Stressed to the Breaking Point
Multiple-Variable Functions
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Objective
Students will explore the relationship between the amount of weight that can be
supported by a spaghetti bridge, the thickness of the bridge, and the length of the
bridge to determine the algebraic equation that best represents that pattern modeled
by the three variables.
Overview of the Lesson
How does the amount of weight that can be supported by a spaghetti bridge relate to
the width (number of spaghetti strands) and the length of the bridge? Students
gather data comparing the amount of weight that can be supported, the number of
strands of spaghetti used, and the length of the bridge. They explore the relationship
between the amount of weight that can be supported and the number of strands
used (the width of the bridge) and discover that this relationship is linear. Students
make a scatterplot and determine the equation for this relationship. Students also
explore the relationship between the amount of weight that can be supported and
the length of the bridge. Again, they make a scatterplot and determine that as the
length of the bridge increases, the amount of weight that can be supported decreases.
Students explore in detail both relationships—the linear and the inverse models—
and they determine how the three variables—weight, length of the bridge, and
width or number of strands of spaghetti—are related and expressed in one equation.
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