Do-it-Yourself K-12 STEM Enrichments
Box Problem, Level 3 - Grades 10-11

Learning Objectives
• You will create an Algebraic equation that models volume of a box
• You will generate a scatter plot on a graphing calculator
• You will use Algebra to determine how to create a box with the most volume

Description
Students build open top rectangular boxes from a standard sheet of paper by cutting congruent squares from each corner. Data is collected that pairs the length of the side of the cut out square with the volume of the resulting box to create a scatter plot. Students will be guided to define a variable representing the size of the square and to write a function for the box volume. Students learn to describe a clear pattern shown in the scatter plot, and develop a function through analysis of the box design. Based on this function, the length of the side of the square is determined to create a box of maximum volume, and two squares that will produce a box of equal volume. Students will investigate this problem using physical models, tables, and graphs. Graphing TI-83+ calculators are required to create a table with more values and to graph the function.

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

Grade Level
10th - 11th grade Mathematics students

Materials and Equipment Needed
• Student Handout
• Answer Key

Box Problem, Level 3 - Video