standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Narrative
This warm-up prompts students to compare four representations. The reasoning here prepares students to connect the previous multiplication work to the division work of this lesson. It gives students an opportunity to use precise terms such as “factors,” “product,” and “quotient” in making comparisons (MP6). During the synthesis, ask students to explain the meaning of any terminology they use.
Launch
Groups of 2
Display images and expression.
“Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2-3 minutes: partner discussion
Share and record responses.
Student Facing
Which one doesn’t belong?
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
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Activity Synthesis
“What equation can each diagram represent?” (The array represents
\(4\times6=24\)
because there are 4 rows of 6 dots, and there are 24 dots in the array. The area diagram could represent
\(4\times7=28\)
or
\(28\div4=7\)
since the sides are 4 and 7, and the area is 28. The tape diagram could represent
\(24\div3={?}\)
or
\(3\times{?}=24\)
because we know the total is 24 and there are 3 groups, but we don’t know how many are in each group.)


aligns: no