## Tuesday, 23 June 2015

### Exeter Conference - Day 3

This is what I tweeted out this morning:

Next up: Visual Patterns. I started by showing them Fawn's site: visualpatterns.org. I love this site so much. The (optional) homework I gave yesterday was a set of visual patterns.

Each of these patterns is linear and we talked about how we saw each one growing. It was really useful to have the linking cubes when we talked about the surface area of the second pattern. The third pattern is my favourite because there are so many ways of seeing it and you can show that they are equivalent using algebra. If you want to know more, I wrote about it here.

Then I gave them the second set of visual patterns:

It turns out (not by accident) that each of these patterns is quadratic. My big message was that I wanted them to see the pattern in the pictures, not go straight to the numbers. The first pattern has a square in the middle that has side length equal to the step number, so the number of tiles in the middle can be represented by n^2. Each also has 4 extra tiles on the corners so the rule here is n^2 + 4. We found two ways of finding the rule for the number of football helmet in the second pattern. There is one way shown here. See if you can find another. Although some participants did not want to stop working on the patterns, I decided we should move on and look at the other three patterns tomorrow.

I introduced 3-act math tasks with basketball shots from Andrew Stadel found on this page (he is also the creator of Estimation 180). I mentioned that Dan Meyer has many 3-act tasks and that Kyle Pearce has also curated a great collection.

We were running out of time, but I quickly described speed dating. This is a fun way of having students practice a skill that may not be that exciting. I chose factoring trinomials. I have blogged about it here.

I then quickly referenced Michael Fenton's fun Desmos activity: Match My Parabola to end today's class.

I also went to a couple of CWiC sessions today which were great. Philip Mallinson's talk, Solving Quadratic Equations with Origami, was about how to find the roots of a polynomial geometrically. It was great. I'm sure I have seen him give this talk before, but it still made me think and was brilliant.

Julie Graves did a talk entitled Quadratic Models without Quadratic Regression. It was really, really good. We saw how, given a partial data set, we could determine where the vertex of the parabola was and come up with an equation to model the data using only linear regressions. This was repeated for an exponential decay function. I generally love all sessions given by the North Carolina School of Science and Math teachers - they always make me think and I walk away with new tools and ideas.

#### 1 comment:

1. Looks awesome - can't wait for next year!