18 Are graphs just pictures?
We now consider some situations involving the representation of changes in speed and distance over time.
Having a grasp of these relationships is essential to the topics of calculus and kinematics that students study in the later years of high school, however the intuition should be developed in students much earlier. The key trickiness in each of the following situations is the impression that the visual information provides us with, and how this can confuse us when trying to transform that information into the relationship as represented on a graph.
Speed over time
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Once you’ve arrived at a tentative conclusion, you can see a worked solution using Scratch (YouTube).
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Modelling gravity
Build the algorithm yourself from the video above (or see the program’s project page and click on the “see inside” button), then explore how changing the initial values of each of the variables affects how the cat jumps.
Acknowledgement
The problems presented under the heading Speed over time have been adapted from The Language of Functions and Graphs (1985) by Shell Center for Mathematical Education (this version modified by Deakin University and licensed under CC BY NC 4.0 with permission from Shell Centre for Mathematical Education)
