1.3 Place Value of Decimals

1.3

Place Value of Decimals

? Essential Question How do you read, write, and represent decimals through

thousandths?

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

Lesson Opener

Making Connections

Invite 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 Lesson

Work 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 Task

Connect 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.

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 PROCESSES 5.1.D Communicate mathematical ideas and reasoning

Are You Ready?

Access Prior Knowledge Use 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

Resources

For the student

For the teacher

Interactive Student Edition provides students with an interactive learning environment!

Math on the Spot Video Tutor

iTools Virtual Manipulatives

Digital Management Center organizes program resources by TEKS!

eTeacher Edition

Online Assessment System

Soar to Success Math Online Intervention

Lesson 1.3 17A

Unlock the Problem

Read 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.

Math Talk

Mathematical Processes

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.

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.

? Houghton Mifflin Harcourt Publishing Company ? Image Credits: (tr) ?Jeremy Graham/Alamy Images

Name

1 . 3 Place Value of Decimals

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

Number and Operations--5.2.A Also 5.2.B

MATHEMATICAL PROCESSES 5.1.D

UUnnlloocckk tthhee PPrroobblleemm

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.

Tens Ones

Tenths

1?

7

1?1 1.0

7

?

_1_ 10

0.7

Hundredths 2

2

?

__1_ 100

0.02

Thousandths 6

6

?

__1___ 1,000

0.006

The Brooklyn Battery Tunnel passes under the East River.

} Value

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

The place value of the digit 6 in 1.726 is thousandths. The value of 6 in 1.726 is 6 _1_,01_0_0_, or 0.006.

Standard Form: 1.726 Word Form: one and seven hundred twenty-six thousandths

Math Talk

Mathematical Processes

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

Expanded Form: 1 + 0.7 + 0.02 + 0.006

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

A Standard Form: 2.35

Word Form: two and _th_ irty-fiv_ e hun_ dredth_ s

Expanded Form: 2 + ___ 0.3 + _ 0.05 _

B Standard Form: _ 3.61_ 4

Word Form: three and six hundred fourteen thousandths

Expanded Form: _3_ + 0.6 + _0.0_ 1 + _ 0.00_ 4

Module 1 17

English Language Learners

Leveled Activities

Beginning: Activity 38 Intermediate: Activity 23 Advanced: Activity 41 Advanced High: Activity 6

ELPS 1.B.1, 2.D.1, 3.B.3 2.I.4, 2.I.5, 3.F.1 4.F.3, 4.F.8 2.I.5, 3.G.2, 4.G.2

for the ELL Activity Guide containing these leveled activities.

17 Module 1

ELL Language Support

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

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.

0.253 two hundred fifty-three thousandths

? 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.

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?

Count the number of decimal place-value positions to the digit 3 in 0.3 and 0.003.

_ 0.3 has 2 fewer decimal places than 0.003

2 fewer decimal places: 10 ? 10 = _10_ 0

0.3 is _10_ 0 times as much as 0.003

__ _1__

0.003 is

100

of 0.3

So, the thread is _10_ 0 times as thick as the garden spider's silk.

The thickness of the garden spider's silk is

__101__ 0_ that of the thread.

SShhaarree aanndd SShhooww

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

Ones

Tenths

3? 5

3?1 3

5

?

_1_ 10

0.5

Hundredths 2

2

?

_1__ 100

0.02

Thousandths

4

4

?

__1___ 1,000

0.004

} Value

Write the value of the underlined digit.

2. 0.543

3. 6.234

_ four h_ undre_ dths, o_ r 0.04

_two_ tenth_ s, or 0_ .2

4. 3.954

f_ our th_ ousan_ dths, o_ r 0.004

Write the number in two other forms. 5. 0.253

t_ wo hu_ ndred_ fifty-th_ ree th_ ousan_ dths _ 0.2 + 0_ .05 +_ 0.003___ ______

6. 7.632

_ seven_ and si_ x hund_ red th_ irty-tw_ o _ thousa_ ndths____ _ 7 + 0.6_ + 0.0_ 3 + 0_ .002 __

18

Enrich

Visual / Kinesthetic Individual

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.

Ones Tenths Hundredths Thousandths

9 8 7 65

01 2 3

4

.

2

? 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.

Go to Go to for additional enrichment activities in the Enrich Activity Guide.

? Houghton Mifflin Harcourt Publishing Company

Example

Work 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,_01_0_0.

Share and Show

The 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.

3

2 1

Quick Check

IF

a student misses the checked exercises

THEN

Differentiate Instruction with RtI Tier 1 Lesson 2

COMMON ERRORS

Error 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.

Lesson 1.3 18

Problem Solving

Exercise 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.

Math on the Spot videos are in the Interactive Student Edition and at .

Name

PPrroobblleemm SSoollvviinngg

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 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 0.300 0.300

3 tenths

_ 30 hundredths _ 300 t_ housa_ ndths

3

?

_1_ 10

_ 30

?

__1_ 100

_30_ 0 ? _1_,0_ 1_0_0_

Possible explanation: In 3.675, the digit 6 is in the tenths place, so its value is 6 ? _110_, 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.

PPrroobblleemm SSoollvviinngg

Use the table for 9?11.

9. What is the value of the digit 7 in New Mexico's average annual rainfall?

seven hundredths, or 0.07

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. See the table.

11. Which of the states has an average annual rainfall with the least number in the thousandths place?

Wisconsin

Average Annual Rainfall (in meters)

California New Mexico New York Wisconsin Maine

0.564 0.372 1.041 0.820 1.074

Write Math Show Your Work

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?

the carrot

13.

What's the Error? Damian wrote the number four

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

Possible description: Damian did not include

a place holder in the tenths place; 4.023.

Module 1 ? Lesson 3 19

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19 Module 1

3

2

RtI Tier 1 Lesson 2

1

Name

LESSON 2

Place Value of Decimals

OBJECTIVE Read and write decimals through thousandths.

1 5.2.A

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.

Ones

3 3? 1

3.0

Tenths

8

8

?

_1_ 10

0.8

Hundredths

4

4?

_1_ 100

0.04

Thousandths

7

7?

__1 _ 1,000

0.007

Value

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: 3.847

Expanded Form: 3 + 0.8 + 0.04 + 0.007

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

Word Form: three and eight hundred forty-seven

thousandths

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

Ones

Tenths

Hundredths

Thousandths

2

6

9

5

2? 1

6

?

_1__ 10

9

?

_1_ 100

5

?

__1___ 1,000

2

0.6

0.09 0.005 Value

Write the value of the underlined digit.

2. 0.792

3. 4.691

9 hundredths, 6 tenths,

or 0.09

or 0.6

4. 3.805

5 thousandths, or 0.005

Number and Operations

3

? Houghton Mifflin Harcourt Publishing Company

Enrich 3

Name

Decimals as Scores

Four gymnasts competed in three events at a gymnastics meet. The table shows the gymnasts' scores.

Gymnast Cara Addison Shelby Meg

Balance Beam 8.975 9.152 8.575 9.5

Uneven Bars 9.025 9.25 9.375 8.85

Floor Exercise 9.537 8.805 8.75 9.05

Use the data in the table to answer the questions.

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

Shelby; balance beam

2. Who earned a score of 9 3 1 1 2 3 (_110_0_) 1 5 3 (_1,_01_0_0)? In which event did she earn that score?

Cara; uneven bars

3. Who earned a score with a 3 in the tenths place? In which event did she earn that score?

Shelby; uneven bars

4. Who earned a score of nine and five hundredths? In which event did she earn that score?

Meg; floor exercise

5. Who earned a score with a 2 in the thousandths place? In which event did she earn that score?

Addison; balance beam

6. Who earned a score of 8 3 1 1 8 3 (_110_) 1 5 3 (_1,_01_0_0)? In which event did she earn that score?

Addison; floor exercise

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

2 gymnasts

Enrich ? Houghton Mifflin Harcourt Publishing Company

E3

Enrich 3

DDaaiillyy AAsssseessssmmeenntt TTaasskk

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

Mathematical Processes Model ? Reason ? Communicate

TEXAS Test Prep

17. In 24.736, which digit is in the thousandths place? A4 B7 C3 D6

20

3

Daily Assessment Task

2 1

Can students read and write decimals through thousandths?

IF

THEN

NO

? Soar to Success Math

Warm-Up 2.28, 4.28

YES

? Enrich 3

? Homework and Practice

Lesson 1.3

TEXAS Test Prep Coach

In the Test Prep exercise, if students selected:

A, B, or C They incorrectly identified the decimal place-value

? Essential Question

Write Math

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.

? Houghton Mifflin Harcourt Publishing Company

Differentiated Centers Kit

Literature Dewey and His Decimals Students read about the Dewey Decimal system used to order books in the library.

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

Lesson 1.3 20

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