I have a confession to make. I love math, but I don’t love teaching all the math topics. Polynomial long division, factor trees for simplifying radicals, hyperbolas, and the formulas for chords and secants and tangent lengths of circles.
Last weekend, I was fortunate to attend the CPM Conference in San Francisco, and meet some new people and have lots of conversations about math. Julie, a #MTBoS friend who I finally got to meet in person, asked me what is my favorite thing to teach? The answer was easy: trig. Specifically, the unit circle and everything about the unit circle.
But this got me thinking, what would be in my list of top 10 things I love to teach or do with my students ? (Oh, and I’m an introvert and this is a great conversation starter at any teacher conference.)
10. I taught Geometry for so many years. My second year of teaching, I bought this workbook (it was 2004 and the internet wasn’t a great resource yet).
There was an activity in which you fold a dollar bill into an equilateral triangle, and then unfold it. The diagram you end up with has so much in it. I loved to do this activity on a minimum day because it didn’t feel like they were doing math, but by the end of the period, they could easily tell me 100 true things about the figure.
9. In Geometry, using graph paper to help students conceptualize area and the area formulas.
When they piece together the area formulas for parallelograms and triangles… the look on their faces. When they finally make sense of something they already knew, it’s my favorite thing.
Specifically, pattern #106. I was stumped the first time I saw this pattern. I don’t want to give anything away, but the number of ways you can describe how this pattern grows is breathtaking.
I love visual patterns because there is always a low-floor and high-ceiling. If is teaching with these where I saw the power in multiple representations to describe the same thing, gives you a more complete picture. My Algebra 1 students at the time, could confidently discuss if a pattern was linear and discuss from the table, graph, equation, and scenario. And they were better at it than my pre calculus students.
7. Using tables for everything in Algebra 1 after we switched to Common Core. The first year my students look at a table of a linear, quadratic, and exponential function and discussed rate of change, I was floored. I had some students do rate of change twice on a quadratic and discover that the “second slope” as they called it, was constant. They didn’t believe me when I told them that they’d just figured something out I didn’t learn until Calculus.
6. Transformations of parent functions with graph dancing. Because dancing is awesome and anytime you can get them up and moving is better than sitting and writing. I stole this from my Alg 2/ Pre Calc teacher.
5. Doing a table to explain zero power and negative exponents. Especially when it’s with a student who was just taught the rule, not why. So 2^1=2, and 2^2=4, and 2^3=8. Then 2^4=16. 2,4,8,16, what’s the pattern? As the exponent increases 1, you multiply 2 to the last on. So 2^5=32. 16•2=32. If you look at the sequence backwards…. 32,16,8,4,2… the pattern is division of 2. Or multiply by (1/2). So the next number is 2^0=1. 2/2=1. And then 2^(-1)=1/2 and 2^(-2)=1/4.
4. For years, I played Deal or No Deal as a culminating activity with my pre Cal students at the end of permutations, combinations, and probability unit. I started by making my own “briefcases” with notecards and progressed to a free version of the game on the Internet. It was the most fun day of the year. And no one ever went home with a million dollars.
3. Reading “the Dot and the Line: a romance in lower mathematics” to my students on Valentines Day. I haven’t done this in a while. I missed Valentines Day, maybe prom?
2. Desmos anything. Marble slides. Polygraph. Desmos graph. All of it. The amount of self checking and exploration and learning and connections my students are able to do with Desmos each year is phenomenal.
1. The Unit Circle. I taught Pre Calculus for 10 consecutive years. There are so many patterns and discoveries in that thing. I was still finding more the last time I taught Pre Cal a few years ago.
So now I’m curious. What are your favorites?