B/W Chapter 3- Accepting

Example 2: Isosceles Triangle

Observations

1. Are all isosceles related in some way?
2. Why are these triangles so important?
3. Is there a way for the sides to be equal lengths and not the angles?
4. How is the thrid side related to the first two? Is this always the case?

I would have to agree with the authors about people familiar with Geometry only coming up with questions like 1 & 2. It has bee a very long time since I have taken geometry and I've never taught it, so I tended to just hink about the shape (not rerally the math). But for problems like x² + y² = z² I only approached it from a mathematical sense because I am so familiar with algebra.

Example 3: Geoboards

What would I do with it?

1. Make a fun design with different colored rubber bands
2. See how far I could stretch a rubber band around the nails
3. Determine how many shapes I can make with only using a certain number of pegs

Example 4: Pythagorean Triples

Questions, Patterns, Observations

1. There is a much bigger gap between corresponding x's and y's than y's and z's
2. x is mostly odd, y is mostly even z is all odd
3. How many triples are there if we say x is 1-100?

"How much is lost by searching for a less exact analysis or a less precise strategy?"

I really liked this question. I think in many math classrooms approximations and educated guesses are regarded as wrong. It is very important for students to look at a problem like 214 + 497 and realize their answer should be around 700 (and if they get something far away form that they need to go back and check it). So many times my students are so focused on getting the answer that they aren't checking to see if it makes sense in problem or if they could estimate the answer. Making guesses and predictions is a very important life strategy that math class could help foster if we change our focus.