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: Problem 1
Ms. Roll is making a mural using square tiles. She has 96 tiles and wants the mural to be 8 tiles tall.
a.   How many tiles long will Ms. Roll’s mural be?
b.   Write one or more equations to show how you solved this problem.
Problem 2
Ayana starts to draw an area model to solve
$$79\div3$$
, which is shown below.
[IMG]
a.   Why did Ayana make a rectangle with an area of 60 and a length of 20?
b.   How much of the dividend still needs to be divided by 3? How do you know?
c.   Complete the area model by extending the one Ayana started above.
d.   Write the quotient and remainder for
$$79\div3$$
. Where are those values represented in the area model above?
e.   Use multiplication to check your answer.
Problem 3
a.   Solve each of the following word problems. Show or explain your work.
The price of a video game is $52. A video game costs 2 times as much as a jigsaw puzzle. What is the price of the jigsaw puzzle?
Ms. Needham squeezed 85 ounces of orange juice. She wants to pour it into glasses that hold 6 ounces each. How many glasses will Ms. Needham need to hold all the juice?
b.   Did you use an area model to represent either or both problems above? If not, could you have? Why or why not?


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