# Modeling with Polynomials—An Introduction

### Modeling with Polynomials—An Introduction

Student Outcomes

• Students transition between verbal, numerical, algebraic, and graphical thinking in analyzing applied polynomial problems.

### New York State Common Core Math Algebra II, Module 1, Lesson 16

Worksheets for Algebra II, Module 1, Lesson 16

Classwork

Mathematical Modeling Exercise You will be assigned to a group, which will create a box from a piece of construction paper. Each group will record its box’s measurements and use said measurement values to calculate and record the volume of its box. Each group will contribute to the following class table on the board.

Using the given construction paper, cut out congruent squares from each corner, and fold the sides in order to create an open-topped box as shown on the figure below.

1. Measure the length, width, and height of the box to the nearest tenth of a centimeter.
2. Calculate the volume.
3. Have a group member record the values on the table on the board.
4. Create a scatterplot of volume versus height using technology.
5. What type of polynomial function could we use to model the data?
6. Use the regression feature to find a function to model the data. Does a quadratic or a cubic regression provide a better fit to the data?
7. Find the maximum volume of the box.
8. What size square should be cut from each corner in order to maximize the volume?
9. What are the dimensions of the box of maximum volume?

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