**Cathy Yenca** gives Graphing Stories a go and the going gets tough (and interesting) when she runs into Christopher Danielson’s step-function:

The last video we tried today was Ponies in Frame. I heard the most awesome muttering as soon as the video began. “Oh! I get it. This one’s discrete.” [..] It wasn’t all lollipops and rainbows. A comment laced with negativity that resonated with Lauren and me was an outburst that “graphing used to be so easy, and this just made it hard.” How would

youtake a comment like that? What does that comment say about the student’s true level of understanding?

**Jonathan Newman** has his students analyze parametric motion by creating stop-motion videos.

**Nicora Placa** reminds us that the one of the best ways to assess a student’s understanding of direct proportions is to give her an indirect proportion and see if she treats it directly.

At a workshop last week, the following task caused a bit of confusion. “If a small gear has 8 teeth and the big gear has 12 teeth and the small gear turns 96 times, how many times will the big gear turn?” Several participants were convinced it was 144.

**Megan Schmidt** uses one of the Visual Pattern tasks and surprises us (me, at least) with all the different interesting equivalent ways there are to express the pattern algebraically:

They came up with the following pre-simplified expressions for the nth step:

2n(n+1) + 3

1 + (n^{2}+n^{2}) + (n+1) + (n+1)

2[n(n+1)] + 3

2n(n+1) + 3

3 + [(n+1)n] + [(n+1)n]

3+2(n+1) + 2[(n+1)(n-1)]

2n^{2}+ 2n + 3For each of these, I had the student put the expression on the board. I then had different students explain the thinking of the student who came up with the expression and relate it to the pictured pattern. I saw a real improvement here from when I had them do this activity the first time last week. I had many more students volunteer to explain the thinking of their cohorts and much less hesitation to work out what the terms in the expressions represented.