Use this dynamic worksheet to answer the questions that follow and determine the equation for the area of any rectangle.
1. Let's start by clicking on the "Show variables" check box. Since we're going to derive the formula, let's make sure we're using the same terms. No other variables should be part of the equation you derive. When you're done, uncheck the "Show variables" check box.
2. Slide the base slider bar until there are only three columns.
3. Slide the height slider bar until there is only one row.
4. Click on the check box to "Show unit square."
5. Use it to count the number of squares.
6. Click on the check box to "Show area."
7. The number of squares within the figure is the area of the figure. What do you think will happen when you slide the Height slider bar to double the number of rows? Why? Test your conjecture.
8. Experiment by doing the following several times:
a) uncheck the "Show Area" check box;
b) move the Length and Width slider bars;
c) calculate the area on your own using the variables "l" for length and "w" for width -- click on the "Show dimensions" check box for a quick count of length and width;
d) check the "Show area" check box to verify.
e) click on the reset button in the upper right hand corner to reset this construction before repeating.
9. When you are satisfied, write down the equation for area in terms of length and width. Check your answer by checking the "Show equation" check box. If you have difficulty, raise your hand so your teacher can help.
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Dynamic worksheet created by T. Gastauer, Created with