What happens when you make a quadrilateral (a four sided object) and connect the midpoints of each side? What if you did this over and over again?
Here is an activity that investigates that!
Wacky Quadrilaterals
- Draw any quadrilateral that takes up most of the page. Measure the interior angles and add them all together and record this. Measure and record the perimeter
- Measure and determine the midpoint of each line. Connect the midpoints and make a new quadrilateral. (Iteration 1) Measure the interior angles of the new quadrilateral and perimeter.
- Repeat step 2, and fill in the chart with the sum of the new angles and perimeter.
- Estimate what the sum of the angles and perimeter will be the for 10th shape. (Do not make the 10th shape, simply estimate based on the pattern).
- Color in your shape to make a creative design.
What do you notice? Wonder? What would be the sum of the interior angles of iteration 10? Perimeter?
Here is a recording sheet.
A possible example:
Extension:
Simply show this animation and ask "What is this visually proving?"
A possible video to show is here:
I love problems/tasks that "have legs". These problems can be re-experienced by students to become richer and deeper in their exploration and analysis. In senior grades, if you created ordered pairs: (figure number, sums of the lengths of the sides) as you do the constructions using the midpoints. what do you think the graph would look like? Your justification? OK -- now test your conjecture.
ReplyDeleteGreat task.
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