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Activity Overview |
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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.
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Before the Activity |
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See the attached PDF file for detailed instructions for this activity
Print pages 87 - 95 from the attached PDF file for your class
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During the Activity |
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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
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After the Activity |
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Students complete the Questions sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary
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Other Downloads |
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view standards alignment
view textbook alignment
Subject Area:
Math : Algebra I : Polynomial Functions
Author:
Texas Instruments
Level:
5-8
Activity Time:
100 Minutes
Device:
TI-83, TI-83 Plus Family, TI-84 Plus Family
Apps:
Software:
Accessories:
Other:
This is Activity 9 from the EXPLORATIONS Book:
Graphing Calculator Activities for Enriching Middle School Mathematics
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