Diagonals in Rectangles

2024 marks the 10th anniversary of CAMI (!) and to honor all we have learned and all the ways we have grown as a group, we are going into the vaults for a few CAMI meeting, to reopen and revisit some of our early explorations together. This month’s meeting was a new take on a problem we explored in June 2016 at Making and Testing Conjectures: The Diagonal Problem.

We started with a Which One Doesn’t Belong?

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Function Diagrams

I decided to lead a meeting on function diagrams because I’m intrigued by the possibilities of teaching with them and because I wanted to introduce the resources that the math educator Henri Picciotto makes available. I have to admit that I haven’t spent that much time thinking about to teach with function diagrams, but I was interested to see what we can learn together by exploring this visualization. 

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Billiards!

Today we looked at a problem involving rebounding balls on a billiard table.

The rules of our problem:

  • A “table” can have different dimensions (measurements of height and width).
  • A “ball,” modeled by a straight line, is launched at 45 degrees from the bottom left corner of a table.
The ball always starts on the bottom left and goes up towards the top right at 45 degrees
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