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: