Do-it-Yourself K-12 STEM Enrichments
Box Problem, Level 2 - Grades 8-9

Learning Objectives
You will calculate volume and investigate how to make a paper box with the largest volume possible by defining variables for box volume and utilizing graphing calculators to solve a function for box volume with the different variables.

Description
Suppose you have a rectangular piece of cardboard that you want to use to make a box for storing marbles. You will make the box by cutting squares from the corners of the cardboard and then fold up the edges. The box will have no top. What size squares should you cut to make the box with the largest volume? You will investigate this problem using physical models, tables and graphs. You will define a variable representing the size of the squares that should be cut out of the paper to make a box, and you will write a function for the box volume. Graphing TI-83+ calculators are required to create a table with more values and to graph the function.

Instructions
Use the Student Handout and the video to complete this activity.

Grade Level
8th - 9th grade Mathematics student

Materials and Equipment Needed
• Student Handout
• Answer Key
• TI-83+ graphing calculators

Box Problem, Level 2 - Video