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Project Summary

Difficulty	1
Time required	Very Short (a day or less)
Prerequisites	None
Material Availability	Readily available
Cost	Very Low (under $20)
Safety	No issues

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Abstract

Objective

In this experiment you will test the relationship between the three different dimensions (length, width and height) of a three-dimensional object with a constant volume.

Introduction

Geometry is the study of how to use math to describe and investigate different points, lines and shapes. A very basic three-dimensional shape is the rectangular prism. A rectangular prism is a shape like a box or a book. It has six different sides, and if all six sides are the same, then it is called a cube. A cube is the same shape as a die (i.e., one of a pair of dice), where each side is a perfect square. Cubes and rectangular prisms can be measured with the same geometrical formulas.

A formula is the way a shape is described in geometry. A formula is simply a mathematical way to calculate different properties of a shape: size, area or volume. Volume is a unique property of three-dimensional shapes because three-dimensional shapes take up space in three different directions: length, width and height.

In this experiment you will use Play-Doh to make a model of a rectangular prism. You will measure the three dimensions (length, width and height) and use a formula to calculate the volume. You will use a dimensional meta-morpher (rolling pin) to change one dimension (height) and see what effect this had on the other two dimensions. By changing the dimensions. of the rectangular prism, you will test the relationship between the dimensions of a three-dimensional object at a constant volume.

Terms, Concepts and Questions to Start Background Research

To do this type of experiment you should know what the following terms mean. Have an adult help you search the Internet, or take you to your local library to find out more!

• three-dimensional (3-D) object
• cube
• rectangular prism
• volume (V)
• length (l)
• width (w)
• height (h)

• How do the dimensions of a rectangular prism change with respect to each other?
• If one dimension decreases, will the other dimensions increase or decrease?

Bibliography

• This site is a really good site for kids to review math skills, solve puzzles and read stories about math. They also have a section on geometry:
  Karen, 2005. "Cool Math 4 Kids," Coolmath.com, Inc. [accessed: 3/3/06] http://www.coolmath4kids.com/
• NCES, 2006. "Create a Graph," National Center for Education Statistics (NCES) U.S. Dept. of Education. [accessed: 3/3/06] http://nces.ed.gov/nceskids/createagraph/
• East, T., 2005. "Educational Software Index: Geometry." [accessed: 3/3/06] http://homepage.mac.com/teast/index.html

Materials and Equipment

• Play-doh (or home-made salt dough)
• ruler
• flat surface
• rolling pin
• graph paper
• 3 large-tip permanent markers in red, green and blue

Experimental Procedure

1. First, you will need to buy Play-Doh or make some salt dough. Here is a basic recipe for salt dough that you can make for yourself:

   SALT DOUGH RECIPE:
   2 cups of Plain Flour
   1 cup of table salt
   1 cup of water

   OPTIONAL INGREDIENTS:
   1 tablespoon of vegetable oil (makes it a little easier to knead)
   1 tablespoon of wallpaper paste (gives the mixture more elasticity)
   1 tablespoon of lemon juice (makes the finished product harder)

2. Use a chunk of dough about as large as your fist. The amount of dough is going to be a constant (meaning that it will not change) so do not add to or take away from your chunk of dough once you have started your experiment.
3. Make your dough into a cube shape, approximately square on all sides.
4. Using the 3 colors of permanent markers, color along the 3 edges that come out from one of the corners. Mark one edge in red, one edge in green and one edge in blue. These three edges will represent the three dimensions of your cube (length in red, width in green and height in blue).
5. Place your dough on the graph paper and measure all 3 dimensions (length in red, width in green and height in blue) by tracing them on the graph paper with the matching colored marker. Write down the words "Trial #1" on the top of the sheet of graph paper.
6. After you have measured the 3 dimensions, you are ready to change the shape of your dough.
7. Put the dough cube on a flat surface with the green and red sides (length and width) on the surface and the blue side (height) pointing up.
8. Use your rolling pin to flatten the cube a little bit by rolling on the top of the cube. Keep the corners square as you go by patting in from the sides with your hands.
9. The three colored edges should stay colored even though they may squish or stretch as you roll. If they begin to lose their color, mark over the edge again with the matching color of permanent marker.
10. Repeat step 5 with a new piece of graph paper. Write down the words "Trial #2" on the top of the sheet of graph paper.
11. Repeat steps 6-9, rolling the dough a bit more each time between measurements. Remember to keep the corners square as the cube becomes flat. Continue to measure each dimension after rolling and write the data on a new piece of graph paper labeled on the top with "Trial #___" until you have at least 10 different measurements.
12. Now you are ready to measure your data for each trial with a ruler and write the measurements in a data table:

    Trial Number	Length red (cm)	Width green (cm)	Height blue (cm)	Volume (cm3) V = L × W × H
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10

13. For each trial, use a ruler to measure the three lines using centimeters, then write the measurement into the data table in the correct box.
14. For each trial, multiply the length × width × height to calculate the volume of the shape. Are they all the same?
15. From the data table, make a graph of your results. The best type of graph for this experiment is a bar graph. For each set of measurements, make a bar for each dimension: length, width and height. You can make your graph by hand or you can try using the Create a Graph web site for kids from the National Center for Education Statistics.
16. What happens as one dimension (the one you flattened with the rolling pin) decreases? Do the other two dimensions. increase or decrease? Why does this depend on the volume staying the same? What do you think would happen if the volume changed?

Variations

• In this experiment you changed the length and width of the sides, but kept the volume (or amount of dough) constant. What would happen if the amount of dough changed? Would the volume also change? Try the experiment adding or taking away some dough, forming the dough into a cube and measuring the dimensions of the shape. What happens to the dimensions as you add more dough? Take away dough? Does the volume increase or decrease?
• In this experiment, you collected data from 10 different trials for ten different measurements. For a more advanced project, you could graph the linear relationship between the side you are rolling and the other two sides. Make an X,Y dot plot of the height vs. width, height vs. length, or height vs. width + length. Then you can draw a line of best fit. What is the equation for that line? What does this tell you about the relationship between the measurements of a three dimensional rectangular shape under constant volume? You can make your graphs by hand or you can try using the Create a Graph web site for kids from the National Center for Education Statistics.
• In this experiment we used a three dimensional rectangular shape. For a more advanced project, try this experiment with other more complex shapes, like a pyramid, cylinder or sphere. You can use the Geometry Applet to help you or download a program like Geometry by Travis East.

• For more science project ideas in this area of science, see Pure Mathematics Project Ideas.

Credits

Sara Agee, Ph.D., Science Buddies

Last edit date: 2006-04-20 00:54:21

Career Focus

If you like this project, you might enjoy exploring careers in Pure Mathematics.

Statistician Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician!

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