Testing Bridge
Lengths
The Gadsden Group
Goals and Objectives
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Collect and express data in the form of
tables and graphs
Look for patterns to make predictions
from tables and graphs
Distinguish between linear and nonlinear relationships from tables and
graphs
Standards and Benchmarks
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Standard #2: Algebra
Definition: Students will understand algebraic concepts and applications.
Benchmark #2-D:
Analyze changes in various contexts
1. Use graphs, tables, and algebraic representations to make predictions
and solve problems that involve change.
2. Estimate, find, and justify solutions to problems that involve change
using tables, graphs, and algebraic expressions.
3. Use appropriate problem-solving strategies (e.g., drawing a picture,
looking for a pattern, systematic guessing and checking, acting it out,
making a table or graph, working a simpler problem, writing an algebraic
expression or working backward) to solve problems that involve change.
5. Analyze problems that involve change by identifying relationships,
distinguishing relevant from irrelevant information, identifying missing
information, sequencing, and observing patterns.
7. Recognize the same general pattern of change presented in different
representations.
Standards and Benchmarks cont’d
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Standard #5: Data Analysis and Probability
Definition: Students will understand how to formulate questions, analyze
data, and determine probabilities.
Benchmark #5-A:
1. Represent two numerical variables on a plot, describe how the data
points are distributed and identify relationships that exist between the two
variables.
3. Organize, analyze, and display appropriate quantitative and qualitative
data to address specific questions including: plots charts and tables.
5. Simulate an event selecting and using different models.
Benchmark #5-B:
3. Analyze data to make decisions and to develop convincing arguments
from data displayed in a variety of formats that include: graphs scatter plots
charts and tables
4. Interpret and analyze data from graphical representations and draw
simple conclusions (e.g., line of best fit).
5. Evaluate and defend the reasonableness of conclusions drawn from data
analysis.
7. Identify simple graphic misrepresentations and distortions of sets of data
(e.g., unequal interval sizes, omission of parts of axis range, scaling).
Standards and Benchmarks cont’d
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Benchmark #5-C:
Develop and evaluate inferences and predictions that are based on data
2. Describe how reader bias, measurement errors, and display distortion
can affect the interpretation of data, predictions, and inferences based on
data.
3. Conduct simple experiments and/or simulations, record results in charts,
tables, or graphs, and use the results to draw conclusions and make
predictions.
4. Compare expected results with experimental results and information
used in predictions and inferences.
Lesson: Non-Linear Models
“In this investigation, students will encounter a different
kind of relationship: an inverse relationship. In an
inverse relationship, as one variable decreases the other
increases, but not in a linear fashion - that is, not by
constant decreases. There is an underlying constant in
inverse relationships: when the two variables are
multiplied, they yield a constant product. Students will
see that the pattern of change in the data is similar to
that in the other inverse relationships they will
investigate.” (Lappan, et al, Thinking With Mathematical
Models, p. 36a).
Lesson Cont’d
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Students will explore non-linear relationships by
testing the lengths of bridges and their breaking
weight.
Launch:
 What do you expect to happen in this experiment?
 We are using equipment similar to what we have used
before. What are the variables this time? (Length
and breaking weight)
 What will the data look like? What shape do you think
the graph will be?
Lesson cont’d
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Explore:
Have students conduct the experiment and
discuss the questions within their group.
Ask each student to make a table/graph and
write his or her own answers.
Each group will compare their data and come to
a consensus in order to create a group poster of
their table and graph.
Lesson cont’d
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Summarize:
After students have displayed and presented their group work, then ask:
 Are there similarities in the results of the various groups? Are there
differences? What might have caused those differences?
 As bridge length increases, what happens to the number of pennies that
can be supported? (It decreases)
 As bridge length decreases, what happens to the number of pennies
that can be supported? (It increases)
Focus the class’s attention on this inverse relationship.
 What shape or pattern do you see in your graph? Is it linear? (no, it is
definitely a curve)
 How might you be able to tell from your table that the graph model might
be a curve? (The difference between two consecutive breaking weights
decreases less and less as the length increases; it is not a constant
change)