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 How Many Do You See is for students to use grouping strategies to describe the images they see.
When students use grouping to find the total in a multiple of tens, they look for and make use of structure (MP7).
Launch
Groups of 2
“How many do you see? How do you see them?”
Flash the image.
30 seconds: quiet think time
Activity
Display the image.
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Facing
How many do you see? How do you see them?
[IMG]
Student Response
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Activity Synthesis
“What expressions could we record for the different ways that students saw the tens?” (
\(6 \times 10\)
, because some students saw 6 groups of 10.
\(3 \times (10 \times 2)\)
, because some students saw 2 rows of 10, then multiplied by 3.
\((3 \times 10) \times 2\)
, because some students multiplied 3 times 10 for each column, then multiplied by 2.)
Consider asking:
“Who can restate in different words the way _____ saw the tens?”
“Did anyone see the tens the same way but would explain it differently?”
“Does anyone want to add an observation to the way _____ saw the tens?”


aligns: no