Introduce “Same Shape”. The purpose of this activity is for students to begin developing an informal intuition about what “same shape” means. Students should justify their explanations.
Students discuss in groups whether or not pairs of shapes are similar using the Similar Shapes task handout. Certain pairs are meant to target possible misconceptions. The teacher can circulate to check in with groups. The teacher might choose to pre-select certain groups to share out ideas during the debrief. Student thinking and misconceptions:
- Classifications. Students may see two right triangles as having the same “shape” by classification even if they are not similar. (e.g. #4 on the task-card)
- Proportional sides. Students may think that proportional sides are sufficient (e.g. #5).
- Transformations. Students may not see shapes as similar when they have been rotated or reflected
The final mathematical goal of this debrief is to collaboratively construct a definition of similar shapes that contains both congruent angles and proportional sides.
Licensed under Creative Commons Attribution 3.0 by Dan Meyer, Sarah Kate Selling, Kathy Sun & Jo Boaler