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Chapter 3
You will need
• number lines
• a ruler
GOAL
Identify multiples to solve problems.
The comet Kojima takes about seven years to go around
the Sun once. Kojima was seen from Earth in 2000.
Which years between 2000 and
Canada’s 200th birthday will Kojima
likely be seen from Earth?
Oleh’s List
I can solve the problem by identifying multiples of 7.
I’ll keep multiplying 7 by each counting number
(1, 2, 3, and so on) to create a list of multiples.
multiple
A number that is
the product of two
whole-number
factors
For example, 8 is
a multiple of 4
because 4 ⫻ 2 ⫽ 8.
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Multiples of 7
Multiply 7 by
Product
1
7
2
14
3
I’ll add each multiple to 2000 to show the years that
Kojima will likely be seen from Earth.
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Léa’s Number Line
The first two multiples of 7 are 7 and 14.
I’ll keep adding 7s, starting at 2000 on the number line.
I’ll write the years on the number line to show when
Kojima will likely be seen from Earth.
+7
2000
+7
2007
2014
A. Use Oleh’s method to identify the next multiple of 7
after 14.
B. Use Léa’s method to identify the next year after 2014
that Kojima will likely be seen from Earth.
C. Which years between 2000 and Canada’s 200th
birthday will Kojima likely be seen from Earth? Show
your work.
Communication Tip
A list of multiples of
a whole number
begins with the
whole number and
ends with three dots
to show that the list
goes on forever.
For example, 2, 4,
6, 8, … are multiples
of 2.
0 is also a multiple
of 2, but it is often
left out of lists of
multiples.
NEL
D. How do you know that 7 must be a factor of
each multiple of 7?
E. Why is it possible to list all the factors but not
all the multiples of a whole number?
Checking
1. The comet Mueller 4 takes about nine years to go
around the Sun once. It was seen from Earth in 2001.
a) List the first 10 multiples of 9.
b) Which years before 2067 will Mueller 4 likely be
seen from Earth? Use your list of multiples from
part a).
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Practising
2. List the first five multiples of each number. Explain
what you did to make one of your lists.
a) 2
d) 15
b) 3
e) 25
c) 12
f) 50
3. What is the same about a list of multiples of 3 and 9?
What is different?
4. a) List the first five multiples of 99.
b) What patterns do you notice in your list?
c) Use the patterns to list the next five multiples.
moon cakes
5. Pauline expects between 70 and 80 people at the
Chinese Mid-Autumn Moon Festival party.
She wants to buy picnic plates and picnic glasses.
a) Plates come in packages of 8. How many plates are
in 1 to 10 packages?
b) How many packages of plates does Pauline need
to buy? Explain your thinking.
c) Glasses come in packages of 12. How many glasses
are in 1 to 10 packages?
d) How many packages of glasses does Pauline need
to buy? Explain your thinking.
6. Decide whether each statement is true or false.
Explain how you know.
a) 60 is a multiple of 2.
c) 4 is a factor of 84.
b) 3 is a factor of 39.
d) 60 is a multiple of 7.
7. Reena was one of 36 girls in a dance competition.
Every third girl wore a coin necklace. Every fourth girl
wore a flower in her hair. How many girls wore both a
coin necklace and a flower?
8. a) What do you notice about the multiples of 1?
b) What do you notice about the multiples of 0?
9. Madeline said, “If numbers are 9 apart, they are
multiples of 9.” Do you agree? Explain.
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