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Chapter 6
You will need
• counters (2 colours)
ratio
A comparison of
numbers or
quantities that are
measured in the
same units; the ratio
that compares a to b
is read “a to b” and
is written a:b.
For example,
consider the dogs
and cats shown
below. The part-topart ratio of dogs
to cats is 3:2.
(The unit is animals.)
This ratio compares
the numbers in two
different parts of
the whole.
GOAL
Identify and model ratios to describe situations.
One of the Inuit events in the Arctic Winter Games is the
Airplane. The person who is the “airplane” must keep his
body totally straight while the other three team members
“fly” him around the room. The team that flies its
“airplane” the farthest wins.
You can use a ratio to compare the number of “airplanes”
to the number of other team members.
The part-to-part ratio of “airplanes” to other team
members is 1:3, since there are three team members
holding up each “airplane.”
What other ratios can you use to
describe a team in the Airplane
event?
The part-to-part
ratio of cats to dogs
is 2:3.
The part-to-whole
ratio of dogs to all
the animals is 3:5.
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Daniel’s Comparison
I can use the part-to-whole ratio 1:4 to describe a team.
I’ll model this ratio using 1 blue counter to represent
the “airplane” and 3 red counters to represent the
other team members.
1
I can use the fraction 4 to describe the part of a team
that is the “airplane.”
Communication Tip
• The two numbers
in a ratio are
called terms.
Neither term can
be 0.
• Before you write
the numbers in a
ratio, you may
want to write in
words what the
numbers describe.
For example, if
you are describing
a group with
one peach and
six apples, you
could write
“peaches : apples
is 1:6.”
A. The ratios 1:3 and 3:4 can also be used to describe
the members of a team in the Airplane event.
What do the terms in these ratios represent?
B. Is 1:3 in Part A a part-to-whole ratio or a part-to-part
ratio? Explain.
C. Is 3:4 in Part A a part-to-whole ratio or a part-to-part
ratio? Explain.
D. What other ratios can be used to describe a team in
the Airplane event?
E. Why can you use a fraction to represent a
part-to-whole ratio?
F. Suppose a team had four people holding up
the “airplane.” Why could you use the ratios
1 :4, 4:1, and 1:5 to describe the members of
the team?
Checking
1. At the start of a hockey game, there are six players on
the ice: three forwards, two defense, and one goalie.
Write four ratios to describe the players on the ice.
Write both part-to-part and part-to-whole ratios, and
identify them.
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2. Look at the design on the right.
a) Write two part-to-part ratios.
b) Write two part-to-whole ratios.
Practising
3. Write at least three ratios for each model. Identify the
ratios as part-to-part or part-to-whole.
a)
b)
4. Use counters to model each part-to-part ratio.
Sketch each model.
a) 4 to 3
b) 1:7
c) 3:5
d) 6 to 4
5. a) Choose one ratio from Question 4. What other
part-to-part ratios and part-to-whole ratios does
your model show?
b) What fractions can you use to describe the
part-to-whole ratios for your model?
6. Tara is mixing lemonade from concentrate. She adds
four cans of water for each can of concentrate.
a) Write a ratio to compare the amount of
concentrate to the amount of water.
b) Model the ratio using counters. Sketch your model.
c) If Tara uses one can of concentrate, how many
cans of lemonade will the container need to hold?
d) What fraction describes the part of the lemonade
that is water?
e) What other ratios can be used to describe the
lemonade?
7. Irina has a set of nesting dolls.
a) Write three ratios to describe the nesting dolls.
Explain what each ratio compares.
b) Describe another doll that you could add to the set
so that the ratio 4:2 would describe the dolls.
Model this ratio using counters. Sketch your model.
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8. a) List all the blue-to-red ratios you could model
using five counters from the counters at the left.
Sketch each model.
b) Name each model using another ratio. Write the
ratio as a fraction.
9. a) Use two colours of counters. Model the fraction 68.
Sketch your model.
b) List three ratios that your counters show. Describe
what is being compared in each ratio.
10. What ratios can you use to compare these two lengths?
5 cm
5 cm
4 cm
10 cm
11. a) What ratio can you use to compare the length of
the rectangle at the left to its width?
b) What ratios can you use to compare the length to
the perimeter and the width to the perimeter?
12. The ratio of the length of one side of a shape to the
perimeter of the shape is 1: 6. Could the shape be a
rectangle? Explain your thinking.
13. Different shades of blue paint are created by mixing
white paint with blue paint in different ratios.
Which of these ratios makes the lighter shade?
Explain your thinking.
• blue : white ⫽ 3:1
• blue: white ⫽ 1:3
14. Describe five ratios you can see in your classroom.
Write them in the form ■ : ■.
15. How are ratios like fractions? How are they different?
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