Teaching the Lesson materials

Key ActivitiesStudents examine the millimeter marks on their centimeter rulers. They measure line segmentsin millimeters and centimeters. Then they measure illustrations of various invertebrates in millimeters and convert their measurements to centimeters.

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]

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

Ongoing Learning & Practice materials

Students take a 50-facts test. They use a line graph to record individual and class scores. Then students find the median and calculate the mean of class scores.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students explore the needfor a metric unit of measuresmaller than a centimeter.

Students explore theconcept of scale bycomparing what humanscould do if they had bodieslike different animals.

Students measure line segments to the nearest millimeter.

� Teaching Master (Math Masters,p. 134)

� scissors; ruler� If You Hopped Like a Frog

See Advance Preparation

EXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 1, p. 104� Study Link Master (Math Masters,

p. 133)� Teaching Aid Masters (Math

Masters, pp. 413, 414, and 416)

2

� Math Journal 1, pp. 101–103� Study Link 4�9� Teaching Aid Master (Math

Masters, p. 429)� centimeter ruler� slate� scissors� highlighter

See Advance Preparation

1

Lesson 4�10 289

Objectives To guide students as they measure lengths

to the nearest millimeter; and to provide practice converting

measurements between millimeters and centimeters.

Technology Assessment Management System

Mental Math and ReflexesSee the iTLG.

Additional InformationAdvance Preparation For Part 1, make one copy of Math Masters, page 429 per fourstudents. 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 byDavid M. Schwartz (Scholastic Press, 1999).

290 Unit 4 Decimals and Their Uses

101

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 alsocalled the spinal column.) Some invertebrates live on land, others in water. The mostcommon land invertebrates are insects.

The invertebrates shown on page 102, except the earthworm, bumblebee, andmealybug, 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 themealybug about 3 times its actual size.

0.88E F

6.262C D

12.5125A 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

Ongoing Assessment:Recognizing Student Achievement

Use Mental Math and Reflexes to assess students’ automaticity withmultiplication facts. Students are making adequate progress if they are able tosolve the and problems correctly. Some students may be able tosolve extended facts in the problems.

[Operations and Computation Goal 3]

� Math Message Follow-Up(Math Journal 1, p. 101)

If students have difficulty naming things that measure about1 millimeter, suggest these possibilities: the thickness of the wirein a paper clip; the width of a pencil point; or the edge of a dime.

Students should conclude that both line segments they drew arethe same length. Thus, 8 centimeters � 80 millimeters.

In this lesson students use millimeters to measure very smallinvertebrates. They also practice converting millimeters tocentimeters.

WHOLE-CLASS

ACTIVITY

1 Teaching the Lesson

Getting Started

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 theirtable 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

Mental Math

and Reflexes �

�

Adjusting the Activity

Adjusting the Activity

� Measuring Lengths in Millimeters and Centimeters(Math Journal 1, p. 101; Math Masters, p. 429)

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

Demonstrate how to use the centimeter side of the ruler by havingstudents measure the line segment they drew in Math MessageProblem 3. Instruct students to place the centimeter side of thefolded ruler above the line segment with 0 aligned with the leftend of the segment. Then demonstrate how to use the millimeterside of the ruler by having students measure the line segmentthey drew in Problem 4. Instruct students to place the millimeterside of the folded ruler under the line segment with 0 aligned withthe 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 theirmeasurements 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 tothink 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 segmenton journal page 101 vary slightly. Ask students to explain why they think thismight happen. Possible response: “The spaces between millimeter marks are sosmall. 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 theboard. 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

ELL

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

WHOLE-CLASS

ACTIVITY

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

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

102

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

4.2131

0.1 0.4 0.8

2310

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-pencilalgorithm.

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

b. 89.6 � 21.7 � 111.3

c. 56.4 � 23.8 � 33

d. 5.17 � 3.86 � 10 falsetrue

truetrue

4. Name two properties of a regular polygon.

a.

b.

same measure.The angles have the length.The sides are the same

129

97

182 183

10–15

128 130

2. Complete.

a. 7 cm � mm

b. 15 cm � mm

c. 500 cm � m

d. cm � 40 mm

e. cm � 8 m8004

515070

7,875 1,102

36 37148

6. Complete.

a. Is 326 closer to 300 or 400?

b. Name the number halfway between 500 and 800.

650

300

Sample answers.

Answers vary.

Math Journal 1, p. 104

Student Page

Measuring Land Invertebrates continuedLESSON

4 �10

Date Time

Refer to the pictures on page 102to 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 mm About cm

b. dragonfly About mm About cm

c. water scavenger beetle About mm About cm

d. ground beetle About mm About cm

e. lacewing About mm About cm

f. horsefly About mm About cm

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

3. The bee has been drawn to twice its actual size. In reality, which is longer, the bee or the horsefly?

How much longer? About mm

4. The mealybug has been drawn to 3 times itsactual size. In the space at the right, drawa mealybug that is about the actual size.

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

6. How did you solve Problem 5?

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

What is its length in centimeters? cm In meters? m0.30630.6

12 mm by 3 to find its actual size—4 millimeters.12 millimeters long, which is 3 times its actual size. So I dividedSample answer: The size of the mealybug in the picture is

4

8horsefly

12.323550

4.4443.4346.8684.747

1 centimeter (cm) � 10 millimeters (mm)1 millimeter � 0.1 centimeter

4 mm

128 129

103

Math Journal 1, p. 103

Links to the Future

Student Page

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

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

illustrations of land invertebrates on page 102. Explain how tomeasure the length or wingspan of the invertebrates by measuringthe distance between the guidelines. Students should use theirregular centimeter ruler to measure in millimeters (not the papercm/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 tocreate scale drawings and use scale drawings to find area.

� Taking a 50-Facts Test(Math Masters, pp. 413, 414, and 416)

See Lesson 3-4 for details regarding the administration of the50-facts test and the recording and graphing of individual andclass results.

� Math Boxes 4�10(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 6previews Unit 5 content.

� Study Link 4�10(Math Masters, p. 133)

Home Connection Students convert between metric units.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

WHOLE-CLASS

ACTIVITY

2 Ongoing Learning & Practice

PARTNER

ACTIVITY

� Exploring the Need for Millimeters(Math Masters, p. 134)

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

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

M. Schwartz (Scholastic Press, 1999). This book compares whathumans could do if they had bodies like different animals. Afterstudents have read the book, have them answer the questionsposed at the back of the book.

� Measuring to the Nearest MillimeterTo practice measuring to the nearest millimeter, have studentsdraw line segments, measure them to the nearest millimeter, andrecord the measurements in millimeters and centimeters. Partnersmeasure each other’s line segments and compare answers.

5–15 Min

PARTNER

ACTIVITYEXTRA PRACTICE

15–30 Min

PARTNER

ACTIVITYENRICHMENT

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options 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