The Exercise Bike Problem
Jennifer Bostic Schmalzbach
MATH 565
Adapted from a lesson idea from Dr. Bardzell
Student Outline
Objective: Students will explore the relationship between work
and “steepness” of the landscape by sketching a graph of the
elevation required to achieve a sample exercise bike workout
Warm-up: Sketch a graph that
demonstrates a positive or negative
correlation between two variables.
• Discussion: exercise bikes, effort, and reading the screen of
an exercise machine
• Activity: You will be asked to sketch the landscape that
would be responsible for the workout that you are presented
• Discussion: the relationship between effort and elevation,
the relationship between effort and “steepness”
Summary Question
6
Create a sketch of the landscape
elevation that would be required for
this exercise profile.
Effort Level
5
4
3
2
1
0
Minutes
Differentiation
• There are times throughout the lesson for the
teacher to have a 1 on 1 conversation and lesson
with students that struggle
• Students that lack the vocabulary and background
knowledge for a discussion on slope can discuss the
activity in terms of “steepness”
• Alternate Activity: Some students may find it
difficult to go from the abstract (bike screen) to the
real world (elevation). Alternatively, some students
could be given the assignment in reverse. With a
given elevation sketch, they would have to chart the
effort required over time to ride the terrain