Unit 7 M
easurement and Data:
Conversion
Introduction
In this unit, students will learn about metric units of length and distance,
and metric units of mass. Students will reinforce the notion of place value
by noting similarities in the relationships between different units and the
relationships between different place values. As they convert and compare
measurements throughout the unit, students will add, subtract, multiply,
and divide numbers, including decimals to thousandths. For details, see
the prior knowledge required section for each lesson.
To help students visualize the relative size of the units they are learning,
create a class measurement display and add to it every time you introduce
a new unit. Make sure the items are clearly labeled, stating the unit and
which dimension is equal to the unit. Example: “Thickness = 1 mm”
Examples:
1 mm – thickness of cardboard, width of some beads, thickness
of some buttons
1 cm – thickness of some books, width of a centimeter cube, width
of a tens block
1 m – length of some scarves, length of a piece of yarn
1 km – length of a spool of fishing line, length of several spools of yarn
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Mass vs. weight. At this level, we use the terms “weight” and “mass”
interchangeably. Weight technically refers to the force of gravity pulling an
object down (that’s why people weigh less in lower gravity). Pan balances
and playground seesaws compare weight. Mass technically refers to the
amount of matter in an object, and it does not change in outer space where
the force of gravity is lower. It is appropriate at this level to use the word
“mass” to mean “how strongly an object pulls down when you try to lift it.”
Measurement and Data
H-1
MD5-1 Centimeters and Millimeters
Pages 166–167
STANDARDS
5.MD.A.1, 5.NBT.A.1
Vocabulary
centimeter (cm)
convert
line
line segment
measurement
millimeter (mm)
Goals
Students will measure lengths in centimeters and millimeters, and
convert between centimeters and millimeters.
PRIOR KNOWLEDGE REQUIRED
Understands the concept of linear measurement
Understands that smaller units require more units
Can multiply whole numbers by 10
Is familiar with decimals to tenths
Can locate a number on a number line, including decimal tenths
MATERIALS
centimeter and millimeter rulers
benchmarks for centimeters and millimeters
Introduce centimeters. Point out the centimeter marks on a ruler, and
explain to students that a centimeter is a unit of measurement. Write the
word “centimeter” on the board, circle the letters “c” and “m,” and write the
abbreviation “cm.” Explain that these are the two ways to write centimeter.
Show students some objects that they can use as benchmarks for
centimeters, such as centimeter cubes, buttons, a book that is 1 cm thick.
You can keep a display of such objects, with labels such as “thickness =
1 cm,” for students to use as a reference.
0 cm
12345
ACTIVITY
Students use rulers to find items that have the given length, width,
or thickness.
a) 6 cm c) 1 cm
e) between 12 cm and 15 cm
b) 10 cm
d) greater than 15 cm
f) about 35 cm long
Introduce lines and line segments. Explain that we use the word line for
straight lines that can be drawn with a ruler. A line can be extended at both
ends, as much as we want. However, when we are interested in a piece
of line that has a specific length (such as 5 cm), we call that piece of line
a line segment.
H-2
Teacher’s Guide for AP Book 5.1
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12345
Draw a number line and explain that counting on a number line is just like
using a ruler. Demonstrate this by asking a volunteer to use a number line
to count (by “hopping”) to five. Then ask another volunteer to demonstrate
how to measure 5 cm with the ruler.
Drawing a line segment. Follow the steps below to demonstrate how to
draw a line segment of length 2 cm.
Step 1: D
raw a vertical dash to mark where the line segment starts. Place
the ruler so that the dash is at the zero mark.
Step 2: C
ount forward from zero by hops (two hops for 2 cm, three hops
for 3 cm, and so on). Make sure not to move the ruler.
Step 3: D
raw a second vertical dash to mark the other end of the line
segment. (For 2 cm, draw the dash at the 2 cm mark.)
Step 4: Draw a line segment connecting the dashes.
Exercises: Use the steps to draw a line segment of the given length. Have
a partner measure your line segment.
a) 3 cm
b) 5 cm
c) 8 cm
Check that students do not move the ruler while counting by hops, and
that they place the ruler properly in Step 1. Students who have difficulty
performing the first three steps together might also benefit from using a
pre-drawn line, where they only need to mark the beginning and the end
of the line segment.
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Introduce millimeters. Identify the length and marking of a millimeter on
a ruler, and explain to students that a millimeter is a unit of measurement
that is smaller than a centimeter. Write the word “millimeter” on the board,
circle the two “m”s, and write the abbreviation “mm.” Explain that these
are the two ways to write millimeter. Add benchmarks representing 1 mm
to the display.
cm
mm
1
10
2
20
3
30
4
40
Converting centimeters to millimeters. Draw a 5 cm ruler and explain that
there are 10 millimeters in 1 centimeter. If available, show two rulers side by
side—one that shows centimeters only and another that shows millimeters
only—to show how each measurement in centimeters corresponds to a
measurement in millimeters, as on p. 166 in the AP Book.
ASK: How many millimeters are there in 2 centimeters? Explain to students
that one way to find the answer is by skip counting. Using the 5 cm ruler,
skip count by tens from 0 cm to 2 cm. Say “20” at the 2 cm mark. Extend
the ruler to 10 cm and skip count by tens as a class to determine how many
millimeters are in 10 cm.
On the board, draw the T-table as shown in the margin. Ask students to fill
in the measurements in millimeters. Extend the table a few more rows and
have students continue the pattern.
(MP.7)
Then ASK: How can you get the number in the right-hand column from
the number in the left-hand column? What mathematical operation takes
1 to 10, 2 to 20, and so on? (multiply by 10)
Exercises: Convert to millimeters.
a) 3 cm
b) 8 cm
c) 15 cm
d) 50 cm
Bonus: 2,345 cm
Measurement and Data 5-1
H-3
Answers: a) 30 mm, b) 80 mm, c) 150 mm, d) 500 mm, Bonus: 23,450 mm
Comparing measurements. ASK: Which is longer, 2 hours or 5 minutes?
Which number is greater, 5 or 2? Point out that even though 5 is more than
2, 2 hours is still longer than 5 minutes. The units are different, and we need
to take the size of the units into account when comparing measurements.
Write on the board:
7 cm
30 mm
ASK: Which number is greater, 7 or 30? Does this mean that 30 mm is
longer than 7 cm? (no) Explain that to compare measurements correctly,
you need to convert them to the same unit. It is usually more convenient
to use the smaller unit, so convert the measurement in the larger unit. Ask
students to change 7 centimeters to millimeters. Which is longer, 70 mm
or 30 mm? So which is longer, 7 cm or 30 mm? (7 cm)
Exercises: Which measurement is longer?
a) 35 mm or 2 cm
d) 65 cm or 643 mm
b) 48 mm or 20 cm
c) 765 mm or 90 cm
e) 46 cm or 3,456 mm
Bonus
f) 12,345 mm or 7,892 cm
g)
654,234 mm or 8,893 cm
Answers: a) 35 mm, b) 20 cm, c) 90 cm, d) 65 cm, e) 3,456 mm,
Bonus: f) 7,892 cm, g) 654,234 mm
Measuring in millimeters. Explain to students that counting every
millimeter in a measurement can take a long time, but there is a quick way
to do it. Draw a ruler representing 30 mm and tell the class that you want
to count 26 mm. Then demonstrate how to skip count by tens to the tens
place value preceding the amount, and count on from there by ones.
(10, 20, 21, 22, 23, 24, 25, 26)
Review decimal tenths on number lines. Remind students that when
one whole is divided into 10 equal parts, the parts are called tenths, and
decimals are a convenient way to write fractions with denominator 10, 100,
1,000, and so on. We write 1/10 as 0.1, 3/10 as 0.3, and 5 4/10 as 5.4.
Have students read and write a few decimal tenths.
Draw a number line divided into tenths, from 0 to 3. Remind students how
to find a number on this number line. For each decimal below, point to
several locations on the line and have students signal thumbs up if the
location is correct, and thumbs down if it is not.
Exercises: Indicate the location of the decimal on a number line.
a)
0.4b)
1.1c)
2.8d)
1.5
H-4
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Have volunteers demonstrate this shortcut method by counting to several
different numbers. Then have students practice measuring different objects
to the closest millimeter.
Answers: 0.4
1.11.5
2.8
0 1 23
Converting millimeters to centimeters using a ruler. Point out that
1 mm is one tenth of a centimeter, so this means you can write a
decimal measurement 1 mm = 0.1 cm. ASK: How can you write 2 mm in
centimeters? (0.2 cm) PROMPT: 2 mm is how many tenths of a centimeter?
(2/10) Repeat with 5 mm, 9 mm, then 16 mm. (0.5 cm, 0.9 cm, 1.6 cm)
Ask students to look at a millimeter ruler. How is the ruler the same as the
number line you drew? How is it different? (each centimeter is divided into
ten units, but there is a longer mark for every five millimeters, not every ten)
Have students locate 23 mm on a ruler. SAY: Think of 1 cm as one whole.
What position on a number line does 23 mm show? (2.3 cm) Point out that
as you count by tens of millimeters, you are counting by centimeters, so
counting by millimeters is counting by tenths. Work through the next few
Exercises as a class, then have students work individually.
Exercises: Use a ruler to convert to centimeters.
a) 14 mm
b) 32 mm
c) 27 mm
d) 45 mm
Answers: a) 1.4 cm, b) 3.2 cm, c) 2.7 cm, d) 4.5 cm
Extensions
1. Draw each object to the given measure.
a) a shoe 6 cm long
b) a tree 5 cm high
c) a glass 3 cm deep
2. a) i)Draw a collection of alligators, each one being 1 cm longer
than the previous one.
ii)A pencil shrinks when it is sharpened. Draw a collection of
pencils, each one being 1 cm shorter than the previous one.
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iii)Draw a sequence of toboggans in which each one is 2 cm
longer than the last one.
iv)A carrot shrinks when it is eaten. Draw a collection of carrots,
each one being 2 cm shorter than the previous one.
b)Write a story about one of the growing or shrinking items in
part a) or invent your own! Tell a story about how the item grows or
shrinks. How does the carrot get eaten? Who wants to ride
the toboggans? Write the story to go with the pictures that you
have drawn.
3.A nickel is about 2 mm thick. Josie has a stack of nickels 10 mm high.
How much money does Josie have?
Answer: 5 nickels = 25¢
Measurement and Data 5-1
H-5
MD5-2 Centimeters and Millimeters (Advanced)
Pages 168–169
STANDARDS
5.MD.A.1, 5.NBT.A.1
Vocabulary
centimeter (cm)
convert
measurement
millimeter (mm)
round down
round up
rounding
Goals
Students will convert between centimeters and millimeters.
PRIOR KNOWLEDGE REQUIRED
Understands the concept of linear measurement
Understands that smaller units require more units
Can multiply and divide decimals and whole numbers by 10
Can locate a number on a number line, including decimal tenths
Knows that 10 mm = 1 cm
Can convert whole centimeters to millimeters
Can use a ruler to convert millimeters to centimeters
Knows that measurements can be in fractions of a unit
MATERIALS
rulers
variety of objects to measure
Review relevant prior knowledge. Remind students that there are 10
millimeters in each centimeter, so if an object is 4 cm long, it is also 40 mm
long. Review how students can multiply by 10 to convert measurements in
centimeters to measurements in millimeters. Have students convert several
measurements in centimeters to measurements in millimeters.
Exercises: Convert to millimeters.
a) 6 cm
b) 12 cm
c) 89 cm
d) 103 cm
Measuring to the closest centimeter and to the closest millimeter. On
the board, draw a centimeter ruler and a bar that goes from 0 cm to a point
between 5 cm and 6 cm (say about 52 mm). ASK: How long is the bar? Is
it longer or shorter than 5 cm? (longer) Is it longer or shorter than 6 cm?
(shorter) SAY: We can see that the bar is not exactly 5 cm long and not
exactly 6 cm long—the bar is between 5 and 6 cm long. ASK: Is the bar
closer to 5 cm long or closer to 6 cm long? Write the words “closer to” on
the board. Highlight the distances between the end of the bar and the 5 cm
and 6 cm marks on the ruler. Explain that the bar ends closer to the 5 cm
mark, so we say the bar is “about 5 cm long” or “5 cm long when measured
to the closest centimeter.” Write both expressions on the board.
Add millimeters to the ruler. ASK: What is the length of the bar in millimeters?
(52 mm) How many millimeters are in 5 cm? (50) In 6 cm? (60) Is 52 closer
to 50 or to 60? (50) What are we doing when we change 52 to 50 because
it is closer to 50 than to 60? (rounding) When you are rounding 52, will you
round up to 60 or down to 50? (down to 50) Finally, write on the board:
The bar is 52 mm long. The bar is about 5 cm long.
H-6
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Answers: a) 60 mm, b) 120 mm, c) 890 mm, d) 1,030 mm
Draw a bar of a different length (say, 37 mm) and have students raise the
number of fingers that correspond to the length of the bar in centimeters.
Then have students say the length in millimeters. Have students write two
sentences about the length of the bar as shown in the previous example.
Draw a bar 45 mm long. Is 45 closer to 40 or closer to 50? (neither) When
you round 45 to the nearest 10, will you round down to 40 or up to 50?
(up to 50) Explain that you do the same when determining the length to the
closest centimeter—you round up by saying that the bar is 5 cm long when
measured to the closest centimeter.
ACTIVITY
Give students various objects that have lengths between exact
numbers of centimeters. Students measure them to the closest
centimeter and closest millimeter. Partners exchange objects and
check each other’s answers.
Identifying measurements between other measurements. Write these
pairs of measurements on the board:
A: 8 cm and 9 cm
B: 9 cm and 10 cm
C: 10 cm and 11 cm
Ask students to say which pair of measurements (A, B, or C) the
measurement 87 mm is between. (A) Repeat the question for 93 mm. (B)
Ask students to find another millimeter measurement between each pair
of lengths.
Now write these pairs of measurements in millimeters on the board. Ask
students to find a measurement in whole centimeters that is between the
lengths in each pair:
A: 56 mm and 63 mm B: 78 mm and 86 mm C: 102 mm and 114 mm
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Sample answers: A: 6 cm, B: 8 cm, C: 11 cm
(MP.3)
Review multiplying and dividing decimals and whole numbers by 10.
Remind students that they shift the decimal point 1 place right to multiply
and 1 place left to divide. Remind them that they can write zeros after the
decimal point and the number will not change. For example, 6.7 = 6.70.
ASK: Why is that true? (the decimal part is 7/10 = 70/100) As well, remind
students that even though we do not write the decimal point in whole
numbers, we can still add it without changing the number. For example,
12 = 12.0. Use the questions below as a test to make sure that all students
can perform the required multiplication and division.
Exercises: Multiply or divide.
a)25 ÷ 10 = e)0.4 × 10 = b) 3 ÷ 10 = f) 5.3 × 10 = c) 122 ÷ 10 = d) 32.4 ÷ 10 =
g) 1.89 × 10 = h) 0.08 × 10 =
Answers: a) 2.5, b) 0.3, c) 12.2, d) 3.24, e) 4 = 4.0, f) 53, g) 18.9, h) 0.8
Measurement and Data 5-2
H-7
Using multiplication and division to convert between centimeters
and millimeters. Remind students that they multiplied by 10 to convert a
measurement in centimeters to millimeters. ASK: What operation would
you use to convert a measurement in millimeters to centimeters? (divide
by 10) PROMPT: Which operation is the opposite of multiplication? Convert
the first few measurements in each Exercise as a class, then have students
work individually.
Exercises
1. Convert to centimeters.
a) 6 mm
b) 12 mm
c) 89 mm
d) 103 mm
Answers: a) 0.6 cm, b) 1.2 cm, c) 8.9 cm, d) 10.3 cm
2. Convert to millimeters.
a) 7.2 cm
b) 0.8 cm
c) 0.89 cm
d) 10.3 cm
Answers: a) 72 mm, b) 8 mm, c) 8.9 mm, d) 103 mm
(MP.4)
Solving problems requiring conversions. Work through the following
problems as a class. Encourage multiple solutions. For example, for the
first problem, students can convert to millimeters and perform operations
with decimals.
Exercises
a)An eastern box turtle is 14.8 cm long. A New Mexico whiptail lizard is
192 mm long. Which reptile is longer? How much longer? Write the
answer in centimeters and in millimeters.
b)A dime is about 18 mm wide. Amy laid out 7 dimes side by side. How
wide is the row in centimeters?
Answers: a) The lizard is 44 mm = 4.4 cm longer, b) 12.6 cm
1.To change a measurement in millimeters to a mixed measurement
in centimeters and millimeters, remind students that the number of
centimeters is the number of tens of millimeters. Therefore all they need
to do is to separate the ones and the tens, or imagine the number made
from ones and tens blocks. For example, there are 17 tens and 3 ones
in 173, so there are 17 cm 3 mm in 173 mm. In other words: 173 mm =
170 mm + 3 mm = 17 cm + 3 mm = 17 cm 3 mm.
Change each measurement to a mixed measurement in centimeters
and millimeters using the least number of millimeters.
a) 17 mm d) 2 cm 25 mm b) 47 mm e) 32 cm 425 mm c) 125 mm
f) 421 cm 1,232 mm
Answers: a) 1 cm 7 mm, b) 4 cm 7 mm, c) 12 cm 5 mm, d) 4 cm 5 mm,
e) 74 cm 5 mm, f) 544 cm 2 mm
H-8
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Extensions
2.To convert from a mixed measurement to millimeters, change the
centimeters to millimeters, then add the leftover millimeters. Example:
33 cm 2 mm = 330 mm + 2 mm = 332 mm.
Convert to millimeters.
a) 5 cm 8 mm
d) 67 cm 89 mm
b) 78 cm 9 mm
e) 79 cm 56 mm
c) 44 cm 1 mm
f) 60 cm 1,234 mm
Answers: a) 58 mm, b) 789 mm, c) 441 mm, d) 759 mm, e) 846 mm,
f) 1,834 mm
3. Find the difference in length between the lizard and the turtle.
Lizard
Turtle
a)
2 cm 5 mm
3 cm 1 mm
b)
7 cm 8 mm
12 cm 3 mm
c)
2 cm 17 mm
5 cm 26 mm
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Answers: a) 6 mm, b) 45 mm = 4.5 cm, c) 39 mm = 3.9 cm
Measurement and Data 5-2
H-9
MD5-3 Meters and Centimeters
Pages 170–171
STANDARDS
5.MD.A.1, 5.NBT.A.2
Vocabulary
centimeter (cm)
conversion
convert
estimate
estimating
measurement
meter (m)
meter stick
millimeter (mm)
Goals
Students will estimate and measure in meters, and convert
measurements between meters and centimeters.
PRIOR KNOWLEDGE REQUIRED
Can measure in centimeters and millimeters
Understands that smaller units require more units
Can multiply and divide decimals and whole numbers by 10
Is familiar with decimals to hundredths
Can locate a number on a number line, including decimal hundredths
Can convert between centimeters and millimeters
Knows that measurements can be in fractions of a unit
MATERIALS
rulers
measuring tapes
meter sticks
pieces of string
items 1 m long
Introduce meters. Identify the length and marking of a meter on a ruler
or measuring tape, and explain to students that a meter is another unit
of measurement. Write the word “meter” and the abbreviation “m,” and
explain that these are the two ways to write meter.
Introduce estimation. Explain that sometimes you want to know how
long an object is, but you do not need to know the precise length. Giving
a number that is about the right length is called estimating the length, and
the number itself is called an estimate. Explain that one possible tool to
produce a good estimate of a distance in meters is giant steps.
ACTIVITY
Large steps are about a meter long. Using tape, make two lines
one meter apart on the floor. Students stand with their heels to one of
the lines and make a step so that the heel of the front foot touches the
other line. Students perform the step several times to make sure they
can all do it.
Divide students into pairs. One partner takes five steps they think will
be about a meter each. The other partner measures the distance using
H-10
Teacher’s Guide for AP Book 5.1
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Show students a meter stick and explain that it is a tiny bit longer than one
meter long. It has about 1 cm of extra length at both ends, just as many
rulers do.
a meter stick. Emphasize that it is much more difficult to take five big
steps all in a row than to take five steps walking normally. Suggest
that students lead off with the same foot each time: take one giant
step; bring your back foot forward and place it next to your other foot;
then take another giant step. Students repeat the exercise to make the
distance of 5 steps as close to 5 meters as possible.
SAY: I want to know about how many meters long the classroom is. Have
students take giant steps across the room to help you find out. Remind
them to take identical-sized steps and to lead off with the same foot each
time. Then have a volunteer use a meter stick to measure the length of
the classroom. ASK: Did we get the same answer both ways? Were our
answers close? Which way was faster? Explain that when we are in a hurry
and we just need to know about how long a room is in meters, we can use
giant steps instead of meter sticks to find out. Discuss situations in which it
is important to know exact measurements (examples: in a race, making a
ruler to sell, choosing paper to put in a book, making legs for a table).
Encourage students to suggest items that are 1 m long (a scarf, a pool
noodle, etc.) for the class measurement display (see Lesson MD5-1). Then
measure the items with a meter stick to verify their length.
ACTIVITY
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Students use a string and a ruler to measure the lengths of various
body parts (such as arm length, arm span, height from floor to armpit,
distance around the head), and compare the measurements to
1 meter. Encourage students to predict the answers before measuring.
Converting meters to centimeters. Explain that there are 100 centimeters
in 1 meter. Draw a number line on the board and label the increments
above the number line 0 m, 1 m, 2 m, and so on to 10 m. Label the first
two increments below the number line 0 cm and 100 cm. ASK: How many
centimeters would be in 2 meters? (200) What number will we skip count
by to find the answer? (100) Have students skip count by hundreds and
invite volunteers to write the corresponding numbers of centimeters on the
number line below the increments.
m
cm
1
2
3
4
Measurement and Data 5-3
On the board, draw the T-table in the margin and ask students to fill in the
measurements in centimeters. Extend the table a few more rows and have
students continue the pattern. Then ASK: How can you get the number
in the right-hand column from the number in the left-hand column? What
mathematical operation takes 1 to 100, 2 to 200, and so on? (multiply by
100) ASK: How is converting meters to centimeters the same as converting
centimeters to millimeters? (we also multiply) How is it different? (we
multiply by 10 to get millimeters from centimeters and by 100 to get
centimeters from meters) Summarize on the board:
H-11
× 100 × 10
m cm
cm mm
Exercises: Convert from meters to centimeters.
a) 4 m
b) 16 m
c) 52 m
Bonus: 2,775 m
Answers: a) 400 cm, b) 1,600 cm, c) 5,200 cm, Bonus: 277,500 cm
Comparing measurements. ASK: Which measurement is longer, 2 cm
or 5 mm? Which number is greater, 5 or 2? Remind students that even
though 5 is more than 2, 2 cm is longer than 5 mm. The units are different,
and we need to take the size of the units into account when comparing
measurements. It is necessary to convert measurements into the same unit
before comparing them.
Exercises: Point your thumbs toward the larger measurement.
a) 300 cm or 7 m
d) 765 cm or 90 m
b) 305 cm or 2 m
c) 480 cm or 2 m
e) 6,500 cm or 643 m f) 89 m or 34,567 cm
Bonus
g) 120,345 cm or 7,892 m
h) 654,234 cm or 89,893 m
Answers: a) 7 m, b) 305 cm, c) 480 cm, d) 90 m, e) 643 m, f) 34,567 cm,
Bonus: g) 7,892 m, h) 89,893 m
Review writing decimal hundredths: 1 cm = 0.01 m. Remind students
how to read numbers such as 0.67, 2.34, and 0.08. Then ASK: If 1 m =
100 cm, what fraction of 1 meter is 1 centimeter? (1 hundredth) How can
we write this with decimals? (1 cm = 0.01 m) Write on the board:
cm
1
2
...
m
1 m = 100 cm, so 1 cm = 0.01 m
ASK: How many hundredths of 1 m is 2 cm? (2 hundredths) On the board,
draw the table in the margin and have students help you fill it in up to 10 cm.
Exercises: Convert to meters.
a) 9 cm
b) 17 cm
c) 324 cm
d) 607 cm
Answers: a) 0.09 m, b) 0.17 m, c) 3.24 m, d) 6.07 m
ASK: How many hundredths of 1 meter is 40 centimeters? (40 hundredths)
H-12
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Determining measurements between other measurements. On the
board, draw a number line from 2 m to 5 m. ASK: Where would 453 cm be
on this number line? (between 4 m and 5 m) To prompt students to see the
answer, have volunteers write the measurements in centimeters below the
measurements in meters. Repeat the Exercise with 231 cm (between 2 m
and 3 m) and 379 cm (between 3 m and 4 m). Then ask students to give
a different example of a measurement in each of the intervals. Finally, ask
students what measurement in an exact number of meters is between
283 cm and 341 cm. (3 m)
Write on the board:
40 cm = 0.40 m
ASK: What other way can we write 0.40? (0.4) Remind students that they
can remove zeros or write zeros after the last non-zero digit to the right of
the decimal point. So 40 cm = 0.40 m = 0.4 m.
Exercises: Convert to meters.
a) 90 cm
b) 50 cm
c) 320 cm
d) 2,670 cm
Answers: a) 0.90 m = 0.9 m, b) 0.5 m, c) 3.2 m, d) 26.7 m
Reverse the task. ASK: How many centimeters are in 0.8 m? To prompt
students to see the answer, ask them to write 0.8 as hundredths. (0.80)
Write on the board (and read as you are writing):
0.8 m = 0.80 m = 80 cm
Repeat with 0.7 m, and 1.3 m. (70 cm, 130 cm)
Exercises: Convert to centimeters.
a) 0.5 m
b)
5.4 m c)
3.21 m d)
2.67 m
Answers: 50 cm, b) 540 cm, c) 321 cm, d) 267 cm
Extension
(MP.4)
a)A CD case is 142 mm long. How many CDs will fit on a display shelf
that is 3.5 m long?
b)Ron stacks CDs on a display shelf. He stacks a book 21 cm wide
between every 5 CDs and leaves open ends so there are 5 CDs at each
end. How many books and CDs can he stack on the 3.5-m long shelf?
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Answers: a) 24 CDs, b) 20 CDs and 3 books
Measurement and Data 5-3
H-13
MD5-4 Meters and Centimeters (Advanced)
Pages 172–173
STANDARDS
5.MD.A.1, 5.NBT.A.1,
5.NBT.A.2
Goals
Students will convert between centimeters and meters.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
centimeter (cm)
conversions
convert
line
measurement
meter (m)
millimeter (mm)
mixed measurement
Understands the concept of linear measurement
Understands that smaller units require more units
Can multiply and divide decimals and whole numbers by 100
Knows that 1 m = 100 cm
Can convert whole meters to centimeters
Can compare decimals to hundredths
Can convert between dollar and cent notations
MATERIALS
meter sticks
grid paper
Review multiplying and dividing decimals and whole numbers by 100.
Remind students that they shift the decimal point 2 places right to multiply
and 2 places left to divide. Remind them that they can write zeros after the
decimal point, and the number will not change. For example, 6.7 = 6.70.
ASK: Why is that true? (the decimal part is 7/10 = 70/100) As well, remind
students that even though we do not write decimal point in whole numbers,
we can still add it without changing the number. For example, 12 = 12.00.
Use the questions below as a test to make sure all students can perform the
required multiplication and division.
Exercises: Multiply or divide.
a)25 ÷ 100 = b) 3 ÷ 100 = c) 12.2 ÷ 100 = d) 387 ÷ 100 =
e)0.4 × 100 = f) 5.3 × 100 = g) 1.89 × 100 = h) 0.08 × 100 =
Using multiplication and division to convert between centimeters
and meters. Remind students that they multiplied by 100 to convert a
measurement in meters to centimeters. ASK: What operation would you
use to convert a measurement in centimeters to meters? (divide by 100)
PROMPT: Which operation is the opposite of multiplication? Convert the
first few measurements in each Exercise as a class, then have students
work individually.
Exercises
1. Convert to meters.
a) 26 cm
e) 6 cm
H-14
b) 52 cm
f) 0.7 cm
c) 158 cm
g) 80 cm
d) 532 cm
h) 60 cm
Teacher’s Guide for AP Book 5.1
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Answers: a) 0.25, b) 0.03, c) 0.122, d) 3.87, e) 40, f) 530, g) 189, h) 8
Answers: a) 0.26 m, b) 0.52 m, c) 1.58 m, d) 5.32 m, e) 0.06 m,
f) 0.007 m, g) 0.80 m = 0.8 m, h) 0.60 m = 0.6 m
2. Convert to centimeters.
a) 7.25 m
e) 0.065 m
b) 30.82 m
f) 0.2 m
c) 0.09 m
g) 20.9 m
d) 0.03 m
h) 0.3 m
Answers: a) 725 cm, b) 3,082 cm, c) 9 cm, d) 3 cm, e) 6.5 cm, f ) 20
cm, g) 2,090 cm, h) 30 cm
(MP.7)
Comparing money to meters and centimeters. SAY: 1 m = 100 cm. What
other unit do we know that has 100 smaller units in it? (a dollar has 100
cents in it) Point out that the relationship between meters and centimeters
is very similar to the relationship between dollars and cents. Conversions
work very similarly: 625¢ = $6.25, and 625 cm = 6.25 m. Point out that
when students convert money amounts in cents to dollars, they divide by
100. ASK: How are dollars and cents different from meters and centimeters?
(there is a unit—millimeters—that is smaller than centimeters, but there is
no money unit smaller than cents)
Using mixed measurements. Explain that we often think of prices such
as $5.75 as 5 dollars and 75 cents. This measurement combines dollars
and cents. Similarly, we can express a measurement using a combination
of meters and centimeters (e.g., 5 m 75 cm). This is called a mixed
measurement. To write the length of a desk in that form, we could measure
the desk in meters, write how many whole meters fit along the desk
(1 meter, replace the meter stick along the desk as you did when making
the 1 m mark), then measure just the remainder in centimeters (show how
to do this). Model measuring another object in meters and centimeters.
ACTIVITY
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Students measure several objects in the classroom (e.g., their own
height) in meters and centimeters. For example, to measure the height
of a student, draw a vertical line on the wall and have the student stand
against the wall, with their back to the line. Make a mark on the line
showing the height of the student. Then use a meter stick to make
a mark 1 m from the ground, and measure the rest of the height in
centimeters. Have students record their measurements two ways, for
example, as 1 m 14 cm and as 114 cm.
Writing measurements in different ways: meters and mixed
measurements. ASK: How many dollars and cents are in $5.34?
(5 dollars 34 cents) Remind students that meters and centimeters work
like dollars and cents. How many meters and centimeters are in 5.34 m?
(5 m 34 cm) Emphasize that centimeters are hundredths of meters, so
the whole number is the number of meters and the hundredths are the
number of whole centimeters.
Measurement and Data 5-4
H-15
Exercises: Convert the measurement in meters to a mixed measurement.
a) 3.14 m
b) 5.08 m
c) 12.89 m
d) 24.01 m
Answers: 3 m 14 cm, b) 5 m 8 cm, c) 12 m 89 cm, d) 24 m 1 cm
(MP.3)
Remind students that we can write zeros to the right of the decimal point,
without changing the number. For example, 2.3 = 2.30. ASK: How many
meters and centimeters are in 2.3 m? (2 m 30 cm) Why not 2 m 3 cm?
(2.3 m = 2.30 m, not 2.03 m) Repeat with 4.6 m and 7.5 m. (4 m 60 cm,
7 m 50 cm)
Reverse the task. Do the first three examples as a class, then have students
work individually. You can use the money analogy again: converting 5 m
78 cm to meters is the same as writing 5 dollars 78 cents in dollar notation.
Exercises: Convert the mixed measurement to a measurement in meters.
a) 5 m 78 cm
b) 8 m 20 cm
e) 47 m 72 cm f) 6 m 8 cm
Bonus: 1 m 23.4 cm
c) 2 m 9 cm
g) 78 m 40 cm
d) 24 m 16 cm
Answers: a) 5.78 m, b) 8.20 m = 8.2 m, c) 2.09 m, d) 24.16 m, e) 47.72 m,
f) 6.08 m, g) 78.40 m = 78.4 m, Bonus: 1.234 m
Writing measurements in different ways: centimeters and mixed
measurements. Now have students think of how they will convert a mixed
measurement into centimeters. Point out that part of the measurement
is already in centimeters, so all they need to do is convert the part in
meters into centimeters. Demonstrate how to use grid paper to convert the
measurements as shown in the margin.
4 m = 400 cm,
so 4 m 6 cm
0
+
4
H-16
0
0
cm
6
cm
6
cm
a) 5 m 9 cm
b) 2 m 8 cm
c) 3 m 12 cm
d) 123 m 78 cm
Answers: a) 509 cm, b) 208 cm, c) 312 cm, d) 12,378 cm
Ask students to compare these measurements for the same object:
1 m 24 cm and 124 cm. ASK: Where do the centimeters in the mixed
measurement appear in the measurement in centimeters? (as the tens
and ones digits) Where do the meters in the mixed measurement appear
in the measurement in centimeters? (as the hundreds digit) What is the
connection between the hundreds in the measurement in centimeters
and the meters in the mixed measurement? (100 cm = 1 m) Explain that
this means we have a way to convert between mixed measurements
and measurements in centimeters. To convert from a measurement in
centimeters to a mixed measurement, take the tens and the ones and
leave them as centimeters, and write the hundreds digit as the numbers of
meters. Example: 346 cm = 300 cm + 46 cm = 3 m 46 cm. Have students
convert each centimeter measurement to a mixed measurement. Have
students raise their fingers to show how many whole meters are in each
mixed measurement.
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
4
=
Exercises: Write the measurement in centimeters only.
Exercises: Convert to a mixed measurement.
a) 362 cm b) 540 cm c) 723 cm d) 984 cm
Answers: a) 3 m 62 cm, b) 5 m 40 cm, c) 7 m 23 cm, d) 9 m 84 cm
Ask students to convert 1,352 cm to meters and centimeters. SAY: I know
a student who thinks 1,352 cm = 3 m 52 cm because the hundreds digit
of 1,352 is 3. Is the answer correct? (no) Have students explain the error.
Point out that this question is similar to telling how many dollars and cents
are in 1,352¢. We know that 1,352¢ = $13.52, or 13 dollars and 52 cents.
Since centimeters and meters are related in the same way as cents and
dollars, then 1,352 cm = 13 m 52 cm. Also, the number of meters in a
measurement in centimeters is exactly the number of hundreds, because
1 m is 100 cm. Summarize: to convert a measurement in centimeters to a
mixed measurement, separate the ones and tens from the rest and convert
the remaining hundreds to meters: 1,352 cm = 1,300 cm + 52 cm = 13 m
+ 52 cm.
ASK: How many meters are in 305 cm? (3) How many centimeters are left
over? (5 cm)
Exercises: Write the mixed measurements.
a) 567 cm
e) 6,789 cm
b) 408 cm
f) 1,230 cm
c) 304 cm
d) 801 cm
Bonus: 123,456 cm.
Answers: a) 5 m 67 cm, b) 4 m 8 cm, c) 3 m 4 cm, d) 8 m 1 cm,
e) 67 m 89 cm, f) 12 m 30 cm, Bonus: 1,234 m 56 cm
Extensions
1.Express each measurement in meters and centimeters using the least
number of centimeters.
a) 1 m 327 cm c) 2 m 1,022 cm
b) 4 m 927 cm d) 12 m 1,272 cm
Answers: a) 4 m 27 cm, b) 13 m 27 cm, c) 12 m 22 cm, d) 24 m 72 cm
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
2. a)0.01 m refers to a unit that is one hundredth of a meter, and that
fits in 1 meter a hundred times. Which unit is that?
b)$0.01 refers to a unit that fits into $1 a hundred times. Which unit
is that?
c)How many times does 0.001 m fit into a meter? Which unit is that?
Hint: Use a meter stick.
Answers: a) centimeter, b) cent, c) 1,000 times, millimeter
Measurement and Data 5-4
H-17
MD5-5 Meters and Kilometers
Pages 174–175
Goals
STANDARDS
5.MD.A.1, 5.NBT.A.1,
5.NBT.A.2
Students will convert between meters and kilometers.
PRIOR KNOWLEDGE REQUIRED
Understands the concept of linear measurement
Understands that smaller units require more units
Can multiply and divide decimals and whole numbers by 1,000
Can convert between meters and centimeters
Can compare decimals to thousandths
Vocabulary
centimeter (cm)
conversion
convert
kilometer (km)
measurement
meter (m)
millimeter (mm)
MATERIALS
spool of fishing line or pack of yarn to represent 1 km
Introduce kilometers. Explain to students that a kilometer is a unit of
measurement that is much larger than a meter or centimeter. Write the
word “kilometer” on the board, circle the letters “k” and “m,” and write the
abbreviation “km.” Explain that these are the two ways to write kilometer.
Explain that there are one thousand meters in one kilometer. Add a spool of
fishing line or a pack of yarn representing a kilometer to the measurement
display. (The packaging always labels the length of fishing line or yarn on
each spool in meters; one large spool of line or two large spools of yarn
should suffice.)
(MP.7)
Exploring how many meters are in a kilometer. SAY: A soccer field is
about 100 m long. About how many meters long are two soccer fields?
Three soccer fields? How can you find out? (e.g., skip count by 100s, use
a T-table) Use both methods to see how long 6 soccer fields are in meters.
(600) Then ask students to look for a pattern in the T-table. How many
soccer fields will be in a kilometer? (10)
Converting from whole kilometers to meters. Write on the board:
10 mm = 1 cm
× 10 × 100
mm cm
H-18
?
100 cm = 1 m
1,000 m = 1 km
Review with students how to use multiplication to convert centimeters to
millimeters and meters to centimeters. Summarize on the board:
m km
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Explain that 1 kilometer is about the distance a person can walk in
15 minutes, the length of about 10 football fields, or the length of about
10 small city blocks. If there is a daily school event that takes about
15 minutes, such as a recess break, refer students to this event to help
them to understand how long a 15-minute walk would take. If there is a
familiar place close to school that is about 1 km away, mention that place
to help students understand how far they would have to walk.
SAY: You multiply by 10 to get from centimeters to millimeters. Why?
(because there are 10 mm in 1 cm) You multiply by 100 to get from meters
to centimeters. Why? (because there are 100 cm in 1 m) What operation
would you use to get from kilometers to meters? (multiplication) What
number will you multiply by? (1,000) Why? (there are 1,000 m in 1 km)
Replace the question mark above with “× 1,000.”
Exercises: Convert the measurements in kilometers to meters.
a) 3 km
b) 8 km
c) 15 km
d) 39 km
Bonus
e 100 km f) 25 km = m = cm = mm
Answers: a) 3,000 m, b) 8,000 m, c) 15,000 m, d) 39,000 m,
Bonus: e) 100,000 m, f) 25,000 m = 2,500,000 cm = 25,000,000 mm
Comparing measurements. Write on the board:
5 km
3,000 m
ASK: Which measurement is greater? Remind students that to compare
measurements correctly you need to convert them to the same unit, and
that it is usually more convenient to use the smaller unit. Ask students to
convert 5 km to meters, then decide which measurement is longer. (5 km)
Exercises: Point your thumb toward the larger measurement.
a) 304 m or 2 km
b) 4,090 m or 2 km
c) 4,605 m or 90 km
d) 653 km or 6,500 m e) 89 km or 330,567 m
Bonus:
f) 120,345 m or 765 km
g) 123,765 cm, 3,432 m, or 2 km
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Answers: a) 2 km, b) 4,090 m, c) 90 km, e) 653 km, e) 330,567 m,
Bonus: f) 765 km, g) 3,432 m
Converting between meters to kilometers using place value. Remind
students how to read numbers such as 0.467, 2.304, and 0.008. Also,
remind them that numbers such as 0.05 can be written as 0.050. Then
ASK: If 1 km = 1,000 m, how many times does 1 meter fit into 1 kilometer?
(1,000) What fraction of 1 kilometer is 1 meter? (1 thousandth) How do
we write this with decimals? (1 m = 0.001 km) Write on the board:
m
km
1
2
...
1 km = 1,000 m, so 1 m = 0.001 km
ASK: How many thousandths of 1 km is 2 m? (2 thousandths) Start a table
as in the margin and have students help you fill it in up to 10 m.
Exercises: Convert to kilometers.
a) 9 m
d) 607 m
b) 17 m
e) 500 m
c) 324 m
f) 250 m
Answers: a) 0.009 km, b) 0.017 km, c) 0.324 km, d) 0.607 km,
e) 0.500 km = 0.5 km, f) 0.250 km = 0.25 km
Measurement and Data 5-5
H-19
Remind students that they can remove the zeros to the right of the decimal
point, so 0.500 km can be written as 0.5 km. If students still have zeros in
their answers, have them rewrite the answers without the zeros at the end.
Reverse the task. ASK: How many meters are in 0.748 km? (748 m) How
many thousandths are in 0.06? (60) How do you know? (0.06 = 0.060)
How many meters are in 0.06 km? (60 m)
Exercises: Convert to meters.
a) 0.512 km
e) 8.002 km
b) 5.474 km
f) 0.003 km
c) 3.281 km
g) 0.7 km
d) 24.617 km
h) 26.28 km
Answers: a) 512 m, b) 5,474 m, c) 3,281 m, d) 24,617 m, e) 8,002 m,
f) 3 m, g) 700 m, h) 26,280 m
Review multiplying and dividing decimals and whole numbers by 1,000.
Use the same process you used to review multiplying decimals by 10
and 100. Use the questions below as a test to make sure all students can
perform the required multiplication and division.
Exercises: Multiply or divide.
a)258 ÷ 1,000 = d)4,387 ÷ 1,000 = g)1.89 × 1,000 = b) 35 ÷ 1,000 = e) 0.004 × 1,000 = h) 0.08 × 1,000 = c) 2 ÷ 1,000 =
f) 5.356 × 1,000 =
i) 0.3 × 1,000 =
Answers: a) 0.258, b) 0.035, c) 0.002, d) 4.387, e) 4, f) 5,356, g) 1,890,
h) 80, i) 300
Using multiplication and division to convert between meters and
kilometers. SAY: You multiplied a measurement in kilometers by 1,000
to get the measurement in meters. What operation would you use to
go in the opposite direction, to convert a measurement in meters to
kilometers? (divide by 1,000) PROMPT: Which operation is the opposite
of multiplication? Convert the first few measurements in each Exercise as
a class, then have students work individually.
1. Convert to kilometers.
a) 263 m
e) 6 m
b) 502 m
f) 79 m
c) 1568 m
g) 80 m
d) 1500 m
h) 600 m
c) 0.009 km
g) 20.89 km
d) 0.03 km
h) 1.3 km
2. Convert to meters.
a) 7.259 km
e) 0.065 km
b) 30.825 km
f) 0.2 km
Answers: 1. a) 0.263 km, b) 0.502 km, c) 1.568 km, d) 1.5 km,
e) 0.006 km, f) 0.079 km, g) 0.08 km, h) 0.6 km 2. a) 7,259 m,
b) 30,825 m, c) 9 m, d) 30 m, e) 65 m, f) 200 m, g) 20,890 m,
h) 1,300 m
H-20
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Exercises
Extensions
1. a)An adult female Komodo dragon is about 2 m long. How many
female Komodo dragons lined up end to end will make 1 km?
b)An adult male Komodo dragon is about 3 m long. About how many
adult male Komodo dragons lined up end to end will make 1 km?
c)A newly hatched Komodo dragon is 49 cm long. About how many
Komodo dragons hatchlings lined up end to end will make 1 km?
d)There are 18 eggs in an average Komodo dragon nest. What is the
total length of the hatchlings from a single nest?
e)Scientists found 75 Komodo dragon nests. Is the total length of the
hatchlings in these nests more than 1 km?
Answers: a) 500, b) 333, c) 2,000, d) 882 cm, e) The total length of the
hatchlings from one nest is slightly less than 9 m. The total length of the
hatchlings from 75 nests is slightly less than 675 m or 0.675 km, so the
answer is no.
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2. a)The table lists the highest mountain on each continent. Write the
height of each mountain in meters. Rank the mountains from
highest (1) to lowest (7).
Mountain
Location
Height
(km and m)
Aconcagua
South America
(Argentina)
6 km 962 m
Denali
(McKinley)
North America
(United States)
6 km 195 m
Elbrus
Europe
(Russia)
5 km 633 m
Everest
Asia
(Nepal/China)
8 km 848 m
Kilimanjaro
Africa
(Tanzania)
5 km 963 m
Kosciuszko
Australia
2 km 228 m
Vinson Massif
Antarctica
4 km 897 m
Height
Ranking
(m)
b)Calculate the difference in height between the highest and the
lowest mountains.
Answers: a) 1. Everest 8,848 m, 2. Aconcagua 6,962 m, 3. Denali
6,195 m, 4. Kilimanjaro 5,963 m, 5. Elbrus 5,633 m, 6. Vinson Massif
4,897 m, 7. Kosciuszko 2,228 m; b) 8,848 – 2,228 = 6,620 m
Measurement and Data 5-5
H-21
MD5-6 Perimeter
Pages 176–177
Goals
STANDARDS
5.MD.A.1, 5.NBT.B.7
Students will solve problems related to perimeter of shapes.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
centimeter (cm)
conversion
convert
measurement
meter (m)
perimeter
1 cm
Can multiply and divide decimals and whole numbers by 100
Can convert between meters and centimeters
Can compare decimals to hundredths
Can add decimals
Introduce perimeter. Write the word perimeter and explain to students
that perimeter is the measurement around the outside of a shape. Illustrate
the perimeters of some classroom items by running your hand along the
outside of a desk, the blackboard, or a blackboard eraser. Write the phrase
“the measurement around the outside of a shape.”
Draw on the board the figure in the margin. Explain that each side of
each square represents 1 cm, and that perimeter is calculated by totaling
the outside edges. Demonstrate a method for calculating the perimeter
by marking or crossing out each edge as you count it. Demonstrate this
several times.
Exercises: Each side of a square is 1 cm long. Find the perimeter of
the figures.
a)
b)
c)
Finding perimeter by adding side lengths. Use one of the shapes from
the previous Exercise to demonstrate the method for calculating perimeter
by counting the entire length of each side and creating an addition
statement. Write the length of each side on the picture.
Exercises: Each square is 1 cm long. Write the side length on each side.
Then write the addition statement and find the perimeter.
a)
b)
c)
Answers: a) 1 cm + 3 cm + 3 cm + 1 cm + 2 cm + 2 cm = 12 cm,
b) 12 cm, c) 14 cm
H-22
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Answers: a) 10 cm, b) 10 cm, c) 16 cm
NOTE: Students will often miss one of the sides that is 1 unit long when two
such sides meet making a reflex angle, as the two highlighted sides show
in part b). Have students count the sides of the shape and make sure that
the number of sides they add to find the perimeter matches the number
of sides in the shape. You can also spot some incorrect calculations by
looking for answers that are odd numbers. The perimeter of a shape made
of squares is always an even number.
Review conversion between meters and centimeters using
multiplication. Remind students that they can multiply by 100 to convert
measurements in meters to centimeters. Use the Exercises below to make
sure all students can perform the conversions.
Exercises: Convert to centimeters.
a) 2.35 m
b) 4.5 m
c) 0.08 m
Answers: a) 235 cm, b) 450 cm, c) 8 cm
Finding perimeter of shapes with sides given in meters and
centimeters. On the board, draw a rectangle and mark two of the sides
as 0.75 m and 44 cm. Ask students to determine the length of the opposite
sides. Then explain that you want to find the perimeter of the rectangle.
ASK: Does it make sense to add 0.75 + 44 + 0.75 + 44 to find the
perimeter? (no) Why not? (the lengths of the sides are given in different
units) Remind students that when comparing lengths in different units,
they need to convert the lengths to the same unit before comparing. When
performing mathematical operations on measurements, the situation is
similar: they all need to be converted to the same unit. It is usually easier
to convert all measurements to the smaller unit.
Have students convert 0.75 m to centimeters, then have them find the
perimeter. (75 cm + 44 cm + 75 cm + 44 cm = 238 cm)
Exercises: Convert the measurements to the smaller unit, then find
the perimeter.
a)
2.5 m
1.2 m
b)
72 cm
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85 cm
c)
1.3 m
d)
2.5 m
150 cm
50 cm
1.2 m
2m
Answers: a) 670 cm, b) 384 cm, c) 600 cm, d) 300 cm
Measurement and Data 5-6
H-23
Review converting centimeters to meters by dividing by 100. Remind
students that division by 100 looks like shifting the decimal point 2 places
to the left. Review adding decimals. Then have students convert the
measurements in the Exercises above to meters and find the perimeter.
Ask students to convert the answers to centimeters to make sure they got
the same answers for the same shapes.
Answers: a) 6.7 m, b) 3.84 m, c) 6 m, d) 3 m
Extensions
1.Distribute one piece of string, about 30 cm long, and a geoboard to
each student. Have them tie the ends of the string together to form a
loop, then create a variety of shapes on the geoboard with the string.
Explain that the shapes will all have the same perimeter because the
length of the string, which forms the outside edges, is fixed. How many
different shapes have the same perimeter?
2.Distribute Pentamino pieces (a set of twelve figures each made of five
squares; see BLM Pentomino, p. H-37) to students and have them
calculate the perimeter of each figure and fill in the table below.
Figure
Perimeter
Number of Inside Edges
a) Which shape is different from all other shapes?
(MP.3, MP.7)
b)Double the number of inside edges and add to the perimeter for
all shapes. What do you notice? Try to explain your findings.
(MP.3)
H-24
3.Have students investigate perimeters of shapes made from squares
using BLM Patterns in Perimeters (p. H-38).
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Answers: a) All shapes except shape F (shown in the margin) have
perimeter 12 and 4 inside edges. Shape F has perimeter 10 and 5
inside edges; b) The answer is always 20. Explanation: Each inside
edge belongs to 2 squares. Each edge in the perimeter belongs to
1 square. The answer is the total number of edges on all squares.
There are 5 squares, so the total number of edges is 5 × 4 = 20.
MD5-7 Changing Units of Length
Pages 178–179
Goals
STANDARDS
5.MD.A.1, 5.NBT.A.1,
5.NBT.A.2, 5.NBT.B.7
Students will convert between metric units of length.
PRIOR KNOWLEDGE REQUIRED
Can multiply and divide decimals and whole numbers by
10, 100, and 1,000
Understands that smaller units require more units
Can convert between metric units of length measurement
Can add and subtract decimals
Vocabulary
centimeter (cm)
conversion
convert
decimeter (dm)
kilometer (km)
measurement
meter (m)
millimeter (mm)
MATERIALS
BLM Measurement Cards (pp. H-39–40)
Review conversion from centimeters to millimeters and from meters to
centimeters. Remind students that there are 10 mm in 1 cm, so if an object
is 4 cm long, it is also 40 mm long. Remind students that they can multiply
by 10 to convert from centimeters to millimeters. Multiplying by 10 looks like
shifting the decimal point one place to the right.
Exercises: Convert the measurements in centimeters to millimeters.
a) 6 cm Bonus: b) 12 cm e) 2,345 cm
c) 8.9 cm
d) 0.6 cm
f) 123,456.789 cm
Answers: a) 60 mm, b) 120 mm, c) 89 mm, d) 6 mm, Bonus: e) 23,450 mm,
f) 1,234,567.89 mm
Remind students that there are 100 cm in 1 m. So if an object is 3 m long,
it is also 300 cm long. Remind them that they can multiply by 100 to convert
measurements in meters to centimeters. This multiplication looks like
shifting the decimal point two places to the right.
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Introduce decimeters. Point out that 100 = 10 × 10, so it would be nice to
have a relationship like this:
× 10
mm
10 mm = 1 cm
× 10
cm
10 cm = 1
× 10
10
m
=1m
Explain that there is a unit of measurement that goes in the blanks and
it is called a decimeter. Write the word “decimeter” on the board (circle
the letters "d" and "m") and the abbreviation “dm,” and explain that these
are two ways to write decimeter. Have students fill in the blanks above
with the new term.
Measurement and Data 5-7
H-25
Explain that decimeters are similar to dimes in money. There are 100 cm
in a meter, and 100 cents in a dollar. A decimeter is between centimeters
and meters, the same as a dime is between cents and dollars. There are
10 cm in a decimeter, and 10¢ in a dime. Similarly, there are 10 dm in a
meter, and 10 dimes in a dollar. You might point out that just as people
usually do not say that something costs 7 dimes, even though it would be
a clear indication of cost, people also do not usually say that something is
7 dm long, even though it is a clear indication of length.
On the board, work through Questions 1 and 2 on p. 178 in the AP Book
and have students work simultaneously in their books.
Exploring the relationship between the number of units in a
measurement and the size of the unit. Remind students that when
they measure an object in centimeters and measure the same object
in millimeters, the number of centimeters in the measurement is always
smaller than the number of millimeters. Why does this happen? (millimeters
are smaller, so you need more of them) SAY: John and Kyla each have $2.
Kyla has $2 in dimes, and John has $2 in pennies. Who has more coins?
(John) Why? (because pennies have a smaller value) Point out that to get
the same amount of money, you need more coins of the smaller value (or
unit), and fewer coins of the larger value (or unit). The larger the unit, the
fewer number of units you need to get the same amount or to cover the
same distance.
Converting between centimeters and millimeters. Remind students
that they multiply by 10 to convert a measurement in centimeters to a
measurement in millimeters. ASK: Why do you multiply and not divide to
convert centimeters to millimeters? How is that connected to the size of the
new unit? (the new unit is smaller so you need more units, so you multiply
by 10, not divide by 10) Write on the board:
Change 4.2 cm to mm:
The new units are
so I need
,
units.
by
.
ASK: What are the new units? (mm) What is larger—centimeters or
millimeters? (centimeters) Are the new units smaller or larger than the old
units? (smaller) How many times smaller? (10 times) Fill in the first two
blanks (10, smaller) Do I need more units or fewer units? (more) Fill in the
next blank (more). If I need more units, do I need to multiply or to divide?
(multiply) By how much? (10) Fill in the last two blanks. (multiply, 10)
Then perform the calculation: 4.2 cm × 10 = 42 mm. PROMPTS: Which
way should we move the decimal point? (right) If I move the decimal point
left, how can I tell this is wrong? (0.42 is smaller than 4.2, but I am looking
for a larger number) Is 42 mm correct? (yes) Finally, write the answer:
4.2 cm = 42 mm.
H-26
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
I
times
Repeat with 350 mm to cm, 26 cm to mm, 8.42 cm to mm, 86.9 mm to
cm. (35 cm, 260 mm, 84.2 mm, 8.69 cm) Provide blanks as above and
have volunteers fill them in. Provide help as needed. Then have students
individually practice solving more problems the same way.
Exercises: Convert the measurement.
a) 1,340 mm to cm b) 2.6 cm to mm
c) 0.48 cm to mm
Answers: a) 134 cm, b) 26 mm, c) 4.8 mm
m
dm
cm
mm
m × 10
dm × 10
cm × 10
÷ 10
÷ 10
mm
÷ 10
Converting between different metric units. On the board, draw the
first diagram in the margin. ASK: As you go down the steps, do the units
become larger or smaller? (smaller) How many times smaller with each
step? (10 times) If you go 2 steps down, how many times smaller is the new
unit? (10 × 10 = 100 times) What if you go 3 steps down? (10 × 10 × 10 =
1,000 times) So when you go down the stairs, do you need more units or
fewer units? (more units) When you go down the stairs, will you multiply
or divide? (multiply) Add arrows to the diagram going down the stairs and
label them.
Repeat the questions for going up the stairs, and finish by adding the
arrows. The finished diagram will look like the second picture in the
margin. Solve several conversion questions together as a class. Do the
first question yourself, but have volunteers help you to solve others
(ASK: What do I do now?) Then have students practice individually.
For more practice, use the Activities below.
Exercises: Say how many times larger or smaller the new unit is.
Then convert.
a)
d)
g)
j)
1.6 mm to cm 74 mm to m
0.01 dm to mm 345 mm to cm
b)
e)
h)
k)
72.3 cm to mm 3.8 dm to cm 1,290 mm to dm
0.35 mm to cm c)
f) i)
l)
0.409 m to mm
22 cm to dm
0.24 m to mm
5.4 cm to m
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Answers: a) 10 times larger, 0.16 cm; b) 10 times smaller, 723 mm;
c) 1,000 times smaller, 409 mm; d) 1,000 times larger, 0.074 m; e) 10 times
smaller, 38 cm; f) 10 times larger, 2.2 dm; g) 100 times smaller, 1 mm;
h) 100 times larger, 12.9 dm; i) 1,000 times smaller, 240 mm; j) 10 times
larger, 34.5 cm; k) 10 times larger, 3.5 cm; l) 100 times larger, 0.054 m
ACTIVITIES 1–2
Give students BLM Measurement Cards. Have them cut out the
cards and shuffle the deck well before each of the activities below. The
activities increase in difficulty; weaker students might spend their time
doing the first activity, whereas stronger students should spend more
time doing the third activity.
1.Sort the cards into groups of 4, so all cards in each group have the
same measurement expressed in different units.
Measurement and Data 5-7
H-27
2.Place the cards face down in a rectangle. Player 1 turns over two
cards. If the cards show the same measurement, they place the
cards in the common pile. Player 2 checks that the decision about
the cards is correct. If the cards do not show the same measurement,
Player 1 turns the cards back over and Player 2 takes a turn.
3.Advanced: Students work in partners. Player 1 picks a random
pair of cards and adds the lengths on the cards. Player 2 subtracts
the lengths. Students will need to convert the measurements
to the same unit most of the time. Partners check each other’s
answers, then switch roles.
Extensions
(MP.3, MP.7)
1.Write a measurement in whole decimetres that is between the given two
measurements. Explain how you found the answer.
a) 320 mm and 437 mm
c) 1 1/2 m and 1 3/4 m
b) 507 mm and 622 mm
Answers: a) 4 dm, b) 6 dm, c) 16 dm
(MP.1)
2.John has a strip of paper 1 dm long and 2 cm wide. He folds the
strip so that it has a crease down its center (see sample in margin).
How can John use this strip as a benchmark to make each of these
measurements?
a) 5 cm
b) 3 cm
c) 1 cm
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Answers: a) half the strip from the crease to the end is a benchmark for
5 cm; b) draw a 5 cm line segment, then mark off 2 cm from one end,
using the width of the strip as a benchmark; the 5 cm line segment is
divided into 2 cm and 3 cm line segments; c) draw a 3 cm line segment
as in part b) and mark off 2 cm from its end; the line segment is divided
into 2 cm and 1 cm
H-28
Teacher’s Guide for AP Book 5.1
MD5-8 Problems with Length
Pages 180–181
Goals
STANDARDS
5.MD.A.1, 5.NBT.B.7
Students will solve problems involving conversions between metric
units of length.
Vocabulary
PRIOR KNOWLEDGE REQUIRED
centimeter (cm)
conversion
convert
kilometer (km)
measurement
meter (m)
millimeter (mm)
perimeter
Can multiply and divide decimals and whole numbers by
10, 100, and 1,000
Can convert between metric units of length measurement
Can add and subtract decimals
MATERIALS
grid paper
BLM Measurement Cards (pp. H-39–40)
Finding missing sides in a rectangle given the perimeter and one side.
Draw a rectangle on the board. Write a length on one of the longer sides.
Ask students what the length of the opposite side should be. Add the length
of one of the shorter sides and ask students what the length of the last side
should be. ASK: What is the perimeter of the rectangle? Ask a volunteer to
write the addition equation for the perimeter.
(MP.2, MP.3)
Draw another rectangle and say that its perimeter is 26 m. Say that the
length of one side is 4 m. Ask students to find the lengths of the other sides.
PROMPTS: What is the length of the opposite side? (4 m) What is the total
length of the two remaining sides? (26 m – 8 m = 18 m) How long is one of
these sides? (9 m)
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To prompt students to see a different solution, draw a big dot on one
corner of the rectangle and ask students to imagine walking around the
rectangle, starting from the dot. Trace your finger along the entire perimeter
to illustrate walking, and stop at the opposite corner. ASK: How far did you
go? (13 m) How do you know? (this is halfway around the rectangle, so the
distance is half the perimeter) If these two sides make 13 m, and one side
is 4 m, how long is the other side? (9 m)
Exercises: Find the missing side.
a) perimeter 24 cm
5 cm
b) perimeter 22 m
5m
Answers: a) 7 cm, b) 6 m
Measurement and Data 5-8
H-29
Review adding and subtracting decimals. Remind students to align the
decimal points when performing operations with decimals.
Exercises: Add or subtract.
a)2.6 + 3.5
e)3.5 – 1.9
b) 1.3 + 8.7
f) 2.45 – 1.2
c) 0.85 + 2.567 d) 3.5 – 2.1
g) 8.02 – 7.88
h) 2.2 – 1.87
Answers: a) 6.1, b) 10, c) 3.417, d) 1.4, e) 1.6, f) 1.25, g) 0.14, h) 0.33
Then have students find the missing sides of rectangles with sides given
in decimals.
Exercises: Find the missing side.
a) perimeter 21 cm
3.5 cm
b) perimeter 12.4 m
2.2 m
c) perimeter 6.7 cm
d) perimeter 2.3 km
1.35 cm
0.15 km
H-30
(MP.1)
Now tell students that you would like to check the answers to the
previous Exercises by solving the problems using a different method, so
that the calculation does not include decimals. Ask them to convert the
measurements into smaller units. Then have them find the perimeter of
the rectangles in the new units and check that their answers are the same
using both methods.
(MP.1)
Using organized search to find the dimensions of a rectangle with the
given perimeter. Ask students to find all the rectangles with a perimeter
of 14 units and sides with lengths in whole units (e.g., 3 units, not 3.5).
If students find only one (or zero) rectangles, show them a systematic
method of finding the answer. On grid paper, draw a line segment 1 unit
long, and ask students to finish the rectangle so that the perimeter is
14 units. Repeat with a side 2 units long. ASK: What side length would
you try next? (3 units) When students draw a rectangle starting with
4 units, ask them if this rectangle is different from the previous one. It is
not, so explain that we can stop, because we have stopped producing
new rectangles. Students can try to produce a rectangle starting with sides
5, 6, and 7, to see that they are not producing anything new. (Students will
see that a rectangle with perimeter 14 and sides 7 is impossible. Prompt
them to compare rectangles with sides 5 or 6 with rectangles drawn earlier.
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Answers: a) 7 cm, b) 4 m, c) 2 cm, d) 1 km
They should see that they have already drawn these rectangles, but in a
different orientation.)
Use the problems on p. 181 of the AP Book to review the material learned
in this unit.
ACTIVITY
Students work in pairs. They will need cards from BLM Measurement
Cards. Player 1 picks two cards at random and decides which of the
measurements is longer, and if it is a lot longer than the other. The
player draws a rectangle that is roughly to scale and marks the lengths
of the sides as given by the cards. (For example, if one side is 9 m and
the other is 1.23 cm, the player draws a long thin rectangle.) Player 2
finds the perimeter of the rectangle. Players then switch roles.
Extension
A square has perimeter 0.8 m. What is the length of each side? How do
you know?
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Solution: 0.8 m = 80 cm; the sides of a square are equal, so each side is
80 cm ÷ 4 = 20 cm
Measurement and Data 5-8
H-31
MD5-9 Mass
Pages 82–83
STANDARDS
5.MD.A.1, 5.NBT.B.7
Vocabulary
conversion
convert
gram (g)
kilogram (kg)
mass
meter (m)
mixed measurement
Goals
Students will convert metric units of mass.
PRIOR KNOWLEDGE REQUIRED
Can multiply and divide decimals and whole numbers by 1,000
Can compare and sort objects by weight (heavier/lighter)
Understands the concept of measuring weight
Can add and subtract decimals
Can multiply 2-digit numbers by 2-digit numbers
Can multiply and divide numbers up to 4 digits by 1-digit numbers
Can solve word problems using the four operations
Can convert between metric units of length measurement
MATERIALS
a collection of items such as dry food with weights marked in grams
and kilograms
grid paper
Introduce mass. Ask students how people can check how heavy an object
is. (weigh it, put it on a scale) Explain that in science we usually use the
word mass to describe how heavy objects are, and we say that the heavier
object has the greater mass.
Introduce grams. ASK: In what units is weight measured? Students are
likely to be familiar with pounds, but may remember other units (ounces,
kilograms, grams) from previous grades. Explain that in the metric system,
the mass of small objects is measured in grams. Write “gram” on the
board, circle the letter “g,” and write the abbreviation “g.” Explain that these
are two ways to write grams. Explain that a large paperclip and a large
chocolate chip weigh 1 gram each. A nickel weighs 5 grams.
Point out that since 1 gram is such a small weight, there are very few
everyday items that weigh less than that. For example, grains of rice, pills,
and most insects, such as ants, weigh less than 1 gram. Only very large
insects weigh more than 1 gram.
ACTIVITY
Give students a collection of everyday items that have their weight
listed in metric units (canned food, plastic spice jars, and so on).
H-32
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Name some pairs of objects that have similar mass: a pen and a pencil, a
full water bottle and a book, a truck and a bus. Then name several everyday
objects and have students name an object with a similar mass: What has a
mass similar to an eraser? (e.g., a glue stick)
Have them sort the objects into three groups by mass: less than 100 g,
between 100 g and 500 g, more than 500 g. Then show more objects,
without telling students the mass, and have them signal which group
these objects should be sorted into. Students can show hands at desk
level for the group with mass less than 100 g, hands at shoulder level
for the medium-sized group, and hands up for the objects heavier than
500 g. This will help students to develop a feel for the size of grams.
Introduce kilograms. Point out a few larger objects in the “heavy” group.
ASK: Would 1 gram be a convenient unit to measure the weight of a laptop,
a pile of books, or a human? (no) Why not? (the number of grams will be
very large) Explain that the unit used to measure the mass of objects of
that size is the kilogram. Write “kilogram” on the board, circle the letters
“k” and “g,” and write the abbreviation “kg.” Explain that these are two
ways to write kilogram.
Write on the board:
1 kilometer =
meters
1 km =
m
ASK: What number goes in the blanks? (1,000) Invite a volunteer to circle
the common parts in the words “kilometer” and “meter.” Ask students to
guess what the part “kilo” means. Explain that kilo means 1,000 in Greek.
When you see kilo in a measurement unit, you know right away that there
are 1,000 smaller units in the large unit. Write on the board:
1 kilogram =
grams
1 kg =
g
ASK: What number goes in the blanks? (1,000)
Have students look through the objects in the group “more than 500 g”
to find any objects that weigh more than 1,000 g. If there are no such
objects, ask why that could be. Show an object such as a large package
of flour. Point out that it is more convenient to write the weight of such a
heavy object in kilograms, using decimals, than to write it in grams.
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Converting kilograms to grams. Remind students that they multiplied
by 1,000 to convert the measurement in kilometers to meters. ASK: What
number would we multiply the number of kilograms by to get the number
of grams? (1,000) Why? (there are 1,000 g in 1 kg) As well, remind students
that they can shift the decimal point 3 places to the right to multiply
decimals by 1,000.
Exercises: Convert to grams.
a) 7 kg
d) 2.27 kg
b) 12 kg e) 34.5 kg
c) 3.545 kg
f) 0.8 kg
Answers: a) 7,000 g, b) 12,000 g, c) 3,545 g, d) 2,270 g, e) 34,500 g,
f) 800 g
Measurement and Data 5-9
H-33
Comparing measurements in different units. Remind students that when
they compare two measurements in different units, they need to convert
one of the measurements so the units become the same. For example,
7 km is larger than 300 m, even though 7 is smaller than 300, because
7 km = 7,000 m, and 7,000 m > 300 m.
Exercises: Convert the measurement in kilograms to grams, then compare
the measurements. To signal the answers, students can show a sideways
“V” with their fingers open in the direction of the larger measurement to
resemble a “<” or a “>” sign.
a) 354 g or 3 kg b) 78 kg or 7,800 g c) 24,897 g or 20 kg
d) 37,890 g or 3.789 kge) 2.78 kg or 278 g
Bonus: f) 456,789 kg or 30,000 g g) 1,000,000 g or 10,000 kg
Answers: a) 354 g < 3 kg, b) 78 kg > 7,800 g, c) 24,897 g > 20 kg,
d) 37,890 g > 3.789 kg, e) 2.78 kg > 278 g, Bonus: f) 456,789 kg > 30,000 g,
g) 1,000,000 g < 10,000 kg
Converting grams to kilograms. ASK: If 1 kg = 1,000 g, what fraction of
a kilogram is 1 gram? (one thousandth) Write on the board:
1 g = 0.001 kg
Make a table as shown and ask students to fill it in up to 10 g.
g
1
kg
0.001
2
3
4
…
Remind students that they can remove zeros to the right of the non-zero
digits after the decimal point, so 0.010 kg can be written as 0.01 kg.
ASK: If we multiply by 1,000 to convert from kilograms to grams, what
operation would you use to convert from grams to kilograms? (divide
by 1,000)
a) 7,846 g e) 34,905 g b) 893 g f) 800 g
c) 45 g g) 70 g
d) 2 g
h) 34,300 g
Answers: a) 7.846 kg, b) 0.893 kg, c) 0.045 kg, d) 0.002 kg, e) 34.905 kg,
f) 0.8 kg, g) 0.07 kg, h) 34.3 kg
Mixed measurements. Remind students that they can write length as a
mixed measurement, for example, a shelf is 5 m 23 cm long. Explain that
mass can also be written as a mixed measurement, such as 3 kg 456 g.
Point out that since grams are thousandths of kilograms, the conversion
from kilograms to mixed measurements is easy: all you need to do is to
write the measurement in kilograms up to thousandths. The whole part
then becomes the number of kilograms, and the number of thousandths
after the decimal point is the number of grams. Show an example:
2.35 kg = 2.350 kg = 2 kg 350 g
H-34
Teacher’s Guide for AP Book 5.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Exercises: Convert to kilograms.
Exercises: Write as a mixed measurement.
a) 3.789 kg
b) 78.089 kg
c) 5.78 kg
d) 2.4 kg
Answers: a) 3 kg 789 g, b) 78 kg 89 g, c) 5 kg 780 g, d) 2 kg 400 g
Remind students that to convert a mixed measurement such as 5 m 23 cm
to centimeters, they need to convert meters to centimeters and add the
remaining centimeters:
5 m = 500 cm, so 5 m 23 cm = 500 cm + 23 cm = 523 cm
3 kg = 3,000 g, so 3 kg 456 g
3,
=
+
3,
0
0
0 g
4
5
6 g
4
5
6 g
ASK: How can you convert 3 kg 456 g to grams? Take up different ideas,
then lead students to the idea of converting the part in kilograms and
adding the remaining grams. Students should perform the addition on a
grid, as shown in the margin. Do the first two Exercises below as a class,
then have students individually convert the measurements to grams.
Exercises: Convert to grams.
a) 2 kg 4 g b) 13 kg 67 g c) 5 kg 159 g e) 52 kg 604 g f) 643 kg 600 g g) 8 kg 15 g Bonus: i) 100 kg 100 g d) 2 kg 391 g
h) 30 kg 1 g
j) 1,000 kg 10 g
Answers: a) 2,004 g, b) 13,067 g, c) 5,159 g, d) 2,391 g, e) 52,604 g,
f) 643,600 g, g) 8,015 g, h) 30,001 g, Bonus: i) 100,100 g, j) 1,000,010 g
Now reverse the task. Write on the board:
23,765 g =
kg
g
ASK: How many whole kilograms are in 23,765 g? (23) Have a volunteer fill
in the first blank. SAY: This is the number of thousands in 23,765, because
there are 1,000 g in 1 kg. Have a volunteer fill in the second blank. (765)
Exercises: Convert to mixed measurements.
a) 7,893 g b) 82,081 g c) 35,950 g d) 100,009 g
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Bonus: 7,123,456 g
Answers: a) 7 kg 893 g, b) 82 kg 81 g, c) 35 kg 950 g, d) 100 kg 9 g,
Bonus: 7,123 kg 456 g
Solving word problems with masses. Work through the following
problems as a class. Invite and encourage as many students as possible
to contribute answers, explanations, and suggestions.
(MP.4)
Exercises
a)A newborn Siberian tiger cub weighs about 1 kg. It gains 700 grams per
week. How much weight does it gain in 4 weeks? How much does the
tiger weigh after 4 weeks? Express your answer in grams, in kilograms,
and as a mixed measurement.
b)A raccoon weighs 7.45 kg. A beaver is 3,800 g heavier than the
raccoon. How much does the beaver weigh?
Measurement and Data 5-9
H-35
c)A paper coffee cup with a lid weighs about 8 grams. Express your
answer in grams, in kilograms, and as a mixed measurement.
i)Ken buys one cup of coffee every day. What mass of garbage
does he generate in a week from paper cups? In a year?
ii)Blanca buys coffee 3 times a day. What mass of garbage from
paper cups does she generate in a year?
d)A small bag of rice weighs 1,816 g, and a big bag of rice weighs 3 kg.
Three big bags cost as much as 5 small bags. Which combination is a
better buy? Hint: Find the weight of 3 big bags and of 5 small bags first.
Which gives more rice for the same price?
Answers: a) The tiger cub gains 2,800 g in 4 weeks, so its weight is
3,800 g = 3.8 kg = 3 kg 800 g; b) 11,250 g = 11.25 kg = 11 kg 250 g;
c) i) Ken generates 56 g of garbage from paper cups in a week, 2,912 g =
2.912 kg = 2 kg 912 g in a year; ii) Blanca generates 8,736 g = 8.736 kg =
8 kg 736 g of garbage from paper cups in a year; d) 3 big bags weigh 9 kg,
and 5 small bags weigh 9,080 g = 9.08 kg, so 5 small bags are a better buy
Extensions
(MP.4)
1.A small box of rice weighs 1,362 g, and costs $5.60. A large bag of rice
weighs 2.27 kg and costs $9. How much do 5 small boxes weigh and
cost? How much do 3 large bags weigh and cost? Which combination
is a better buy?
Answer: 5 small boxes weigh 6.81 kg and cost $28. 3 large bags weigh
6.81 kg and cost $27. Three large bags are a better buy.
2.
Milligrams. We measure very small weights in milligrams (mg).
1 g = 1,000 mg
a) Convert to milligrams.
3g=
7g=
12 g =
c) How many milligrams are in 1 kilogram?
Answers: a) 3,000 g, 7,000 g, 12,000 g;
b) 3 g > 456 mg, 5 g < 5,890 mg; c) 1,000,000 mg
3.
Metric Tonnes. We measure very large weights in metric tonnes (t).
1 t = 1,000 kg
a) Convert to kilograms.
4t=
15 t =
100 t =
b) A male elephant weighs 5 metric tonnes. A female elephant weighs
3,897 kg. How much heavier is the male than the female?
Answers: a) 4,000 kg, 15,000 kg, 100,000 kg; b) 1,103 kg
H-36
Teacher’s Guide for AP Book 5.1
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b) Which is heavier: 3 g or 456 mg? 5 g or 5,890 mg?