A B C

Solutions for Session 10, Part A

See solutions for Problems: A1 | A2 | A3

 Problem A1 Answers will vary. Some ideas: Students come up with the triangle inequality through data gathering and checking, but the teacher persists in asking them to explain why it should hold. That stretches students into not just the geometry content, but also the logical deductions. This course covered the triangle inequality, and several of the same ideas came up. One particularly interesting piece is at the beginning of the clip, when students use a geometric model to check if the sum of two lengths is greater than the third length. Many teachers rely on algebra and arithmetic more, and it's nice to remember that many students do have a sense of geometric reasoning as well.

 Problem A2 People have very different, and often very strong, opinions about the use of context in mathematics classrooms. It is important to present students with a variety of lessons. Students can be engaged by problems that are not context-based, as well as by those with real-world connections.

 Problem A3 There were many adaptations. Here are some: The materials were different; Ms. Saenz used what was available at her school. The activity was more directed; students were asked to look particularly at sums of sides rather than to find whatever relationship they could.