I loved seeing and hearing some of them working on this before the bell rang. They were good at finding the pattern and I steered them toward finding the starting value by thinking about what step 0 would look like:
This is where we went with it:
This tied in so nicely with our work with linear relations.
Next up we worked on Fawn Nguyen's staircase steepness activity. They did well and had some good discussions along the way. We consolidated a little by looking at these staircases I drew (sorry for the poor quality of the picture).
They said the height was important so I drew two staircases with the same height. They said that the length was also important. We then tried multiplying the height and length together but ranking those products did not match the steepness of my staircases. Someone suggested dividing (and I heard "rise over run") so we tried that and were happy with the results (interestingly no one suggested dividing height by length). They continued their work with the handout and then compared their final ranking with the original one. No one had gotten it completely correct initially - math is good : ) (or at least better than estimating visually).
We then talked about what the numbers they had just found to represent steepness were... slope! On to some cutting and gluing (the linear part of this and this) in their exercise books. We started filling in those sheets and will continue where we left off tomorrow.