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REACHING ALL LEARNERS
Early Finishers
Students estimate, then calculate, the volume of another room
in the school. They compare the volume of this room to the
volume of their classroom.
Common Misconceptions
➤ Students do not know which unit to use when reporting
a measurement.
How to Help: Have students think about the dimensions
of what is being measured. Explain the meaning of the
superscripted 2 and 3 in cm2 and cm3. When area is
calculated, 2 distances are multiplied, so the unit of
measurement is square centimetres, which is abbreviated
cm2. When volume is calculated, 3 distances are multiplied,
so the unit of measurement is cubic centimetres, which is
abbreviated cm3.
Sample Answers
1. a) Campsite: square units, m2
b) Area of wall-to-wall carpet: square units, m2; length and
width of wall-to-wall carpet: linear units, m
c) Pool cover: square units, m2
d) Cargo space: cubic units, m3
e) Volume of tent: cubic units, m3; material used to make tent:
square units, m2; height of tent: linear units, m
f) Track and field race: linear units, m or km
2. One million; 100 cm 100 cm 100 cm 1 000 000 cm3
• How did you estimate the volume of
the classroom?
(We estimated how many cubic metre skeletons it
would take to cover the floor. Then we estimated how
many layers of skeletons it would take to get to the
ceiling. We multiplied these numbers together to get
our estimate for the volume of the room.)
AFTER
Connect
Invite volunteers to share how they calculated
the volume of the room.
(We measured the length, width, and height of the
room to the nearest centimetre. We converted each
measure to the nearest hundredth of a metre. Then
we used a calculator to multiply the dimensions. We
rounded the volume to 2 decimal places. The volume
is in cubic metres.)
• What other objects might you measure using
cubic metres?
(Moving boxes, the cargo space in a truck)
Work through Connect as a class. Reinforce the
concepts by inviting students to explain their
understanding of the relationship between
linear, square, and cubic units. Ensure the
following points are covered:
• Lengths are one-dimensional, so linear units
are appropriate for measuring lengths.
• Two-dimensional units such as squares are
needed to cover a surface, so square units
are appropriate for measuring area.
• Three-dimensional units such as cubes
are needed to fill space, so cubic units are
appropriate for measuring volume.
Unit 9 • Lesson 4 • Student page 335
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3. a) Each dimension is less than 1 m, so the volume will be
less than 1 m3.
b) The volume is equal to 1 m3. I found the volume by
multiplying the length, the width, and the height.
c) Multiplying the area of the base by the height gives a
volume of 1 000 000 cm3, which is equivalent to 1 m3.
d) The volume is 1 m3. The answer is the same as in part c
because doubling the area of the base and halving the
height does not change the volume.
4. The volume is 1 000 000 cm3. The length is 200 cm, so the
area of the base is 1 000 000 200, or 5000 cm. The width
and height are any two whole numbers whose product is 5000.
The dimensions of the container could be:
200 cm by 1 cm by 5000 cm, 200 cm by 2 cm by 2500 cm,
200 cm by 4 cm by 1250 cm, 200 cm by 5 cm by 1000 cm,
200 cm by 10 cm by 500 cm, 200 cm by 20 cm by 250 cm,
200 cm by 25 cm by 200 cm, 200 cm by 40 cm by 125 cm,
200 cm by 50 cm by 100 cm
5. a) The dimensions of 1 sheet of letter-size photocopy paper
are about 22 cm by 28 cm.
b) The thickness of a package of 500 sheets is about 5 cm.
c) The volume of a package of paper is about 3080 cm3.
I know that 1 000 000 cm3 1 m3. The number of
packages in 1 m3 is 1 000 000 3080, or about 325.
The volume of 325 packages is about 1 m3. There are
500 sheets of paper in a package. So, there are about
325 500, or 162 500 sheets of photocopy paper
in 1 m3.
Have students name items in the classroom that
should be measured using linear units, square
units, and cubic units. Record the names of the
items in a table like the one below.
Linear Units
Square Units
Cubic Units
Practice
In question 5, students require letter-size
photocopy paper. They need single sheets and
packages of 500 sheets. Have calculators
available for all questions.
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Unit 9 • Lesson 4 • Student page 336
1 000 000 cm3
Assessment Focus: Question 5
Students will need a calculator to do this
question. Encourage students to round the
dimensions of the photocopy paper to the
nearest centimetre. Students should recognize
that the thickness of a package of paper is the
same as its height. Students can calculate the
volume of the package by multiplying the length,
the width, and the height. If students have
difficulty determining the number of packages
in 1 m3, remind them that 1 000 000 cm3 equals
1 m3. Some students may forget to multiply the
number of packages in 1 m3 by 500 to find the
approximate number of sheets of paper in 1 m3.
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6. The volume of air in the bathroom is 16.65 m3. The fan
should change that amount of air 10 times in an hour,
or every 6 min. So, every minute, the fan should change
16.65 6, or 2.775 m3 of air. Therefore, the Leungs
should buy the 3.1 m3 fan for their bathroom.
7. There are 1 million centimetre cubes in a cubic metre. If I
placed 1 cube every second, it would take me 1 000 000 s.
There are 60 s in a minute, 60 min in an hour, and 24 h
in a day. To convert 1 000 000 s into days, divide by
60 twice, then by 24. It would take about 12 days to
construct a cubic metre.
REFLECT: Linear units, such as centimetres or metres, measure
distances with one dimension. Square units measure area.
Since I multiply two linear dimensions to get an area, the
units are square centimetres or square metres. Cubic units
measure volume. Since I multiply three linear dimensions to
get a volume, the units are cubic centimetres or cubic metres.
0.731
0.0283
0.1954
0.038 75
Numbers Every Day
Shift the digits 2 places to the right when dividing by 100 and
3 places to the right when dividing by 1000.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand that the volumes
of large objects are measured in
cubic metres.
Extra Support: Students can use Step-by-Step 4 (Master 9.13)
to complete question 5.
Accuracy of procedures
✔ Students can choose from linear,
square, and cubic units to
measure items.
✔ Students can estimate and calculate
volume using cubic metres.
Extra Practice: Have students list 9 items and the attribute
being measured for each item. Three items should require linear
units, 3 square units, and 3 cubic units.
Students can complete Extra Practice 2 (Master 9.19).
Extension: Challenge students to explain how they could
visualize a cubic kilometre.
Recording and Reporting
Master 9.2 Ongoing Observations:
Measurement
Unit 9 • Lesson 4 • Student page 337
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