Properties of Operations: Commutative
Property, Associative Property,
Distributive Property
Apply Properties of operations as strategies to
multiply and divide.
3.OA.5
Day 1
Which shows a picture of 3 x 5 ?
Commutative Property
Day 1
3x6
3 groups of 6
6x3
6 groups of 3
Explain how these two multiplication problems give the
same product.
Commutative Property
Day 1
• How can you think about multiplying both expressions?
• Does it matter?
• 4x6
or
6x4
Commutative Property
Day 2
Multiply the following numbers mentally.
8 and 4
Commutative Property
Day 2
• The teacher passed out boxes of markers to 9 students. Each
box contained 8 markers.
• How many markers are there in total?
• How did you think about the problem?
• Write or tell an expression.
Commutative Property
Day 3
We can group numbers when multiplying three factors, we
can group the factors in different ways.
For example, which two numbers would you multiply first
and why.
5x3x2
Associative Property
• Day 3
• Which two numbers would you multiply first and why?
• 3x6x4
• 4x2x9
Associative Property
Day 3
• True or False
• 2x4x6=6x2x4
• How do you know?
Associative Property
Day 4
We can break numbers up into smaller numbers in order to make
multiplication problems we already know from memory.
For example, I always forget what 7 x 4 is.
• I can split up the 4 into 2 and 2
• I know 7 x 2 = 14
•
•
•
•
7 x 2 = 14
7 x 2 = 14
14 + 14 = 28
So 7 x 4 = 28
Distributive Property
• Day 4
• 7x6=
• I will split up the 7 into 5 and 2
• 5 x 6 = 30
• 2 x 6 = 12
• 7 x 6 = 42
• Can someone break apart 7 x 6 differently? Share with a partner.
• Share with the class and we will record the different ways.
Distributive Property
Day 4
• 6 x 8 How would you break apart these numbers?
• Let’s record all the different ways
Distributive Property
Day 5
7x7
5x7
2x7
Distributive Property
Day 5 How would you split this up to multiply?
Distributive Property
Day 6
True or False
6 x 9 is the same as (6 x 5) + (6 x 4)
Distributive Property
Day 6
Choose one to break apart and be able to explain how you
broke it apart and why.
8x4
9x6
7x4
Distributive Property