MATERIALS FOR EACH GROUP : books of the same thickness (at least 1 inch), small paper cups, 75-80 pennies, strips of paper (11 x 4¼ inch for Experiment 1 and 4¼ inch strips with lengths of 4,6,8,9 and 11 inches for Experiment 2, scotch tape/post-its, chart paper/markers, dots, rulers, graphing calculators)
ESSENTIAL QUESTIONS:

How is the thickness of a bridge beam related to its strength?
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How is the length of a bridge beam related to its strength?
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What other variables might affect the strength of the bridge?
EXPERIMENT 1: We are going to conduct an experiment to explore how the strength of a bridges changes as its thickness changes.
Demonstrate the experiment using a single thickness.
Discuss with students the following:
 accuracy in bridge construction (measuring, cutting, folding)
 consistency in overlapping the ends of the bridge on the book’s edge
 placement of cup
 adding the pennies
 re-using bridges
 what is our definition of “collapse”
 independent and dependent variables
Experiment 1 Instructions:
1.) Fifteen pieces of paper will be needed to build the bridges of thicknesses 1-5. Each piece is made from a 11 by 4 ¼ inch sheet of paper that is folded up 1 inch on each side. Mark the center of each bridge with an “x”.
2.) Suspend one bridge layer between 2 books by about 1 inch.
3.) Place a small cup in the center of the bridge.
4.) Drop the pennies into the cup, one at a time, until the bridge collapses. Record the breaking weight (number of pennies) of the bridge in a table.
5.) Repeat the experiment to find the breaking weight of bridges made from 2, 3, 4 and 5
thicknesses of paper. MAKE SURE YOU USE NEW STRIPS EACH TIME!
6.) Construct a graph of the data.
7.) Determine the equation of a line that would best match your data.
Making Algebraic Connections (MAC)
March, 2011
Activity adapted from Connected Mathematics2, Thinking With Mathematical
Models , Investigation 1. Lappan, Fey, Fitzgerald, Friel, Phillips.
1

8.) Instruct each group to complete Student Activity Sheet Experiment 1.
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Is the relationship linear or nonlinear? How do you know?
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Is the correlation positive, negative or neither? How do you know?
 If you could make a bridge with ½ layer, what breaking weight would you predict for a bridge that is 3.5 inches thick? Explain your reasoning.

Predict the breaking weight for a bridge that is 8 layers thick. Explain your reasoning.
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What would happen to the data in the graph if you used weights heavier than pennies? Sketch the graph.

How would the length of a bridge affect its strength? Are longer bridges stronger or weaker than shorter bridges?
QUESTIONS FOR WHOLE CLASS DISCUSSION:

What patterns do you see in the data?
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How should your data compare to data of other groups in the class?
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For each layer you added to the bridge, what was the approximate increase in the number of pennies it would hold?
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Was the increase in the number of pennies constant? If not, how did you make your predictions for other bridge thicknesses?
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Is the relationship linear? non-linear?
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Positive correlation? Negative correlation? No correlation?

How did you find the equation for the line that best represents your data?

If the relationship is linear, then the graph would eventually cross the x-axis.
What does this mean in this situation?

Review the questions from the group work (above).
Making Algebraic Connections (MAC)
March, 2011
Activity adapted from Connected Mathematics2, Thinking With Mathematical
Models , Investigation 1. Lappan, Fey, Fitzgerald, Friel, Phillips.
2

EXPERIMENT 2: Now we will conduct an experiment to explore how the length of a
bridge is related to its strength.
This experiment is conducted as above except the bridges are constructed of 4 ¼ inch strips of paper with lengths of 4, 6, 8 and 9 inches.
QUESTIONS FOR WHOLE CLASS DISCUSSION

What are the independent and dependent variables?

What do you predict will happen in this experiment?
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Is there a pattern to your data? Describe any patterns you see.

As bridge length increases, what happens to the number of pennies the bridge can support?
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As bridge length decreases, what happens to the number of pennies the bridge can support?

Describe the shape of the data.
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Make predictions for bridges of lengths 3,5,10 and 12 inches.
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Compare the results of the 2 experiments . How is the relationship between bridge thickness and breaking weight similar to that of bridge length and breaking weight? How is it different?
Students should recognize the relationship is not linear. (This is an inverse relationship.)

What shape do the coordinates form?
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Is the change constant?
Using the graphing calculator, explore the patterns between the lengths of the bridges and the number of pennies.

How is this useful in finding an equation that fits the data?
Making Algebraic Connections (MAC)
March, 2011
Activity adapted from Connected Mathematics2, Thinking With Mathematical
Models , Investigation 1. Lappan, Fey, Fitzgerald, Friel, Phillips.
3