Puzzling Problems Preferred

Yesterday morning I determined that I would find something from my day to blog about, and hey! I did! :)

My geometry kids are learning about quadrilaterals. The prior day’s lesson was about properties of rectangles, rhombi, and squares. Here’s the warm-up problem I gave them:

In rhombus QRST, the diagonals QS and RT meet at point U. If QS=12 and RT=16, find the perimeter of the rhombus.

I think it’s a strong problem, because they have to recognize all of these things:

1. that since the rhombus is a parallelogram, the diagonals bisect one another;
   
2. that the diagonals are perpendicular;
   
3. that the four small triangles are right triangles;
   
4. that the Pythagorean theorem will allow them to find the length of one side of the rhombus; and
   
5. that all four sides of the rhombus are congruent.

Almost all of my students struggled with the problem. I gave some hints – “What do you know about the diagonals of a rhombus? Okay, now think about triangles.” One student asked me if it was a “trick question;” I told her that it’s not a trick, just a puzzle.

But once they solved the problem, whether they needed hints or not, they felt proud of their work. That was awesome to me. Some of them told me that they really liked the problem. It was a challenge to them, so they had a sense of accomplishment once they had solved it. One student asked if I could give them more problems like that for their homework; the book’s problems are pretty simplistic and generally don’t require them to make connections across multiple concepts. I really need to get better about giving them more challenging problems for practice.

In other news, I am ordering sample texts for almost every mathematics course we offer for grades 6-12. The math department (all 3 of us) will be meeting at the end of March for a day of articulating who we are, and then using those decisions about curriculum. I’m really excited about this. :)

As part of that process, I’m reviewing the calculus materials available from The Worldwide Center of Math, and so far I am loving their model for the modern textbook. Check it out.