# Activities

• • • ##### Subject Area

• Math: Algebra I: Functions and Relations

• ##### Author 6-8

100 Minutes

• ##### Device
• TI-83
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Graphing Calculator Activities for Enriching Middle School Mathematics

## Box It Up

#### Activity Overview

Students take a numerical and tabular look at finding the maximum value of an open box constructed by folding a rectangular sheet of material with cutout square corners. They also understand the concepts of independent and dependent variables.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 87 - 95 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Use rectangles of grid paper, mark off equal-sized squares at each of the corners
• Cut out the squares and fold to form open boxes
• Notice that the size of the cut-out square determines the height of the box
• Examine the relationship between the dimensions of the box
• Calculate the length, width, and height of the box, and compute the volume
• Repeat the steps for other boxes
• For different sizes of cut-out squares, generate a table of volumes
• Use the calculator, represent the height by a variable x, write an expression using x, specify its start and incremental values, and find the volume
• Analyze the data to determine the relationship between the cut corners and the height of the box
• Observe that the volume increases as the size of the cut square increases and then starts to decrease for further increase in the size of the square
• Find the length of the square which forms a box with the largest volume
• Note that the relationship between height and volume is not linear
• #### After the Activity

Students complete the Questions sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary