1. Multiplication Properties
Commutative, Associative, Identity, Distributive, and Zero

2. One classroom has 3 rows of 6 desks. Another has 6 rows of 3 desks
One classroom has 3 rows of 6 desks. Another has 6 rows of 3 desks. Do both classrooms have the same number of desks?
How do you know?

3. Commutative Property 2 x 5 = 5 x 2
Do 2 groups of 5 marbles equal 5 groups of 2 beach balls?
2 x 5 = 5 x 2

4. You can change the order of the numbers
The answer stays the same.
The numbers commute, they go from one place to another.
2 x 5 = 5 x 2

5. Associative Property You can change the grouping of the factors.
The Product stays the same.
(2 x 5) x 3 = 2 x (5 x 3)
10 x 3 = 2 x 15
30 = 30

6. Identity Property Any number times 1 equals the original number.
5 x 1 = 5

7. Zero Property When you multiply any number by 0, the product is 0.
No groups, nothing there
12 x 0 = 0

8. Distributive Property
Multiplying each term inside the parentheses with the term outside of the parentheses.
You distribute or give a digit to the others.

9. Name that property 537 x 1 = 537 5 x (40 x 9) = (5 x 40) x 9
How do you know?
5 x (40 x 9) = (5 x 40) x 9
What changed?
24 x 32 = 32 x 24
400 x 0 = 0
Identity- multiplied by 1, answer is the same as the original factor
Associative- the groups changed
Commutative- the order changed
Zero Property- mutiplied by zero, the answer is zero

10. Name that property 73 x 14 = 14 x 73 1 x 111 = 111 0 x 1,247 = 0
How do you know?
1 x 111 = 111
0 x 1,247 = 0
8 x (4 x 3) = (8 x 4) x 3
Commutative- the order changed but the numbers and answer are the same
Identity- multiplied by 1, answer is the same as the factor
zero- multiplied by zero, answer is 0
associative- groups changed, not the order

11. Name that Property (9 x 3) x 5 = 9 x (3 x 5) 1 x 90 = 90 x 1
Why?
1 x 90 = 90 x 1
76 x 1 = 76
0 x 563 = 0
associative- groups changed
Identity- multiplied by 1, answer is the factor
identity- multiplied by 1, answer is the factor
zero- multiplied by zero, answer is zero

12. What’s missing? 1,037 x = 1,037 (635 x 47 ) x = 0 75 x = 42 x 75
Which property is it?
How do you know?
(635 x 47 ) x = 0
75 x = 42 x 75
1- identity property, the answer and the factor are the same
0- zero, the product is 0
42- commutative, the group is the same, the order is different

13. What’s Missing 5 x (20 x 9) = (5 x 20) x 8 x 5 = x 8
Which property is it?
How do you know?
8 x 5 = x 8
(9 x 6) x 4= 4 x (9 x )
Which properties is it?
9-associative, order is the same, groups change
5- commutative, group stays, order changes
6- commutative and associative, the order and groups change

14. What is the missing number in the number sentence?
Which property does this show? Why?
(6 x 3) x 8 = 6 x ( x 8) 3
associative because the groups change, not the order, there is no 1 or 0

15. Write a number sentence and Explain why you chose that property.
Two bags with 3 marbles in each bag is the same amount as 3 bags with 2 marbles in each bag. Which property of multiplication does this represent?
Write a number sentence and Explain why you chose that property.
commutative; the order is reversed
2 x 3 = 3 x 2

16. Write a number sentence and explain your property choice.
Two sets of 3 bags with 5 marbles in each bag is the same as 3 sets of 2 bags with 5 marbles in each bag. Which property of multiplication does this represent?
Write a number sentence and explain your property choice.
3 (5 x 2) = 3 x (5 x 2)
associative; the groups change 2 sets of 3, 3 sets of 2 but the number of marbles in side stays the same