standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Task
Part I.
a. How many circles are there in all?  Write down a number sentence that shows how you thought about it.
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b. Alonso said he figured out how many shaded circles there were first and then how many unshaded circles there were second.  Once he knew how many of each, he added them together to find the total.  Write a number sentence Alonso could have used that shows his reasoning.
c. Jennifer said, “I just saw 3 rows of 8 circles.”  Write a number sentence that Jennifer could have used that shows her reasoning.
​Part II.
a. The area model below shows the floor plan for a storage closet.  The storage closet will have a tiled floor with grey tiles on the left and white tiles on the right.  How many tiles are needed for the storage closet in all?  Write down a number sentence that shows how you thought about it.
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b. Think back to how Alonso figured out how many circles there were in Part I.  Use Alonso’s same strategy here to find out how many tiles are needed.  Write a number sentence with Alonso’s reasoning.
c. Think back to how Jennifer figured out how many circles there were in Part I.  Use Jennifer’s same strategy here to find out how many tiles are needed.  Write a number sentence with Jennifer's reasoning.


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