Hints:
The main idea here is to move from the figures and the table to the formula, thus showing multiple representations of the same information.
Participants may come up with lots of different answers. Some may arrive at the pattern before others.
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Time Estimate |
Activity |
Main Idea |
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10 min (:50) |
Can we say this in the language of algebra? Discuss student responses. |
This is a key moment. Formulas come from a problem, they are not "handed down from on high." Agree on a conventional (customary?) form of the formula |
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15 min (1:05) |
Attempt to draw a regular nonagon. Is this possible? What do you need to know? |
Agree on a procedure - line segment, angle, line segment. Discuss accumulation of error for near misses. |
(n-2)180 = Sum of Interior Angles
Step-by-step guide
1. Using a word version of the pattern, ask the participants to convert the pattern into the language of algebra. The pattern is (n-2)180 = angle sum.
2. Discuss various algebraic representations of the verbal form of the pattern. For example, multiply the number of sides times 180 and then subtract 360 degrees from the result.
3. Agree on a conventional formula to represent the pattern.
4. Ensure that everyone has paper. Ask each participant to draw a nonagon using their paper, pencil, protractor, and/or angle ruler. Agree on a procedure for drawing the nonagon. Once you know the angle, you can draw from there using an angle ruler (or protractor).
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