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
The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100 and to help students develop fluency.
When students use known multiplication and division facts to divide larger numbers, 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.
\(30\div3\)
\(60\div3\)
\(63\div3\)
\(54\div3\)
Student Response
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Activity Synthesis
“How did you use division facts that you already know to find some of the other quotients?” (I knew that
\(60\div3\)
would be double the answer of
\(30\div3\)
. Once I knew
\(60\div3\)
, I was able to find
\(63\div3\)
by adding another group of 3 and
\(54\div3\)
by taking groups of 3 away.)


aligns: no