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Derivative Matching Game
In this game, you will be presented with a game board showing graphs of functions on cards. The goal is to match the functions with their derivatives until there are no cards left on the board. You may choose whether to play a game matching functions with just their first derivatives or both first and second derivatives. You may also choose whether there are a small number of matches or a large number to make. There is a “more information” button on the game that will color the graphs to show where the graphs on the game board are positive, negative, increasing, decreasing, or concave up or down.
Clicking on a graph card will cause the card to move to the top open space on the right side of the game area. You don’t drag it there; it will glide to the top available space. If no spaces are available, the cards will shift so that the selected card moves into the top spot and the other cards shift down one or return to their original location on the playing board. For the first derivative match game, there are two headings on the right: “graph of f(x)” and “graph of g(x)”. “graph of f(x)” is for the function itself. “graph of g(x)” is for the first derivative of f. For the first and second derivative match game there is an additional label: “graph of h(x)”. “graph of h(x)” is for the second derivative of f.
Placing the cursor over the orange buttons will provide a brief explanation of what the button does. If you click the “more information” button and then a number 1-4, the graph cards in the main area of the game will be shaded as follows: 1 for positive (regions where the function is positive will be shaded red), 2 for negative (regions where the function is negative will be shaded blue), 3 for increasing (regions where the function is increasing will be shaded yellow), and 4 for decreasing (regions where the function is decreasing will be shaded green). If the first and second derivative matching game has been selected, then press 5 for concave up (regions where the function is concave up will be shaded lavender) and 6 for concave down (regions where the function is concave down will be shaded cyan). To shade a single card, enter a number 1-4 (1-6 for second derivative game) while the cursor is over that card. The card will have a red shadow if the cursor is over it.
If you believe that you have successfully made a match press the “remove match” button. If you are correct, those cards will be removed. Otherwise, a message will appear telling you what to look for when you try to match the graphs.
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Margolius, Barbara, "Derivative Matching Game," Loci (July 2008), DOI: 10.4169/loci002651