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 activity is for students to see how other students solved one of the problems that involves a factor of a teen number. While students look at each other’s work, they will leave sticky notes describing why they think the answer does or does not make sense (MP3). The synthesis will look specifically at examples of how students used the area diagram to represent the problem.
MLR8 Discussion Supports.
Synthesis: As students share their observations about the selected posters, annotate the poster to illustrate connections. For example, circle the factors and the product and write “factors” and “product” respectively.
Advances: Listening, Representing
Required Materials
Materials to Gather
Sticky notes
Launch
Groups of 2
“Before you begin the gallery walk, what are some representations you expect to see as you look at other students’ work?” (I expect to see rectangles because some of the problems were about the area of rectangles. Base-ten blocks because we were multiplying teen numbers.)
Share responses.
Give students sticky notes.
Activity
“As you visit the posters with your partner, discuss what is the same and what is different about the thinking shown on each poster. Also, leave a sticky note describing why you think the solution does or does not make sense.”
8–10 minutes: gallery walk
Monitor for different uses of the area diagram to highlight, specifically:
a fully gridded area diagram with no labels and no decomposition
a gridded area diagram that was gridded, but also decomposed into parts or labeled along the sides or in the parts of the rectangle
a partitioned rectangle that was drawn with no grid, but labeled with side lengths or the area of the parts of the rectangle
Student Facing
As you visit the posters with your partner, discuss what is the same and what is different about the thinking shown on each poster.
Student Response
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Activity Synthesis
Select 2–3 posters that used a diagram to represent the problem. Discuss them in the order shown above.
For each poster, ask:
“How are the factors shown in the diagram?”
“How is the product shown in the diagram?”
“How could we represent this strategy with expressions?”
If students don’t use an ungridded diagram, display one that represents the problems and ask the same questions.
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aligns: yes