1. Module 1 Lessons 7 & 8 Demonstrate the COMMUTIVITY of multiplication,
and practice related facts
by skip-counting objects in array models.

2. Skip Count Skip Count By 2s To 20 … Skip Count by 3s to 30 …
Skip Count by 3s to 30 …
Skip Count by 4s to 40 …

3. Divide Equal Groups  4 + 4 = 8 8 ÷ 2 = 4 8 ÷ 4 = 2
Write an addition sentence for these arrays.
4 + 4 = 8
Write a division sentence for 8 divided into two equal groups.
8 ÷ 2 = 4
Write a division sentence for 8 divided into four equal groups.
8 ÷ 4 = 2

4. Divide Equal Groups 4 + 4 + 4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 
Write an addition sentence for these arrays.
= 12
Write a division sentence for 12 divided into three equal groups.
12 ÷ 3 = 4
Write a division sentence for 12 divided into four equal groups.
12 ÷ 4 = 3

5. As I uncover groups of two, say the multiplication sentence.
Multiply with twos
1 x 2 = 2
As I uncover groups of two, say the multiplication sentence. c
2 x 2 = 4 c
3 x 2 = 6 c
4 x 2 = 8 c
5 x 2 = 10 c
6 x 2 = 12 c
7 x 2 = 14 c
8 x 2 = 16 c
9x 2 = 18 c
10x 2 = 20

6. Application Problem
Anna picks 24 flowers. She makes equal bundles of flowers and gives 1 bundle each to her 7 friends. She keeps a bundle for herself, too. How many flowers does Anna put in each bundle?

7. Rotate Arrays 90 degrees 2 4 6 8 4 x 2 = 8
Draw the array at the left on your white board.
Then skip count by 2s to find the total. 2 4
Write a multiplication sentence where the first factor is the number of rows. 6 8
4 x 2 = 8

8. Rotate Arrays 90 degrees 4 8 2 x 4 = 8
Now, take your board and turn it 90 degrees. 4
Let’s skip count the rows again, and write a new multiplication sentence where the first factor is the number of rows. 8
2 x 4 = 8

9. The factors are the same, but they switched places!
Commutative Property
Talk to your partner: What do you notice about the factors in these multiplication sentences?
The factors are the same, but they switched places!

10. I like to call this the MOVE IT MOVE IT property!
Commutative Property
The COMMUTATIVE PROPERTY is the Law of Math that says you can swap numbers around and still get the same answer when you add or multiply.
I like to call this the MOVE IT MOVE IT property!
Let’s practice!

11. Interpreting Rows & Columns
On your board, draw an array that shows 5 rows & 3 columns.
Write and equation to match your array. Don’t solve it yet!
5 x 3 = _____

12. Interpreting Rows & Columns
Now, WITHOUT erasing, change your array to show 3 x 5.
Write a new equation to match your array. Don’t solve it yet!
3 x 5 = _____

13. Interpreting Rows & Columns
Explain the difference between these two problems to your partner.
3 x 5
We used commutative property to switch the factors.
Did the total change?
NO!
5 x 3

14. Interpreting Rows & Columns
Let’s skip count to solve the problems. 5 10 15 3 6 9 12 15
3 x 5
5 x 3 = 15
3 x 5 = 15
5 x 3 = 3 x 5 = 15
5 x 3

15. Commutative Multiplying4
4 x 2 = 2 x ______

16. Commutative Multiplying3
3 x 2 = 2 x ______

17. Commutative Multiplying5
5 x 9 = 9 x ______

18. Check Yourself!
Children in Mrs. Richardson’s class sit in 2 rows of 9 on the carpet for story time. Erin says, “We make 2 equal groups.” Vincent says, “We make 9 equal groups.” Who is correct? Explain how you know using models, numbers, and words.
Erin and Vincent are both correct BECAUSE the answer depends on how you look at the array.
If Erin’s array is turned sideways, it looks like Vincent’s. They’re the same!

19. Problem Sets