Here’s the version of their documents/ideas we used in class this past week Day 2& Day3.
After discussing a few of our friends issues from Day 1 – Students were asked to work alone on Day 2 – where Blurpo was burping up graphs. After a while – I asked students to turn and discuss their responses with a neighbor – discussing any differences they may have had. We then had a whole class debriefing utilizing desmos. It was a great way to introduce them to desmos.
The sliders really helped when students commented the parabolas – one was wider than the other and others argued they were the same graph, only transitioned down 2 – which made it appear wider at a certain point because the original was “inside” the translated one.
I also had some pipe cleaners to demonstrate the width actually held the same.
What I like most about this day was the 3rd graph, they had to provide the burped up version – and the last graph, where they were given the burped version and had to describe the “eaten” graph.
I used this to share how their brains were processing the patterns to provide structure to apply the pattern to a new questions. And how being given a “backwards” problem required their brain to think in the other direction as well. When many of them continued the original pattern and was wrong, they realized their mistake and was able to correct it. Our brains just grew! Twice! We talked about how it was not a misconception (they didn’t understand it) but a mistake (not paying attention) that they were able to correct on their own- not needing me to tell them “how” to do it.
Day 3 is a perfect intro to visual patterns. Students were given the choice to work on their own, in pairs or a small group. Linking blocks were available for those who wanted to “build” Spikey’s patterns. I enjoyed observing their different approaches to building/drawing the patterns. It was fun listening to their discussions of how to continue the patterns or figuring out how to find the number of blocks required to build the nth pattern without actually building/drawing it. Again, the power of SMP at work.
These are some of the strategies I saw/heard along with some of the equations a few developed.
It was a great way to allow them to see how others were viewing the patterns. And when asked which method was better? Silence. Finally, a student says, well I liked mine best until I saw ___’s and it makes more sense to me now. But we all agreed there were multiple approaches and the one we should choose is the one that our brain sees.
We only used different equations to show they would result in the same number of blocks needed for a given step. I didn’t do a very good job of connecting their equations to the methods used to build the patterns – something I definitely want to improve in the future.
Again – I want to shout out to @cheesemonkeysf and @samjshah (was @mathdiva77 in on this as well?) – thanks guys!