## Reflection: Staircase of Complexity Quiz on Graphing Polynomials and Intro to Modeling with Polynomials - Section 2: Group Work on Maximizing Volume of a Box

At face value, the task of building a Skittles box from a notecard and tape is a very simple task. It is not obvious how polynomial expressions will factor into this task, and, in fact, seems irrelevant to the challenge altogether. I like that. There will always be some students who know that I have a mathematical motive behind my task assignment and will look for the ‘correct’ answer immediately upon attempting the task. However, most students will begin this task at step one: build a box, paying attention to the rules of construction) and hope that mine holds the most. If I were to ask, “Why did you build it that size,” the answer would surely be some form of “I just thought it would be the biggest.” At which point, I might say, “Were you right?” Step 2! Compare and contrast your box with others around you. Maybe record the data of the boxes in ranked order. Do we notice anything? Does anything seem surprising? How confident are we that the ‘winning’ box could not be beaten by another ‘better’ box? Step 3! Is there some way that mathematics can prove beyond a doubt what the dimensions of the ultimate winning box would be?

Presenting the task in this way allows students to climb gradually from the problem to the mathematics, thus turning the math into a tool that helps guarantee their success rather than an imposed framework that seems irrelevant.

One Step at a Time
Staircase of Complexity: One Step at a Time

# Quiz on Graphing Polynomials and Intro to Modeling with Polynomials

Unit 4: Polynomial Theorems and Graphs
Lesson 12 of 15

## Big Idea: Polynomials can be used to model some real world situations like maximizing volume; graphing polynomial functions can help us understand the model.

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95 minutes

### Colleen Werner

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