www.everydaymathonline.com

Lesson 4�10 289

Advance PreparationFor Part 1, make one copy of Math Masters, page 429 per four students. Cut the sections apart along

the dashed lines.

For the optional Enrichment activity in Part 3, obtain the book If You Hopped Like a Frog by

David M. Schwartz (Scholastic Inc., 1999).

Teacher’s Reference Manual, Grades 4–6 pp. 217, 218

Key Concepts and Skills• Use extended multiplication facts to convert

between metric measurements. 

[Operations and Computation Goal 3]

• Use a scale to determine actual size. 

[Operations and Computation Goal 7]

• Measure lengths to the nearest millimeter. 

[Measurement and Reference Frames Goal 1]

• Describe the relationship among metric

units of length. 

[Measurement and Reference Frames Goal 3]

Key ActivitiesStudents examine the millimeter marks on

their centimeter rulers. They measure line

segments in millimeters and centimeters.

Then they measure illustrations of various

invertebrates in millimeters and convert their

measurements to centimeters.

Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal 3]

MaterialsMath Journal 1, pp. 101–103

Study Link 4�9

Math Masters, p. 429

centimeter ruler � slate � scissors � highlighter

Math Boxes 4�10Math Journal 1, p. 104

Students practice and maintain skills

through Math Box problems.

Study Link 4�10Math Masters, p. 133

Students practice and maintain skills

through Study Link activities.

READINESS

Exploring the Need for MillimetersMath Masters, p. 134

scissors � ruler

Students explore the need for a metric unit

of measure smaller than a centimeter.

ENRICHMENTInvestigating RatiosIf You Hopped Like a Frog

Students explore the concept of scale by

comparing what humans could do if they

had bodies like different animals.

EXTRA PRACTICE

Measuring to the Nearest Millimeter ruler

Students draw line segments and measure

them to the nearest millimeter.

EXTRA PRACTICE

Taking a 50-Facts TestMath Masters, pp. 413 and 414;

p. 416 (optional)

pen or colored pencil

Students take a 50-facts test. They use a

line graph to record individual and optional

class scores.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

�������

Measuring in Millimeters

Objectives To guide students as they measure lengths

to the nearest millimeter; and to provide practice converting

measurements between millimeters and centimeters.

t

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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290 Unit 4 Decimals and Their Uses

Measuring in MillimetersLESSON

4 �10

Date Time

128

Math Message

On your centimeter ruler, the numbered marks are for centimeters and

the little marks between the centimeter marks are for millimeters.

1. Look at your centimeter ruler. How many millimeters are in 1 centimeter? mm

2. Name something that measures about 1 millimeter.

3. Draw a line segment that is 8 centimeters long.

4. Draw a line segment that is 80 millimeters long.

Measure each line segment below using both the millimeter side and the

centimeter side of the cm/mm ruler. Record both measurements.

5.

Length of AB� � mm � cm

6. Length of CD� � mm � cm

7. Length of EF� � mm � cm

Measuring Land Invertebrates

An invertebrate is an animal that does not have a backbone. (The backbone is also

called the spinal column.) Some invertebrates live on land, others in water. The most

common land invertebrates are insects.

The invertebrates shown on page 102, except the earthworm, bumblebee, and

mealybug, have been drawn to about actual size. The earthworm can grow to about

4 times the length shown. The bumblebee is shown about twice its actual size and the

mealybug about 3 times its actual size.

0.88E F

6.262C D

12.5125

A B

Sample answers:

10

thickness of the wire in a paper clip; widthof a pencil point; the edge of a dime

Math Journal 1, p. 101

Student Page

Mental Math

and Reflexes �

�

Ongoing Assessment:Recognizing Student Achievement

Use Mental Math and Reflexes to assess students’ automaticity with

multiplication facts. Students are making adequate progress if they demonstrate

automaticity with the and problems. Some students may demonstrate

automaticity with the problems.

[Operations and Computation Goal 3]

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Journal 1, p. 101)

If students have difficulty naming things that measure about 1 millimeter, suggest these possibilities: the thickness of the wire in a paper clip; the width of a pencil point; or the edge of a dime.

Students should conclude that both line segments they drew are the same length. Thus, 8 centimeters = 80 millimeters.

In this lesson students use millimeters to measure very small invertebrates. They also practice converting millimeters to centimeters.

Math MessageComplete Problems 1–4 on journal page 101.

Study Link 4�9 Follow-Up Ask students to circle the most difficult problems. Then have students see if someone at their table can suggest a solution strategy.

Mental Math and ReflexesPose multiplication facts and extended facts. Suggestions:

0 ∗ 6 = 0 6 ∗ 6 = 36 40 ∗ 5 = 200

9 ∗ 1 = 9 3 ∗ 4 = 12 300 ∗ 6 = 1,800

2 ∗ 7 = 14 7 ∗ 7 = 49 70 ∗ 80 = 5,600

5 ∗ 8 = 40 4 ∗ 6 = 24 40 ∗ 90 = 3,600

10 ∗ 3 = 30 6 ∗ 3 = 18 500 ∗ 30 = 15,000

Getting Started

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Adjusting the Activity

Adjusting the Activity

100

2030

4050

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160m

m5

1525

3545

5565

7585

95105

115125

135145

155

10

23

45

67

89

1011

1213

1415

16cm

0.51.5

2.53.5

4.55.5

6.57.5

8.59.5

10.511.5

12.513.5

14.515.5

Fold

100

2030

4050

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8090

100110

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140150

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m5

1525

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115125

135145

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45

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89

1011

1213

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16cm

0.51.5

2.53.5

4.55.5

6.57.5

8.59.5

10.511.5

12.513.5

14.515.5

Fold

100

2030

4050

6070

8090

100110

120130

140150

160m

m5

1525

3545

5565

7585

95105

115125

135145

155

10

23

45

67

89

1011

1213

1415

16cm

0.51.5

2.53.5

4.55.5

6.57.5

8.59.5

10.511.5

12.513.5

14.515.5

Fold

100

2030

4050

6070

8090

100110

120130

140150

160m

m5

1525

3545

5565

7585

95105

115125

135145

155

10

23

45

67

89

1011

1213

1415

16cm

0.51.5

2.53.5

4.55.5

6.57.5

8.59.5

10.511.5

12.513.5

14.515.5

Fold

Name Date Time

A cm/mm Ruler

Math Masters, p. 429

Teaching Aid Master

Measuring Land InvertebratesLESSON

4 �10

Date Time

Bumblebee(2 times actual size)

Horsefly Mealybug(3 times actual size)

Water scavenger beetle

Mayfly

Dragonfly

LacewingGround beetle

Earthworm

Threadworm

Math Journal 1, p. 102

Student Page

Lesson 4�10 291

40

13

0.4

4.2

0.8

23

1

0.1

10

� Measuring Lengths in WHOLE-CLASS ACTIVITY

Millimeters and Centimeters(Math Journal 1, p. 101; Math Masters, p. 429)

Pass out the quarter-sheets of Math Masters, page 429 and have students cut out the cm/mm rulers. Then have them fold the rulers carefully along the center line. Encourage students to use a highlighter to mark mm and cm on the ruler so that the units are emphasized.

Demonstrate how to use the centimeter side of the ruler by having students measure the line segment they drew in Math Message Problem 3. Instruct students to place the centimeter side of the folded ruler above the line segment with 0 aligned with the left end of the segment. Then demonstrate how to use the millimeter side of the ruler by having students measure the line segment they drew in Problem 4. Instruct students to place the millimeter side of the folded ruler under the line segment with 0 aligned with the left end of the segment.

Now ask students to measure line segments AB, CD, and EF (Problems 5–7) using both sides of the cm/mm ruler. Record their measurements on the board: 125 mm = 12.5 cm; 62 mm = 6.2 cm; 8 mm = 0.8 cm.

NOTE When converting between millimeters and centimeters, tell students to

think of the centimeter as the ONE, or the unit, and the millimeter as 1

_ 10 .

Some students may note that the measurements of each line segment

on journal page 101 vary slightly. Ask students to explain why they think this

might happen. Possible response: “The spaces between millimeter marks are so

small. A measurement is never exact—it is only an approximation.”

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

Write several millimeter/centimeter conversion problems on the board. Ask students to write their answers on their slates. Suggestions:

1 cm = mm 4 cm = mm 2.3 cm = mm

10 mm = cm 130 mm = cm 42 mm = cm

1 mm = cm 4 mm = cm 8 mm = cm

Have students use their cm/mm rulers as concrete models for

conversions between metric units. Pose millimeter/meter conversions to students.

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

ELL

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292 Unit 4 Decimals and Their Uses

104

Math Boxes LESSON

4 �10

Date Time

5. Without measuring, estimate the height

of your chair. Then measure it.

a. Estimate:

About cm

b. Measurement:

About cm

1. Solve mentally or with a paper-and-pencil

algorithm.

a. 4,647 b. 2,500

+ 3,228 - 1,398

3. Tell whether each number sentence

is true or false.

a. 2.34 - 0.09 = 2.25 true

b. 89.6 + 21.7 = 111.3 true

c. 56.4 - 23.8 < 33 true

d. 5.17 + 3.86 > 10 false

4. Name two properties of a regular polygon.

a. The sides are the same

length.

b. The angles have the

same measure.

129

97

182 183

10–15

128 130

2. Complete.

a. 7 cm = 70

mm

b. 15 cm = 150

mm

c. 500 cm = 5

m

d. 4

cm = 40 mm

e. 800

cm = 8 m

7,875 1,102

36 37 148

6. Complete.

a. Is 326 closer to 300 or 400?

300

b. Name the number halfway

between 500 and 800.

650

Sample answers.

Answers vary.

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Math Journal 1, p. 104

Student Page

Links to the Future

Measuring Land Invertebrates continuedLESSON

4 �10

Date Time

Refer to the pictures on page 102

to answer the following questions.

1. Measure the following invertebrates to the nearest millimeter by finding the

distance between the two guidelines. Then give the lengths in centimeters.

a. mayfly About 47

mm About 4.7

cm

b. dragonfly About 68

mm About 6.8 cm

c. water scavenger beetle About 34

mm About 3.4

cm

d. ground beetle About 44

mm About 4.4

cm

e. lacewing About 50

mm About 5

cm

f. horsefly About 23

mm About 2.3

cm

2. How much longer is the ground beetle than the water scavenger beetle? About 1

cm

3. The bee has been drawn to twice its actual size.

In reality, which is longer, the bee or the horsefly? horsefly

How much longer? About 8

mm

4. The mealybug has been drawn to 3 times its

actual size. In the space at the right, draw

a mealybug that is about the actual size.

5. What is the actual size of the mealybug in millimeters? 4

mm

6. How did you solve Problem 5?

Sample answer: The size of the mealybug in the picture is

12 millimeters long, which is 3 times its actual size. So I divided

12 mm by 3 to find its actual size—4 millimeters.

7. When straight, the threadworm in the drawing is 306 millimeters long.

What is its length in centimeters? 30.6

cm In meters? 0.306

m

1 centimeter (cm) = 10 millimeters (mm)

1 millimeter = 0.1 centimeter

4 mm

128 129

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Math Journal 1, p. 103

Student Page

� Measuring Invertebrates PARTNER ACTIVITY

in Metric Units(Math Journal 1, pp. 101–103)

Science Link Ask students to read about measuring land invertebrates on journal page 101 and to examine the

illustrations of land invertebrates on page 102. Explain how to measure the length or wingspan of the invertebrates by measuring the distance between the guidelines. Students should use their regular centimeter ruler to measure in millimeters (not the paper cm/mm ruler) and then convert the measurements to centimeters.

Drawing and measuring line segments to the nearest millimeter is a Grade 5 Goal.

In Unit 8 of Fourth Grade Everyday Mathematics students use measurements to

create scale drawings and use scale drawings to find area.

When students have finished journal page 103, have them look at the picture they drew for Problem 4. Ask them to use “times-as-many” language to compare the length of their drawing to the length of the mealybug picture on journal page 102. Sample answer: The picture is 3 times as long as my drawing. Then ask them to use a multiplication equation to represent this comparison. 4 ∗ 3 = 12

2 Ongoing Learning & Practice

� Math Boxes 4�10 INDEPENDENTACTIVITY

(Math Journal 1, p. 104)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-8. The skill in Problem 6 previews Unit 5 content.

� Study Link 4�10 INDEPENDENTACTIVITY

(Math Masters, p. 133)

Home Connection Students convert between metric units.

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STUDY LINK

4 �10 Decimals and Metric Units 129

Name Date Time

Use your tape measure or ruler to help you fill in the answers below.

1. a. 4.2 cm � mm b. 64 mm � cm c. 2.6 m � cm

2. a. 6.5 cm � mm b. 26 mm � cm c. 6.1 m � cm

3. a. 5 cm � mm b. 30 mm � cm c. 3 m � cm

4. a. 80 cm � mm b. 110 mm � cm c. m � 500 cm

5. a. 43 cm � mm b. 98 mm � cm c. m � 34 cm

6. a. 0.6 cm � mm b. 4 mm � cm c. 5.2 m � mm5,2000.460.349.8430

5118003003506102.6652606.442

Symbols for Metric

Units of Length

meter (m)centimeter (cm)decimeter (dm)millimeter (mm)

0 1 dm

1 decimeter

1 m � 10 dm  1 dm � 0.1 m

0 1 2 3 4 5 6 7 8 9 10 cm

10 centimeters

1 m � 100 cm 1 cm � 0.01 m 1 dm � 10 cm 1 cm � 0.1 dm

0 10 20 30 40 50 60 70 80 90 100 mm

100 millimeters

1 m � 1,000 mm 1 mm � 0.001 m 1 dm � 100 mm 1 mm � 0.01 dm1 cm � 10 mm 1 mm � 0.1 cm

Practice

7. 21, 49, and 56 are multiples of .

8. 45, 63, and 18 are multiples of . 3 and 97

Math Masters, p. 133

Study Link Master

Lesson 4�10 293

LESSON

4 �10

Name Date Time

Centimeters and Millimeters

128

Cut out the ruler below. Use it to measure the pencils to the nearest centimeter.

1. a.

Pencil A is about cm long.

b.

Pencil B is about cm long.

2. One pencil is longer than the other. Which pencil is longer? Circle your answer.

Pencil A Pencil B

3. How did you figure out which pencil is longer?

Sample answer: I measured both pencils. Pencil A is a little bit shorter than 12 cm, and Pencil B is a little bit longer.

4. Marco wants to know the difference in length between the two pencils. Can you tell him? Why or why not?

No. Sample answer: The ruler is not precise enough to be able to report the difference in length. I need a ruler divided into smaller units.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Centimeters

12

12

Math Masters, p. 134

Teaching Master

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Exploring the Need for 5–15 Min

Millimeters(Math Masters, p. 134)

To explore the need for standard units of measure, have students cut out the ruler at the bottom of Math Masters, page 134, and use it to measure the pencils in Problem 1. Discuss the need for a unit of metric measure that is smaller than a centimeter.

ENRICHMENT PARTNER ACTIVITY

� Investigating Ratios 15–30 Min

Literature Link To further explore the concept of scale, have students read If You Hopped Like a Frog by David

M. Schwartz (Scholastic Inc., 1999). This book compares what humans could do if they had bodies like different animals. After students have read the book, have them answer the questions posed at the back of the book.

EXTRA PRACTICE PARTNER ACTIVITY

� Measuring to the Nearest 5–15 Min

MillimeterTo practice measuring to the nearest millimeter, have students draw line segments, measure them to the nearest millimeter, and record the measurements in millimeters and centimeters. Partners measure each other’s line segments and compare answers.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Taking a 50-Facts Test 5–15 Min

(Math Masters, pp. 413, 414, and 416)

See Lesson 3-4 for details regarding the administration of the 50-facts test and the recording and graphing of individual and optional class results.

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