1. Commutative Property
Lesson 3.1:

2. Commutative Property of Multiplication
Write two multiplication and two division sentences for this array.

3. Commutative Property of Multiplication
Write two multiplication and two division sentences for this array.

4. Commutative Property of Multiplication
Write two multiplication and two division sentences for this array.

5. Commutative Property of Multiplication
Write two multiplication and two division sentences for this array.

6. Application Problem
Geri brings 3 water jugs to her soccer game to share with teammates. Each jug contains 6 liters of water. How many liters of water does Geri bring?
Draw a tape diagram and write a number sentence to solve the problem.

7. Problem 1
Which tape diagram represents the Application Problem? How do you know?

8. Problem 1
Draw both tape diagrams in your notebook. Write a multiplication sentence for each.
How are the multiplication sentences related?
They use the same numbers.
Both have a product of 18. They use the same factors, but in a different order. The product is the same.

9. Problem 1
This is an example of the commutative property that we studied in Unit1. What does this property tell us about the product and its factors?
Even if the order of the factors changes, the product stays the same!

10. Problem 1 Earlier in the year we learned our threes.
If we know 3 × 6, what other fact do we know?
6 × 3
What is the product of both 3 × 6 and 6 × 3?
To show that 3 × 6 and 6 × 3 equal the same amount, we can write 3 × 6 = 6 × 3.
Using the commutative property as a strategy, we know many more facts than just the ones we’ve practiced!

11. Problem 1 Draw a tape diagram to show 2 × 7.
What is the product of 2 x 7?
Draw a tape diagram to show 7 × 2.
What is the product of 7 x 2?
How does knowing 2 x 7 help you know 7 x 2?
2 x 7 = 7 x 2
This is an example of the Commutative Property of Multiplication.

12. Problem 1 Draw a tape diagram to show 5 eights.
What is the product of 5 eights?
Draw a tape diagram to show 8 fives.
What is the product of 8 fives?
How does knowing 5 x 8 help you know 8 x 5?
5 x 8 = 8 x 5
This is an example of the Commutative Property of Multiplication.

13. Problem 2
Multiplication Chart
Row 3

14. Problem 2
Multiplication Chart

15. Problem 2
We know the shaded facts.

16. Practice
Complete the chart. Each bag contains 7 apples.

17. Practice
Use the array to write two different multiplication sentences.

18. Practice Complete the equations. a. 2 sevens = ________ twos
b. 3 ________ = 6 threes
c. 10 eights = 8________
= ________
d. 4 × _______ = 6 × 4

19. Practice Complete the equations. e. 8 × 5 = ________ × 8 = ________
f. _______ × 7 = 7 ×_______
= ________
g. 3 × 9 = 10 threes – _______ three
h. 10 fours – 1 four = _______ × 4

20. Practice Complete the equations. i. 8 × 4 = 5 fours + _______ fours
= ________
j. _______fives + 1 five = 6 × 5
k. 5 threes + 2 threes = _____× _____
l. ______ twos + ______ twos = 10 twos
= ______