Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Item 892

How is Polynomial Expansion Related to Ice Cream?

Consider a triple scoop ice cream cone. You can have any combination of Vanilla (V), Chocolate (C), or Strawberry (S). What are all of the triple scoop ice cream cone combos if order doesn't count and repetition is allowed?

How is \( (a+b+c)^3 \) related to that?

Can this be generalized?
Would this analogy work with \( (a+b+c+d)^5 \) or \( (a+b)^7 \)?

What other mathematical aspects of this caught your attention? What do you wonder about the situation?

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Notice, Wonder
David Marain
PRE-CALC

Source: David Marain

Vanilla (V), Chocolate (C), Strawberry (S) Have Ss list all triple scoop ice cream cone combos where VVS ≄ VSV? Connection to (a+b+c)ł,# of combos If order doesn't count?
— David Marain (@dmarain) November 25, 2020

More Information:
Noticing and wondering is a tool to help students:
- Understand the story, the quantities, and the relationships in the problem.
- Understand what the problem is asking and what the answer will look like. Have some ideas to begin to solve the problem.
More Here at NCTM