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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
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