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: Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for products of 4 and 6 as they relate to products of 5. These understandings help students develop fluency and will be helpful later when students consider solutions for and solve two-step word problems.
When students use products of 5 to determine products of 4 by thinking of them as one fewer group or one fewer object in each group, or work from products of 5 to determine products of 6 by thinking of them as one more group or one more object in each group, they look for and make use of structure (MP7).
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(5 \times 7\)
\(4 \times 7\)
\(6 \times 7\)
\(4 \times 8\)
Student Response
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Activity Synthesis
“How does knowing
\(5\times7\)
help you find some of the other products?” (I can remove a group of 7 to find
\(4\times7\)
or add a group of 7 to find
\(6\times7\)
.)
Consider asking:
“Who can restate _____’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone approach the problem in a different way?”
“Does anyone want to add on to _____’s strategy?”


aligns: no