value of the digit 6 in 1.726 is thousandths. The value of 6

in 1.726 is 6 1 _____ 1,000

, or 0.006.

Standard Form: 1.726

Word Form: one and seven hundred twenty-six thousandths

Expanded Form: 1 + 0.7 + 0.02 + 0.006

▲ The Brooklyn Battery Tunnel passes under the East River.

} Value

A Standard Form: 2.35

Word Form: two and _____

Expanded Form: 2 + _____

B Standard Form: __Word Form: three and six hundred fourteen thousandths

Expanded Form: __ + 0.6 + __ + __

Try This! Use place value to read and write decimals.

1 × 1 7 × 1 __ 10 2 × 1 ___ 100

6 × 1 _____ 1,000

1.0 0.7 0.02 0.006

Tens Ones Tenths Hundredths Thousandths

1 7 2 6•

Explain how the value of the last digit in a decimal can help you read a decimal.

Possible explanation: The last digit of a decimal determines the name of the decimal, such as tenths, hundredths, and thousandths.

thirty-fi ve hundredths

3.614

3

0.3 + 0.05

0.01 0.004

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English Language Learners Language SupportELL

ELPS 3.B.3, 4.F.6, 4.G.4Leveled Activities ELPS

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

Intermediate: Activity 23 2.I.4, 2.I.5, 3.F.1

Advanced: Activity 41 4.F.3, 4.F.8

Advanced High: Activity 6 2.I.5, 3.G.2, 4.G.2

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

Auditory / Visual Small Group

Strategy: Model Language• Reading and writing decimals may be difficult for English learners.

Model how to pronounce and write decimals as students work through the lesson.

• As students work on standard form, read the numbers slowly. Ask students to repeat what you say. Write the word form and then have students copy it.

• Continue by changing one or two digits in a number. Have students read it and write the word form.

Unlock the ProblemRead and discuss the problem. Direct students’ attention to the place-value chart.

• How does each decimal place value compare to the place value to its left? Each place value is 1 __ 10 of the place value to its left.

• How does each decimal place value compare to the place value to its right? Each place value is 10 times as much as the place value to its right.

• The last row in the place-value chart shows the value of each digit. What pattern do you notice as you move from one place value to the next lesser place value? Possible answer: Another zero is written to the right of the decimal point, between the decimal point and the digit.

Try This!Students use place value to read and write decimals.

• For Example B, explain how you can write the standard form of the decimal. Possible answer: I can read the word form of the decimal. The “and” represents the decimal, so “three and” means “3.” Then “thousandths” means that the last digit is in the thousandths place. I can write 614 for “six hundred fourteen” and place the last digit 4 in the thousandths place to get 3.614.

Math Talk Use Math Talk to focus on students’ understanding of how to read a decimal. Point out to students that the decimal point is written in word form and read as and.

Mathematical Processes

0.253

two hundred fifty-three thousandths

17 Module 1

Share and ShowShare and Show

Count the number of decimal place-value positions to the digit 3 in

0.3 and 0.003.

0.3 has _ fewer decimal places than 0.003

2 fewer decimal places: 10 × 10 = __

0.3 is __ times as much as 0.003

0.003 is __ of 0.3

So, the thread is __ times as thick as the garden spider’s silk.

The thickness of the garden spider’s silk is

__ that of the thread.

Write the value of the underlined digit.

2. 0.543

____

3. 6.234

____

4. 3.954

____

Write the number in two other forms.

5. 0.253

______

______

______

6. 7.632

______

______

______

Example Use place value to compare.

The silk spun by a common garden spider is about 0.003 millimeter thick.

A commonly used sewing thread is about 0.3 millimeter thick. How does

the thickness of the spider silk and the thread compare?

1. Complete the place-value chart to find the value of each digit.

Ones Tenths Hundredths Thousandths

3 5 2 4

3 × 1 2 × 1 ___ 100

0.5} Value

•

2

100

100

1 ___

100

100

1 ___

100

5 × 1 __ 10

4 × 1 _____ 1,000

3 0.02 0.004

four hundredths, or 0.04 two tenths, or 0.2 four thousandths, or 0.004

two hundred fi fty-three thousandths seven and six hundred thirty-two

0.2 + 0.05 + 0.003 thousandths

7 + 0.6 + 0.03 + 0.002

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

Enrich

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Visual / KinestheticIndividual

Materials: Place-Value Chart, Spinners (see eTeacher Resources)

• Have students spin a spinner labeled from 0 to 9. Students spin four times. After each spin, they can write the digit in either the ones place, the tenths place, the hundredths place, or the thousandths place of a place-value chart.

• After writing the last digit in the place-value chart, have students write the decimal in standard form, word form, and expanded form.

• Students can continue spinning to form new decimals and write them in standard form, word form, and expanded form.

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Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 2

ExampleWork through the example with students. Be sure students recognize that the value of each place is 1 __ 10 the value of the place to its left or 10 times as much as the value of the place to its right.

• How do you know that 0.3 is greater than 0.003? Possible answer: 0.3 is greater because the value of the digit 3 decreases as I move across the place-value chart from left to right. So, 0.3 is 100 times as much as 0.003.

Go Deeper• Explain how to find the unknown factor:

0.035 = 35 × . Possible explanation: I can use the place value of the digit farthest to the right, 5, as the unknown factor, which is 1 thousandth. So, 0.035 = 35 × 1 ____ 1,000 .

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.

COMMON ERRORSError Students may not write a decimal in word form correctly.

Example In word form, 0.489 is written as four hundred eighty-nine tenths.

Springboard to Learning Have students use a place-value chart to put each digit in its correct place-value position. Then ask students to circle the place value farthest to the right. Tell students to name the decimal using this place value.

CE

Ones Tenths Hundredths Thousandths

2 .

Lesson 1.3 18

Problem SolvingProblem Solving

California

New Mexico

New York

Wisconsin

Maine

0.564

0.372

1.041

0.820

1.074

Average Annual Rainfall (in meters)

Problem SolvingProblem Solving

Write MathWrite Math Show Your Work

Name

7. Connect You can use place-value patterns

to rename a decimal. Complete the chart

to rename 0.3 using other place values.

8. Write MathWrite Math Explain how you know that

the digit 6 in the numbers 3.675 and 3.756 does

not have the same value.

0.300 3 tenths 3 × 1 __ 10

0.300 _ hundredths _ × 1 ___ 100

0.300 ___ ___

Use the table for 9–11.

9. What is the value of the digit 7 in New Mexico’s

average annual rainfall?

10. The average annual rainfall in Maine is one and

seventy-four thousandths meters per year. Complete

the table by writing that amount in standard form.

11. Which of the states has an average annual rainfall

with the least number in the thousandths place?

12. Multi-Step Dan used a meter stick to

measure some seedlings in his garden. One day, a

corn stalk was 0.85 m tall. A tomato plant was 0.850 m.

A carrot top was 0.085 m. Which plant was shortest?

13. What’s the Error? Damian wrote the number four

and twenty-three thousandths as 4.23. Describe and correct his error.

300 × 1 _____ 1,000

300 thousandths

30 30

Possible explanation: In 3.675, the digit 6 is in the tenths place, so its value is 6 × 1 __ 10

, or

0.6. In 3.756, the digit 6 is in the thousandths place, so its value is 6 × 1 ____

1,000 , or 0.006.

See the table.

a place holder in the tenths place; 4.023.

Possible description: Damian did not include

the carrot

Wisconsin

seven hundredths, or 0.07

Module 1 • Lesson 3 19

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E3Enrich

Enrich 3

Decimals as Scores

Four gymnasts competed in three events at a gymnastics meet. The

table shows the gymnasts’ scores.

Gymnast Balance Beam Uneven Bars Floor Exercise

Cara 8.975 9.025 9.537

Addison 9.152 9.25 8.805

Shelby 8.575 9.375 8.75

Meg 9.5 8.85 9.05

1. Who earned a score of eight and five hundred seventy-five thousandths? In which event did she earn that score?

2. Who earned a score of 9 3 1 1 2 3 ( 1 ___ 100 ) 1 5 3 ( 1 ____ 1,000 )?

In which event did she earn that score?

3. Who earned a score with a 3 in the tenths place? In which

event did she earn that score?

4. Who earned a score of nine and five hundredths? In which

event did she earn that score?

5. Who earned a score with a 2 in the thousandths place?

In which event did she earn that score?

6. Who earned a score of 8 3 1 1 8 3 ( 1 __ 10 ) 1 5 3 ( 1 ____ 1,000 )? In which event did she earn that score?

7. How many gymnasts earned a score in which one of the digits has a value of 0.07?

Use the data in the table to answer the questions.

Shelby; balance beam

Cara; uneven bars

Shelby; uneven bars

Meg; floor exercise

Addison; balance beam

Addison; floor exercise

2 gymnasts

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You can use a place-value chart to find the value of each digit in a decimal. Write whole numbers to the left of the decimal point. Write decimals to the right of the decimal point.

The place value of the digit 8 in 3.847 is tenths. The value of 8 in 3.847 is 8 × 1 __ 10 , or 0.8.You can write a decimal in different forms.

Standard Form:

Expanded Form: + + +

When you write the decimal in word form, write “and” for the decimal point.

Word Form: three eight hundred forty-seven

1. Complete the place-value chart to find the value of each digit.

Write the value of the underlined digit.

2. 0.792

3. 4.691

4. 3.805

5.2.APlace Value of DecimalsOBJECTIVE Read and write decimals through thousandths.

LESSON 2

3.847

3 0.8 0.04 0.007

thousandthsand

Value

Value

Ones Tenths Hundredths Thousandths

3 8 4 7

3 × 1 8 × 1 __ 10 4 × 1 __ 100 7 × 1 ___ 1,000

3.0 0.8 0.04 0.007

Ones Tenths Hundredths Thousandths

2 6 9 5

2 × 1 9 × 1 __ 100

0.62 0.09 0.005

9 hundredths, or 0.09

6 tenths, or 0.6

5 thousandths, or 0.005

5 × 1 _____ 1,000

6 × 1 ___ 10

Number and Operations 3

Enrich 3RtI Tier 1 Lesson 2

Problem SolvingExercise 7 Students should recognize that zeros written at the end of a decimal change the way the decimal is read, but do not change its value.

• Compare the values of 0.3 and 0.30. Possible answer: 0.3 is 3 tenths. 0.30 is 30 hundredths, which is the same as 3 tenths.

• How does writing a zero at the end of a decimal change it? Possible answer: The value is not changed, just the way you read the decimal.

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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19 Module 1

Mathematical Processes

Daily Assessment TaskDaily Assessment Task

Fill in the bubble completely to show your answer.

14. Although the average turkey sandwich in Turkeyton costs 3.456

dollhorts, the cost of a gourmet turkey sandwich at Sandwich Palace

is 5.032 dollhorts. What does the 3 in 5.032 dollhorts represent?

A 3 dollhorts

B 3 tenths of a dollhort

C 3 hundredths of a dollhort

D 4 hundredths of a dollhort

15. Use Math Language One meter is equal to about 3.281 feet. What is

the word form of this decimal?

A three and twenty-eight hundredths and one thousandth

B three and two hundred eighty-one thousandths

C three and two tenths and eighty-one thousandths

D three point two eighty-one

16. Multi-Step Sam had a piece of ribbon 8.469 centimeters long. He cut

off exactly one tenth of a centimeter from the ribbon. Then he cut off two

hundredths of a centimeter. How long is the ribbon now?

A 8.169 cm

B 8.269 cm

C 8.349 cm

D 8.466 cm

TEXAS Test Prep 17. In 24.736, which digit is in the thousandths place?

A 4

B 7

C 3

D 6

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Daily Assessment Task 1

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Differentiated Centers Kit

• Soar to Success MathWarm-Up 2.28, 4.28

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

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 C They incorrectly identified the decimal place-value

Essential Question? WriteMathWriteMath

How do you read, write, and represent decimals though thousandths? Possible answer: You can use a place-value chart to help you see the value of each digit. Each place is 10 times as much as the place to its right. A decimal can be written in standard form, word form, or expanded form. The last digit determines the name of the decimal.

• Enrich 3

• Homework and Practice Lesson 1.3

Can students read and write decimals through thousandths?

Lesson 1.3 20

TEXAS Test PrepLesson CheckLesson Check

Fill in the bubble completely to show your answer.

7. In the number 5.923, which number is in the

thousandths place?

A 5

B 9

C 2

D 3

8. Which number has the same value as

7 × 1 ____ 1,000

?

A 0.7

B 0.007

C 0.07

D 7.0

9. Multi-Step Which value correctly represents

the number that is 10 times as great as five

hundred eighty-one thousandths?

A 5.81

B 581

C 0.581

D 500.81

10. Which number has the same value

as 3 × 1 __ 10

?

A 0.003

B 3.10

C 0.3

D 0.03

11. Jack’s baby sister crawled three and five tenths

meters today. Which number represents that

distance?

A 3.5

B 3.05

C 3.510

D 3.005

12. Multi-Step Leon measured the distance

each of his four toy cars rolled across the floor.

Which car measurement that has a 4 in the

thousandths place represents the shortest

distance rolled?

A 0.741 meter

B 0.714 meter

C 0.224 meter

D 0.213 meter

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Problem SolvingProblem Solving

Homeworkand Practice

Name

Rename 0.6 using other place values.

1.

2.

Write the number in two other forms.

3. 0.632

4. 4.293

5. A weather reporter reads aloud the number of

meters of snowfall. The amount is 0.103 meter.

What words should the reporter use on the air

to explain the amount of snowfall?

6. Amil says that the snow on the ground is

5 × 1 ___ 100

meter high. How can this number be

expressed as a decimal?

1.3 Place Value of Decimals

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

0.200 2 tenths 2 × 1

__ 10

0.200 20 __ 20 × _

0.200

Rename 0.2 using other place values.

six hundred thirty-two thousandths

one hundred three thousandths

of a meter

0.05 meter

4 and two hundred ninety-three

0.6 + 0.03 + 0.002

4 + 0.2 + 0.09 + 0.003

600 × 1 _____ 1,000

200 × 1 _____ 1,000

600 thousandths

hundredths

200 thousandths

1 ___ 100

6060

thousandths

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Module 1 • Lesson 3 21

0.600 6 tenths 6 × 1

__ 10

0.600 _ hundredths _ × 1 ___ 100

0.600

555555555

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

21-22 Module 1