Model Decimals with Base-10 Blocks - Everyday Math … 5 7 353 LESSON 5 7 Name Date Time Math Message Write the following amounts using a dollar sign and a decimal point: 1. 3 dollar

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352 Unit 5 Place Value in Whole Numbers and Decimals

Advance PreparationCut apart copies of Math Masters, page 138 and place the slips near the Math Message. Set aside space on the board or class Data Pad

for children to record their hand-span measures. For the optional Readiness activity in Part 3, assemble a 10-by-10 grid from Math Masters,

pages 426 and 427 for each small group.

Teacher’s Reference Manual, Grades 1–3 pp. 60, 61

Key Concepts and Skills• Use base-10 blocks and grids to model

tenths and hundredths and write money

amounts in dollars-and-cents notation;

read and write decimal numbers through

hundredths. [Number and Numeration Goal 1]

• Use base-10 blocks and grids to represent

decimal and fraction equivalencies.

[Number and Numeration Goal 5]

• Compare and order decimals on 10-by-10

grids. [Number and Numeration Goal 6]

Key ActivitiesChildren use money and base-10 blocks

to extend their understanding of decimal

notation for tenths and hundredths. They

compare and order decimal numbers.

Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 138. [Number and Numeration Goal 1]

Ongoing Assessment: Informing Instruction See page 354.

Key Vocabularytenths � hundredths

MaterialsMath Journal 1, pp. 114 and 115

Home Link 5�6 � Math Masters, p. 138;

pp. 126 and 127 (optional) � transparency

of Math Masters, p. 425 � overhead base-10

cubes and longs (if available) � base-10

flat � per partnership: at least 10 cubes and

10 longs � slate (optional)

Displaying Data on a Line PlotStudent Reference Book, pp. 79–82,

89A, and 89B

Math Journal 1, p. 64

Math Masters, p. 166A

transparency of Math Masters, p. 166A

(optional)

Children display data of their hand

spans on a line plot.

Math Boxes 5�7Math Journal 1, p. 116

Children practice and maintain skills

through Math Box problems.

Home Link 5�7Math Masters, p. 139

Children practice and maintain skills

through Home Link activities.

READINESS

Exploring Equivalent Names for CoinsMath Masters, pp. 426 and 427

per group: 100 pennies, 10 dimes, slate,

calculator

Children explore equivalent names for a

penny and a dime.

ENRICHMENTWriting Names on Hundred GridsMath Masters, p. 140

optional: calculator, scissors, construction

paper, glue

Children find decimal values for each letter

in their first names.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 132

Children add the terms tenths and

hundredths to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Model Decimals withBase-10 Blocks

Objectives To model decimals with base-10 blocks; and to

review decimals with money.

Or

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Lesson 5�7 353

LESSON

5�7

Name Date Time

Math Message

Write the following amounts using a dollar sign and a decimal point:

1. 3 dollar bills, 5 dimes, and 1 penny

2. 3 dimes and 6 pennies

3. 2 dollar bills and 7 dimes

4. 9 pennies $0.09

$2.70

$0.36

LESSON

5�7

Name Date Time

Math Message

Write the following amounts using a dollar sign and a decimal point:

�

py

gg

pp

yg

g

$3.51

EM3MM_G3_U05_119-166.indd 138 1/10/11 4:45 PM

Math Masters, page 138

Ongoing Assessment: Informing Instruction

Use the Math Message to assess children’s

progress toward reading and writing money

totals in decimal notation. Children are

making adequate progress if they are able to

record the money amounts for the problems,

with coins and bills. Some children may be

able to record the money amounts without

coins and bills.

[Number and Numeration Goal 1]

Math

Message �

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Masters, p. 138)

Children read their answers aloud. The word and in three dollars and fifty-one cents is used to denote the decimal point.

There are 10 dimes in a dollar, so one dime is 1 _ 10 of a dollar.Similarly, there are 100 pennies in a dollar, so one penny is 1 _ 100 of a dollar.

In dollars-and-cents notation, the first digit to the right of the decimal point stands for dimes, or tenths of a dollar; the second digit stands for pennies, or hundredths of a dollar.

Make sure that all children have recorded their hand-span measures on the board or Class Data Pad. The measures will be used for the Part 2 line-plot activity.

� Exploring Tenths with WHOLE-CLASS ACTIVITY

Base-10 Blocks(Math Journal 1, p. 114; Math Masters, p. 425)

Explain that base-10 blocks can be used to model tenths and hundredths. Display the transparency of Math Masters, page 425. Demonstrate that the grid has the same area as the top of a flat. Using the overhead transparency and overhead or regular base-10 blocks, guide children through the activities on journal page 114 as they follow along in pairs.

1. Children place a long on the inside edge of the grid on the journal page. Ask: How many longs do you need to cover the

whole grid? 10 What fraction of the grid is one long? 1 _ 10

Getting Started

Math Message �Take a Math Message slip. Follow the directions.Turn to Math Journal 1, page 64. Record the measure of your hand span on the board.

Home Link 5�6 Follow-Up Children share their number stories for others to solve.

Mental Math and Reflexes Dictate numbers as children write them on their slates or on Math Masters, pages 126 or 127. Suggestions:

213,789; 506,311

700,002; 304,500

7,000,304; 9,078,415

For each number, ask such questions as:

• Which digit is in the thousands place?

• What is the value of the digit x?

• How many ten-thousands are there?

Adjusting the Activity ELL

To support English language learners, clarify

the difference between the ordinal meaning

of tenth and a tenth as part of something; for

example, tenth in line vs. tenth of a dollar.

When saying the decimal place-value names,

exaggerate the th sound in the word.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

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A Flat

Name Date Time

Math Masters, p. 425

Teaching Aid Master

Place Value in DecimalsLESSON

5 � 7

Date Time

If the grid is ONE, then which part of each grid is shaded?

Write a fraction and a decimal below each grid.

1.

fraction:

decimal:

2.

fraction:

decimal:

3.

fraction:

decimal: 0.720.080.5 or�12� or �1

50� or �1

5000�

0.50

�1800� �1

7020�


Student Page


0.1 one-tenth 1—10

0.2 two-tenths 2—10

0.3 three-tenths 3—10

0. 4 four-tenths 4—10

cube long flat big cube

ONE 10 100 1,000

0.01 0.1 ONE 10

2. Hold up a flat in one hand and a long in the other. If this (the flat) is ONE, then what is this? (Hold up the long.) 1 _ 10

3. Write 0.1 on the board. Explain that this is another way of writing 1 _ 10 ; 0.1 is read as one-tenth. Next to 0.1 write one-tenth and 1 _ 10 .

4. Write 0.2 on the board. Partners show this number on their grids with base-10 blocks. Place two longs on the grid. How do you read this decimal? Two-tenths Next to 0.2, write two-tenths and 2 _ 10 . Repeat with other tenths, such as 0.3 and 0.4.

The value of the base-10 blocks depends on which block is ONE.

Ongoing Assessment: Informing Instruction

Watch for children who are having difficulty understanding that the value of

base-10 blocks can change. Explain that base-10 blocks model numbers, but

their values can change depending on which block is defined as the ONE. For

decimals, it’s often better to define the flat as the ONE.

� Exploring Hundredths Using WHOLE-CLASS ACTIVITY

Base-10 Blocks(Math Journal 1, p. 114)

Go through the following procedure with the class:

1. Children place a single cube in a corner along the inside edge of the grid on journal page 114. Ask: How many cubes do you need to cover the whole grid? 100 What fraction of the grid is

one cube? 1 _ 100

2. Hold up a flat in one hand and a cube in the other. If this (the flat) is ONE, then what is this? (Hold up the cube.) 1 _ 100

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Place Value in Decimals continuedLESSON

5 �7

Date Time

5. Color 0.7 of the grid. 6. Color 0.07 of the grid. 7. Color 0.46 of the grid.

9. Color 4 _ 10 of the grid. 10. Color 1

_ 2 of the grid. 11. Color 23

_ 100

of the grid.

4. Which decimal in each pair is greater? Use the grids in Exercises 1–3

to help you.

0.5 or 0.08 0.5 0.08 or 0.72 0.72 0.5 or 0.72 0.72

Color part of each grid to show the decimal named.

8. Write 0.7, 0.07, and 0.46 in order from smallest to largest.

Use the grids in Exercises 5 – 7 to help you. 0.07 0.46 0.7

12. Write 23

_ 100

as a decimal. 0.23

Color part of each grid to show the fraction named.

Try This

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Student Page

Lesson 5�7 355

Adjusting the Activity To illustrate the importance of knowing what the ONE is, hold up a flat in

one hand and a long in the other. Ask: If this (the long) is ONE, what is this? (Hold up the flat.) 10 If this (the cube) is ONE, what is

this? (Hold up the flat.) 100

AUDITORY � KINESTHETIC � TACTILE � VISUAL

3. Write 0.01 on the board and remind the class that this is another way of writing 1 _ 100 . Explain that 0.01 is read as one- hundredth. Next to 0.01, write one-hundredth and 1 _ 100 .

4. Write 0.05 on the board and ask children how to show this number with base-10 blocks on their grids. Place five cubes on the grid. How do you read this decimal? Five-hundredths Next

to 0.05, write five-hundredths and 5 _ 100 . Repeat with other hundredths, such as 0.13 and 0.20.

� Comparing and Ordering INDEPENDENTACTIVITY

Decimals on a Square Grid(Math Journal 1, pp. 114 and 115)

Children write fractions and decimals naming the shaded parts of square grids and use the grids to compare decimals. They color other grids and use them to order decimals from smallest to largest.

2 Ongoing Learning & Practice

� Displaying Data on a WHOLE-CLASS ACTIVITY

Line Plot(Math Journal 1, p. 64; Math Masters, p. 166A; Student Reference Book,

pp. 79–82, 89A, and 89B)

Explain to children that they will make a line plot to show hand-span measures for the class. As needed, review landmark data and line plots with children using Student Reference Book, pages 79-82, 89A, and 89B.

Have children copy the class set of hand-span measures from the board or Class Data Pad onto blank paper in order from shortest to longest.

Distribute Math Masters, page 166A to children. Draw a line for the line plot on the board or display a transparency of Math Masters, page 166A. Have children label the vertical axis Number of Children on page 166A while you write it on the board or transparency. Ask children to suggest a label for the horizontal axis and write it on the line. Sample answers: Measures of Hand Spans in Inches; Hand-Span Lengths in Inches In a similar manner, ask children to suggest a title for the line plot. Sample answer: Class Measures of Hand Spans

Next, discuss the scale for the line plot. The data on hand spans shows measures to the nearest 1 _ 2 inch, so the scale should begin with the shortest hand span, increase in 1 _ 2 -inch increments, and end with the measurement of the longest hand span. Model writing the scale on the board or transparency while the class writes the scale on page 166A. Have children draw Xs to represent the class data on their line plot.

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Number

ofChildren

Hand Spans (Inches)

6 76 12 7 1

2

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X


Name Date Time

LESSON

5�7 Line Plot

Tit

le:

Answers vary.

EM3MM_G3_U05_119-166.indd 166A 1/25/11 12:45 PM

Math Masters, p. 166A

Teaching Master

Date Time

2. For the number 5,749,862

the 4 means 40,000 the 5 means 5,000,000

the 8 means 800

the 7 means 700,000

the 9 means 9,000

4. Solve using any

method you wish.

6. Use a straightedge. Draw a 7-sided

polygon.

Sample answer:

1. Solve.

16 + 9 = 25

16 + 90 = 106

16 + 900 = 916

16 + 9,000 = 9,016

16 + 90,000 = 90,016 18–21

60–63

102–105

35

250–253260

199+499

698

3. What is another name for 3 dollar

bills and 6 pennies? Fill in the circle

for the best answer.

A $3.60

B $3.06

C $30.60

D 3.06¢

5. Write a division story by filling in

the blanks. There are 48 _______

in 6 rows. How many _______

are in each row? _______

Write a number model.

48 ÷ 6 = 8

chairs

chairs

8

Math BoxesLESSON

5 �7

Unit

Unit

EM3cuG3MJ1_U05_102-127.indd 116 12/30/10 5:49 PM


Student Page


Use the line plot to have children identify the maximum, minimum, range, and mode of the hand-span data. Next, find the median measurement of class hand spans by having children cross off an X from each end of the line plot one after another until one or two remain.

� Math Boxes 5�7 INDEPENDENTACTIVITY

(Math Journal 1, p. 116)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-5. The skill in Problem 6 previews Unit 6 content.

� Home Link 5�7 INDEPENDENTACTIVITY

(Math Masters, p. 139)

Home Connection Children write fractions and decimals naming the shaded parts of square grids. They use the grids to compare the decimals. They also color grids and use them to order decimals from smallest to largest.

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Exploring Equivalent 15–30 Min

Names for Coins (Math Masters, pp. 426 and 427)

To provide experience with decimals using a concrete model, have children arrange 100 pennies on the 10-by-10 grid. Ask:

● How many dollars are on your grid? One dollar

● How many pennies are on your grid? 100 pennies

● What part of a dollar is a penny? 1 _ 100 of a dollar

● Write one penny in decimal notation on your slate. $0.01

Children count their pennies using calculators. Have them share their ideas about what they need to enter into the calculator to count the hundredths of a dollar. Casio key sequence: 0.01 [+] [+] 0 [=] [=] ...

TI key sequence: 0.01 [+] [=] [=] ...

They choral count as the calculator counts up: one hundredth, two hundredths, and so on.


LESSON

5�7

Name Date Time

Writing Names on Hundred Grids

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Teaching Master

Lesson 5�7 357

The value of this letter K on a

hundred grid is 0.2 or .20.

1.

fraction:

decimal:

2.

fraction: 9

_ 100

decimal:

3.

fraction: 65

_ 100

decimal: 0.650.09

Name Date Time

Understanding DecimalsHOME LINK

5�7

Your child has been using grids like the ones below to understand the meaning of decimals. The grid is made up of 100 squares. Each square is 1 _

100 or 0.01 of the grid.

Ten squares is 1 _ 10

or 0.10 of the grid. 0.8 is read as “eight-tenths.” 0.04 is read as “four-hundredths.” 0.53 is read as “fifty-three hundredths.”

Please return this Home Link to school tomorrow.

Family Note

33–36

If the grid is ONE, then what part of each grid is shaded?

Write a fraction and a decimal below each grid.

4. Which decimal is greater? Use the grids to help you.

0.3 or 0.09 0.3 0.09 or 0.65 0.65 0.3 or 0.65 0.65

8. Write 0.8, 0.04, and 0.53 in order from smallest to largest.

Use the grids to help you. 0.80.530.04

5. Color 0.8 of the grid. 6. Color 0.04 of the grid. 7. Color 0.53 of the grid.

0.3 or 0.30

3

_ 10 or 30

_ 100

EM3MM_G3_U05_119-166.indd 139 1/7/11 3:28 PM


Home Link MasterChildren exchange each row of 10 pennies on their 10-by-10 grid for a dime. Ask:

● Do the coins on the grid still add up to one dollar? yes

● How many dimes are on your grid? 10 dimes

● What part of a dollar is a dime? 1 _ 10

● Write 1 dime in decimal notation on your slate. $0.10

Children count their dimes using calculators. Have them share their ideas about what they need to enter into the calculator to count the tenths of a dollar. Casio key sequence: 0.10 [+] [+] 0 [=] [=] ...

TI key sequence: 0.10 [+] [=] [=] ...

As soon as they put in the first [=], most calculators will change the display and drop the 0 in the hundredths place. Review with children that this is another way to write tenths. Children choral count as the calculator counts up: one tenth, two tenths, and so on.

ENRICHMENT INDEPENDENTACTIVITY

� Writing Names on 15–30 Min

Hundred Grids(Math Masters, p. 140)

To further explore representing decimal numbers on a 100 grid, have children write each letter of their first names on a separate 100 grid. (See margin.) They figure out the decimal value of each letter and label the letter with the decimal number. If appropriate, have children use a calculator to add the values of individual letters to figure out the total value of the letters in their names using the 100 grid as the whole.

You may want to have children cut out the grids they have made, paste them onto construction paper to form their names, label each letter with its decimal value, and display them in the room.

ELL SUPPORT SMALL-GROUPACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 132)

To provide language support for decimals, have children use the Word Bank template found on Differentiation Handbook, page 132. Ask children to write the terms tenths and hundredths, draw a picture representing each term, and write other related words. See the Differentiation Handbook for more information.


Copyright

© W

right

Gro

up/M

cG

raw

-Hill

166A

Name Date Time

LESSON

5�7 Line Plot

Tit

le:

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Documents

Model Decimals with Base-10 Blocks - Everyday Math … 5 7 353 LESSON 5 7 Name Date Time Math Message Write the following amounts using a dollar sign and a decimal point: 1. 3 dollar