B C

Notes for Session 5, Part B

 Note 2 If you are working in a group, pose the first problem and give everyone a couple of minutes to work on it. Watch for someone with an appropriate solution. Ask that person to share the solution and explain why it works. That's the goal for these problems: to come up with methods that will always work and that don't rely on measurement. Also, make sure that everyone is clear about the "rules of the game," particularly that you have to use all the pieces and you have to be able to describe your method using the language of flip, rotate, and translate. At the end, leave at least 10 minutes to share methods that can be explained, as opposed to those that just look right.

 Note 3 After you have solved Problems B1-B4, reflect on why your cuts work. It's likely that you used something like a "midline cut" to turn a triangle into a parallelogram and then into a rectangle. Consider that we want a single cut to do two different things: connect consecutive midpoints (so that the segments you attach will match up), and form a segment that is parallel to the base (so that the final figure will have parallel sides). This leads into Part C, where we prove that these two segments really are one and the same.