Education Technology

Box It Up

Published on 06/09/2008

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.

    Follow the Activity procedures:

  • 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