Name: __________________
Math 6
Unit 1
Lesson 3
Multiples of Whole Numbers
Helping People
Alyssa and Cameron are boxing rolled oats to send to
hungry families in Africa. They place six canisters of
rolled oats in each box for shipping.
Top View of Box
rolled
oats
rolled
oats
rolled
oats
rolled
oats
rolled
oats
rolled
oats
They pack boxes for five hours on a Saturday morning. What are the possible
numbers of canisters that are ready to ship out when they are done?
Since each box holds six canisters the possible values are multiples of six.
The multiples of six are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120…
Knowing the multiples of six can help you determine how many canisters of
rolled oats have gone out.
Math 6
3-1
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
After working for one hour packing boxes, Alyssa and Cameron have packed 20
boxes of rolled oats. How many canisters of rolled oats have they prepared?
The 20 boxes contain 6 canisters each. 20 x 6 = 120 canisters of rolled oats
Since the answer, 120, is on our list of multiples of 6 this is a reasonable answer
for the number of canisters packed.
Reflection
How many canisters of rolled oats will Alyssa and
Cameron have prepared by the end of 5 hours if they
pack the same number each hour? The answer to this
question would be a multiple of what number?
3-2
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Objectives for this Lesson
In this lesson you will explore the following concepts:
• How to identify multiples for a given number
• Explain the strategy for finding the multiples of a given number
• Solve a given problem involving multiples of a number
Multiples
A multiple is a product of a given number and another number. If you want to
know the multiples of ten, you would multiply 10 by every number, beginning
with the number 1:
10
x1
10
10
x2
20
10
x3
30
10
x4
40
10
x5
50
10
x6
60
The first six multiples of 10 are 10, 20, 30, 40, 50, 60.
Example 1
What are the first eight multiples of 2?
You may know the multiples of 2 from having memorized them in earlier grades.
First eight multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16
If you do not know your multiplication tables, this is a good time to review your multiplication facts from 1 x 1 to 9 x 9.
Math 6
3-3
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Patterns in a Multiplication Table
It is easy to get to know the multiples of the numbers one to ten when you use
a multiplication table. You can find the multiples of a number using the rows and
columns of the table.
The first twelve multiples of 8 are highlighted in the multiplication table:
1
2
3
4
2
4
6
8
3
6
9
4
8
5
6
7
8
9
10 11 12
10 12 14 16 18 20 22 24
12 15 18 21 24 27 30 33 36
12 16 20 24 28 32 36 40 44 48
5
10 15 20 25 30 35 40 45 50 55 60
6
12 18 24 30 36 42 48 54 60 66 72
7
14 21 28 35 42 49 56 63 70 77 84
8
16 24 32 40 48 56 64 72 80 88 96
9
18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132
12 24 36 48 60 72 84 96 108 120 132 144
This helps you identify the first twelve multiples of any number from 1 to 12.
What are the first twelve multiples of 7?
3-4
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Using Arrays to Find Multiples
You can use multiplication arrays to decide if a number is a multiple of a larger
number. An array is a picture model to show the relationship between two
multiples and their product.
3 rows of 5: 3 x 5 = 15
This array shows that 15 is a multiple of 3 and a multiple of 5. You can add a
row of 5 to make a new array:
4 rows of 5: 4 x 5 = 20
This array shows that 20 is a multiple of 4 and a multiple of 5.
Math 6
3-5
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Let’s Explore
Multiples in Arrays
Materials: Use the graph paper below to make your counters.
1. Make an array for 3 x 4 using Counters.
Use your Counters to create the array for each multiple of 4 up to the twelfth multiple of 4.
Did you add rows or columns to your original array?
__________________
How many Counters did you add each time? _______________
Complete this statement: To get the 20th multiple of 4 I would use ___ rows of
___ Counters.
. Make an array for 2 x 6 using Counters.
ow you would change the array to create an array for a product
of 36? Draw a picture of your new array.
. Reflect: How many arrays can be made for the multiples of 8, out of
56 Counters? __________________________
A square number is a number that is formed by an array that makes a square.
For example:
4 rows of 4: 4 x 4 = 16
The square number represented by this array is 16.
3-6
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
. What is a square number that would have a row of 7 Counters?
_______________
5. The following array does not represent a square number. Add Counters to the array to create a square number. What number did you create? _______________
6. What is the next square number in this pattern? 4, 9, 16, 25, 36, ___
Math 6
3-7
Math 6
Unit 1
3-8
Lesson 3: Multiples of Whole Numbers
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Let’s Practice
For 1 – 6: List the multiples described.
1.
the first six multiples of 5: _________________________________
2.
the first eight multiples of 9: _______________________________
3.
the first ten multiples of 6: _________________________________
4.
the first nine multiples of 4: _______________________________
5.
the first twelve multiples of 8: _____________________________
_______________________________________________________
6.
Is 64 a square number? Explain how you know.
Math 6
3-9
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
For 7 – 9: What number am I?
1
2
3
4
2
4
6
8
3
6
9
4
8
5
6
7
8
9
10 11 12
10 12 14 16 18 20 22 24
12 15 18 21 24 27 30 33 36
12 16 20 24 28 32 36 40 44 48
5
10 15 20 25 30 35 40 45 50 55 60
6
12 18 24 30 36 42 48 54 60 66 72
7
14 21 28 35 42 49 56 63 70 77 84
8
16 24 32 40 48 56 64 72 80 88 96
9
18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132
12 24 36 48 60 72 84 96 108 120 132 144
7.
One of my multiples is 24. I am a multiple of six numbers in the 12 x 12 multiplication chart.
8.
When you add my digits you will get 9. If you reverse my digits I am
still a multiple of the same number. I am contained in the 12 x 12 multiplication chart.
9.
I am an odd two-digit number. The sum of my digits is a two-digit number. I am a square number.
3-10
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
For 10 – 14: Is the statement True or False? Give an example to support
your answer.
10. Any multiple of 5 is also a multiple of 2.
11. Any multiple of 10 is also a multiple of 5.
12. Any multiple of 6 is also a multiple of 3.
13. 24 is a multiple of 5.
14. All square numbers are odd.
15. Write two true statements of the form: “Any multiple of _____ is also a multiple of _____.”
16. Cameron says that the product of 9 and any number is twice the product of 3 and that number. Give an example to show that his statement is false.
Math 6
3-11
Math 6
Unit 1
Lesson 3: Multiples of Whole Numbers
Mixed
Review
For 1 – 5: Complete the pattern.
1.
4, 8, 12, ____, 20, 24
2.
3.5, 4, 4.5, 5, _____, 6, 6.5
3.
12, 15, 19, 24, 30, 37, _____
4.
2, 8, 32, _____, 512, 2 048
5.
1, 2, 4, 8, 16, 32, ____, 128
3-12