Students will explore the concept of inverse variation by graphing the relationship between rate and time, using the formula:
Rate X Time = Distance.
y = k/x
is a difficult concept for students to understand, and a new standard for 8thgrade. Students need a concrete representation in order to internalize this concept. The distance formula:
is perfect to show that:
which is an example of inverse variation where the constant of variation is the distance.
The culminating graph will show that as time increases, rate decreases.
Students may need to practice using a stopwatch, since the time for each trial will be recorded in seconds. This may require a few minutes of time during a prior lesson to reach this skill level.
The teacher should determine the height to set up stations before class. One height should be as low as possible for the car to still roll to the end of the track. Another should be high enough to get the car to move quickly, but must be measurable. I use a set of shelves at the back of my classroom: the lowest level is one height, the second shelf is another, and the top ledge is a third. Since a total of 4 heights are required, I also use a tower of books that is between the other heights.
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