Standard: 3.OA.B.5
Apply properties of operations as strategies to multiply and divide.*
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.)
Task Exemplar 1 (Commutative Property) MP 3, 7,8:
Marissa is arranging the chairs for program. She has made 8 rows of
chairs. Each row has 6 chairs. Marissa wonders how many chairs she has
placed so far.
She knows that she can multiply the number of rows times the number
of chairs in each row to find the total number of chairs. She tried to
multiply 8 x 6 = ___, but she hasn’t learned that combination yet.
Draw an array to represent the arrangement
of chairs. What is another multiplication
equation that Marissa could use to find out how many chairs there are?
Explain your thinking.
Task Exemplar 2 (Associative Property) MP 3, 7,8:
Risa and Frank were packing cans of soup in food baskets to take to the
community center. Risa packed 2 baskets and Frank packed 3 baskets.
Risa put 3 soup cans in each bag. Then, she put 4 bags into each basket.
Frank put 4 cans of soup in each bag and put 2 bags in each basket.
When Risa and Frank counted the total number of cans they had packed,
they found that there was the same number of cans in each of the
baskets.
Part A:
Construct a model to show what was in each basket.
Part B:
Write an equation to represent each set of baskets and explain your
thinking.
Part C:
Risa wrote the following equation to represent both sets of baskets.
2 x (4 x 3) = (2 x 4) x 3
Does this equation represent the baskets you drew? Explain.
Task Exemplar 3 (Distributive Property) MP 3, 7, & 8:
Kyshawn was working on his homework when he came to a multiplication
problem that he hasn’t learned yet. The problem was 6 x 5 = ______.
Kyshawn has learned some multiplication facts. He knows that
2 x 5 = 10 and 4 x 5 = 20.
How can Kyshawn use what he knows to find the solution to his homework
problem?
Use drawings, words, or equations to explain.
Task Exemplar 4 MP 1, MP 2, MP 4, MP 6, MP 7
Prove It!
1. Use your tiles to build a 7x6 array.
2. Decompose the array into two smaller rectangles.
3. Decompose the 7x6 array into two smaller rectangles in
two MORE different ways.
4. For each way that you decomposed the array, write an
equation that matches your strategy.
5. Work with a partner to evaluate each other’s arrays.
Critique their strategy and their reasoning.
6. Write a sentence comparing one of your strategies and
your partner’s strategies for decomposing arrays.