Objectives
To guide students as they measure lengths
to the nearest millimeter; and to provide practice converting
measurements between millimeters and centimeters.
1
materials
Teaching the Lesson
Key Activities
Students 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.
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.
ⵧ Math Journal 1, pp. 101–103
ⵧ Study Link 4 9
䉬
ⵧ Teaching Aid Master (Math
Masters, p. 429)
ⵧ centimeter ruler
ⵧ slate
ⵧ scissors
ⵧ highlighter
[Operations and Computation Goal 7]
See Advance Preparation
• 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]
2
materials
Ongoing Learning & Practice
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.
3
materials
Differentiation Options
READINESS
Students explore the need
for a metric unit of measure
smaller than a centimeter.
ENRICHMENT
Students explore the
concept of scale by
comparing what humans
could do if they had bodies
like different animals.
ⵧ Math Journal 1, p. 104
ⵧ Study Link Master (Math Masters,
p. 133)
ⵧ Teaching Aid Masters (Math
Masters, pp. 413, 414, and 416)
EXTRA PRACTICE
Students measure line
segments to the nearest
millimeter.
Additional Information
Advance Preparation For 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 Press, 1999).
ⵧ Teaching Master (Math Masters,
p. 134)
ⵧ scissors; ruler
ⵧ If You Hopped Like a Frog
See Advance Preparation
Technology
Assessment Management System
Mental Math and Reflexes
See the iTLG.
Lesson 4 10
䉬
289
Getting Started
Mental Math and Reflexes
夹
Math Message
Pose multiplication facts and extended facts. Suggestions:
Complete Problems 1–4 on journal page 101.
0ⴱ60
6 ⴱ 6 36
40 ⴱ 5 200
9ⴱ19
3 ⴱ 4 12
300 ⴱ 6 1,800
Study Link 4 9 Follow-Up
2 ⴱ 7 14
7 ⴱ 7 49
70 ⴱ 80 5,600
5 ⴱ 8 40
4 ⴱ 6 24
40 ⴱ 90 3,600
Ask students to circle the most difficult problems.
Then have students see if someone at their
table can suggest a solution strategy.
10 ⴱ 3 30
6 ⴱ 3 18
500 ⴱ 30 15,000
䉬
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and Reflexes
夹
Use Mental Math and Reflexes to assess students’ automaticity with
multiplication facts. Students are making adequate progress if they are able to
solve the
and
problems correctly. Some students may be able to
solve extended facts in the
problems.
[Operations and Computation Goal 3]
1 Teaching the Lesson
䉴 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.
Student Page
Date
Time
LESSON
4 10
䉬
Measuring in Millimeters
Math Message
128
On your centimeter ruler, the numbered marks are for centimeters and
the little marks between the centimeter marks are for millimeters.
10 mm
Sample answers:
thickness of the wire in a paper clip; width
of a pencil point; the edge of a dime
In this lesson students use millimeters to measure very small
invertebrates. They also practice converting millimeters to
centimeters.
1. Look at your centimeter ruler. How many millimeters are in 1 centimeter?
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.
A
B
៮
Length of AB
6.
7.
125
mm 12.5 cm
C
E
D
F
៮
Length of EF
8
៮
Length of CD
mm 0.8
62
mm 6.2
cm
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.
101
Math Journal 1, p. 101
290
Unit 4 Decimals and Their Uses
Students should conclude that both line segments they drew are
the same length. Thus, 8 centimeters 80 millimeters.
Teaching Aid Master
䉴 Measuring Lengths in
WHOLE-CLASS
ACTIVITY
Name
Date
Time
A cm/mm Ruler
Millimeters and Centimeters
cm 0
Fold
mm 0
cm 0
Fold
mm 0
cm 0
Fold
0.5
5
0.5
5
0.5
1
10
1
10
1
1.5
15
1.5
15
1.5
15
1.5
15
2
20
2
20
2
20
2
20
2.5
25
2.5
25
2.5
25
2.5
25
3
30
3
30
3
30
3
30
3.5
35
3.5
35
3.5
35
3.5
35
4
40
4
40
4
40
4
40
4.5
45
4.5
45
4.5
45
4.5
45
5
50
5
50
5
50
5
50
5.5
55
5.5
55
5.5
55
5.5
55
6
60
6
60
6
60
6
60
6.5
65
6.5
65
6.5
65
6.5
65
7
70
7
70
7
70
7
70
7.5
75
7.5
75
7.5
75
7.5
75
8
80
8
80
8
80
8
80
8.5
85
8.5
85
8.5
85
8.5
85
9
90
9
90
9
90
9
90
10
11
12
13
14
15
16
10.5 11.5 12.5 13.5 14.5 15.5
105 115 125 135 145 155
100 110 120 130 140 150 160
9.5
95
10
11
12
13
14
15
16
10.5 11.5 12.5 13.5 14.5 15.5
105 115 125 135 145 155
100 110 120 130 140 150 160
9.5
95
10
11
12
13
14
15
16
10.5 11.5 12.5 13.5 14.5 15.5
105 115 125 135 145 155
100 110 120 130 140 150 160
9.5
95
10
11
12
13
14
15
16
10.5 11.5 12.5 13.5 14.5 15.5
105 115 125 135 145 155
100 110 120 130 140 150 160
9.5
95
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.
10
1
10
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.
5
0.5
5
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.
mm 0
cm 0
Fold
mm 0
(Math Journal 1, p. 101; Math Masters, p. 429)
Math Masters, p. 429
NOTE When converting between millimeters and centimeters, tell students to
1
think of the centimeter as the ONE, or the unit, and the millimeter as 10.
Adjusting the Activity
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
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
Student Page
V I S U A L
Date
Time
LESSON
4 10
䉬
Write several millimeter/centimeter conversion problems on the
board. Ask students to write their answers on their slates.
Suggestions:
1 cm 10 mm
4 cm 40 mm
2.3 cm 23 mm
10 mm 1 cm
1 mm 0.1 cm
130 mm 13 cm
4 mm 0.4 cm
Mayfly
Dragonfly
42 mm 4.2 cm
8 mm 0.8 cm
ELL
Adjusting the Activity
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
Lacewing
Ground beetle
Earthworm
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
Measuring Land Invertebrates
Water scavenger beetle
V I S U A L
Threadworm
Bumblebee
(2 times actual size)
Horsefly
Mealybug
(3 times actual size)
102
Math Journal 1, p. 102
Lesson 4 10
䉬
291
Student Page
Date
䉴 Measuring Invertebrates
Time
LESSON
4 10
䉬
Measuring Land Invertebrates
Refer to the pictures on page 102
to answer the following questions.
continued
1 centimeter (cm) 10 millimeters (mm)
1 millimeter 0.1 centimeter
128 129
PARTNER
ACTIVITY
in Metric Units
(Math Journal 1, pp. 101–103)
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
b. dragonfly
About
c. water scavenger beetle
About
d. ground beetle
About
e. lacewing
About
f. horsefly
About
47
68
34
44
50
23
mm
About
mm
About
mm
About
mm
4.7
6.8
3.4
4.4
5
2.3
About
mm
About
mm
About
cm
cm
cm
cm
cm
cm
2. How much longer is the ground beetle than the water scavenger beetle? About
3. The bee has been drawn to twice its actual size.
In reality, which is longer, the bee or the horsefly?
8
How much longer? About
1
cm
horsefly
mm
4. The mealybug has been drawn to 3 times its
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.
4 mm
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
Links to the Future
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.
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.
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
103
Math Journal 1, p. 103
2 Ongoing Learning & Practice
䉴 Taking a 50-Facts Test
WHOLE-CLASS
ACTIVITY
(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
class results.
䉴 Math Boxes 4 10
Student Page
Date
䉬
Time
LESSON
4 10
䉬
(Math Journal 1, p. 104)
Math Boxes
1. Solve mentally or with a paper-and-pencil
2. Complete.
algorithm.
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.
70 mm
15 cm 150 mm
5 m
500 cm 4 cm 40 mm
800 cm 8 m
a. 7 cm a.
4,647
3,228
b.
7,875
2,500
1,398
b.
1,102
c.
d.
e.
129
10–15
4. Name two properties of a regular polygon.
3. Tell whether each number sentence
is true or false.
true
true
89.6 21.7 111.3
true
56.4 23.8 33
5.17 3.86 10 false
a.
The sides are the same
a. 2.34 0.09 2.25
length.
b.
The angles have the
c.
d.
b.
Sample answers.
5. Without measuring, estimate the height
97
6. Complete.
of your chair. Then measure it.
Answers vary.
About
a. Is 326 closer to 300 or 400?
300
cm
b. Name the number halfway
between 500 and 800.
b. Measurement:
About
650
cm
128 130
104
Math Journal 1, p. 104
292
Unit 4 Decimals and Their Uses
䉴 Study Link 4 10
䉬
(Math Masters, p. 133)
Home Connection Students convert between
metric units.
same measure.
36 37
148
a. Estimate:
INDEPENDENT
ACTIVITY
182 183
INDEPENDENT
ACTIVITY
Study Link Master
Name
3 Differentiation Options
READINESS
䉴 Exploring the Need for
Date
STUDY LINK
4 10
䉬
Time
Decimals and Metric Units
1 decimeter
Symbols for Metric
Units of Length
PARTNER
ACTIVITY
129
0
meter (m)
centimeter (cm)
decimeter (dm)
millimeter (mm)
1 dm
1 m 10 dm
1 dm 0.1 m
10 centimeters
0
1
2
3
4
5
6
1 m 100 cm
1 dm 10 cm
5–15 Min
7
8
9
10 cm
90
100 mm
1 cm 0.01 m
1 cm 0.1 dm
100 millimeters
Millimeters
0
10
20
30
40
1 m 1,000 mm
1 dm 100 mm
1 cm 10 mm
(Math Masters, p. 134)
60
50
80
70
1 mm 0.001 m
1 mm 0.01 dm
1 mm 0.1 cm
Use your tape measure or ruler to help you fill in the answers below.
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.
1. a.
4.2 cm 2. a.
6.5 cm 42
mm
65 mm
5 cm 50 mm
80 cm 800 mm
43 cm 430 mm
0.6 cm 6 mm
3. a.
4. a.
5. a.
6. a.
b.
64 mm b.
26 mm b.
b.
b.
b.
6.4
cm
2.6 cm
30 mm 3 cm
110 mm 11 cm
98 mm 9.8 cm
4 mm 0.4 cm
c.
2.6 m c.
6.1 m c.
c.
c.
c.
260
cm
610 cm
3 m 300 cm
5 m 500 cm
0.34 m 34 cm
5.2 m 5,200 mm
Practice
ENRICHMENT
䉴 Investigating Ratios
PARTNER
ACTIVITY
䉴 Measuring to the Nearest
21, 49, and 56 are multiples of
8.
45, 63, and 18 are multiples of
7 .
3 and 9 .
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 Press, 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
7.
Math Masters, p. 133
PARTNER
ACTIVITY
5–15 Min
Millimeter
To 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.
Teaching Master
Name
Date
LESSON
Time
Centimeters and Millimeters
4 10
䉬
Cut out the ruler below. Use it to measure the pencils to the nearest centimeter.
128
1. a.
Pencil A is about
12
cm long.
Pencil B is about
12
cm long.
b.
2.
One pencil is longer than the other. Which pencil is longer? Circle your answer.
3.
How did you figure out which pencil is longer?
4.
Marco wants to know the difference in length between the two pencils.
Can you tell him? Why or why not?
Pencil A
Pencil B
Sample answer: I measured both pencils.
Pencil A is a little bit shorter than 12 cm,
and Pencil B is a little bit longer.
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
15
Centimeters
Math Masters, p. 134
Lesson 4 10
䉬
293