Measurement Session 1: Notes

A B C

Notes for Session 1, Part C

Note 10

If you are working in a group, first try working individually to make each of the five polygons (using all three triangles each time). Provide hints to colleagues who are having difficulty making a particular shape by starting the puzzle for them; put two of the three triangles in place and let them figure out where the third triangle belongs. Resist simply showing someone a finished puzzle. Once the five polygons have been completed, discuss Problems C2 and C3.

<< back to Part C: Nonstandard Units

Note 11

It may appear to some people that the areas of the five shapes are different. Others will argue that the areas must be the same since each polygon is constructed from the same identical pieces. Reflect on this question, or discuss it if you are working in a group.

<< back to Part C: Nonstandard Units

Note 12

There are different ways to order the polygons by perimeter, all of which require us to first establish a nonstandard unit of measure (e.g., the side of one of the triangles; the length of an eraser) and then to take some measurements in terms of the nonstandard unit. If you are working in a group, share your approaches. Be sure that everyone agrees on the order in which to place the polygons (in terms of perimeter), and that individuals justify their conclusions.

<< back to Part C: Nonstandard Units

Session 1 | Notes | Solutions | Video