## Trying to find math inside everything else

### Making It Stick

After going to Anna Vance’s session on Make It Stick, I implemented some of the ideas she presented and thought I found reasonable success with them. However, as I hadn’t read the book, it was a little half-hearted and could be improved. When I was looking through my library’s education e-book collection and saw it there (amidst a sea of worthless looking books, save Other People’s Children, which I also checked out) I decided to pick it up.

A few things stuck out to me, some of which I tweeted, but the one that I keep thinking about is the Leitner System, which they describe thusly:

This struck me for a few reasons. First, I love the idea that the “flashcards” don’t have to be what we typically think of as flash cards, but rather representations of anything we need to practice. Second, it’s a system that is learner-led, so if I can get my young mathematicians onto the system, they can run it themselves. (And extend it to other parts of their lives.)

So my thought became thus: how can I weave this system into my classroom? Here’s my thoughts. I’d love some feedback.

1. Create a system of boxes (folders? tabs?) – I’m envisioning four in a set – for each student.
2. At the end of each lesson, have the class write on (an) index card(s) something from that lesson that they think they should know. (This practice of summarizing their learning is also mentioned in Make It Stick.) It could be a knowledge fact (the definition of a polygon), a skill (solving a linear equation), or something broader (what are some ways systems of linear inequalities are applied?). If it is a skill or broad question, it should not have a specific example. (So they shouldn’t have a card that has them solving 3x + 2 = 8 every time they see it.) Then put those cards in box 1.
3. Their standing HW is to practice whatever is in Box 1 every day. If it says something like “Solve an equation,” they need to generate their own equation, then solve it. (Generation is also mentioned by Make It Stick as a way to increase stickiness.) When they get it right, move it down a box. When box 2 is full, practice those the next session, and so on.
4. On Fridays, give some time in class for students to practice, especially their box 2 or 3, if they didn’t have the time to do that at home. Then give the usual quiz.
5. After taking a quiz, they should then reflect on what they did and didn’t know, and if there is something they didn’t know that isn’t on one of their cards, make a card for it right then and put it in box 1.
6. To qualify for a quiz retake, all the topics for a quiz need to be on cards in Box 3 or 4. Otherwise, they need to study more before they can retake. (This would mostly be an honor system, as nothing stops them from just putting the cards in there.)

Does that sound feasible? What needs improvement?

### The Secret of the Chormagons

(Doesn’t that title sound like it should be a YA fantasy book?)

I shared this Desmos Activity Builder I made on Twitter, but never wrote a post about it. Oops! Let’s do that now.

First, here’s the activity.

This activity is basically adapted from Sam’s Blermions post that I had helped him think about but he did all the hard work of creating questions and sequencing them. I’ve used the blermion lesson in the past and it went well, but that last part lacked the punch I was hoping for, having to work with analog points and compiling them together myself. But then I thought – wait, Desmos AB does overlays that will do this beautifully, if I can just figure out how to get the Computation Layer to do what I want. So I set to it.

The pacing helped pause things to conjecture about what chormagons are – I stopped them at slide 5 so they can make those conjectures. I then advanced the pacing to 6 for the “surprise,” and 7-8 to make further conjectures. Look at some of theirs below.

Even showing them everyone’s, I tended to get conjectures about the shape their points make – a trapezoid, a pentagon, a heptagon, etc. (One person seemed to guess the truth, but that was uncommon.)

Then I showed them the overlay.

I saw at least one jaw literally drop, which totally made my day. We talked about why it might be a circle, and what that means for these shapes, then I introduce the proper terminology “cyclic quadrilaterals.” (I taught this lesson as an interstitial between my Quads unit and my Circles unit.)

Speaking of proper terminology, you may notice I called them Chormagons here, as opposed to Blermions. That’s important – Blermions is very google-able, it leads right to Sam’s post! But Chormagons led them nowhere. (And they were so mad about that!)

Now Chormagons will lead right here. So this is an important tip if you use this DAB: make sure you change the name of the shape!