Weird Geometry

Warning, this post contains a large amount of links that are intended to open student’s minds and then blow them away. Use at your own discretion.

I started my geometry class this year with some weird geometry activities. The first was this task from the Harvard project, Balanced Assessments in Mathematics. It asks them to imagine life on a cubical planet. Then after looking more at scale, measurement, and the distance and midpoint formulas, we dove into some taxicab geometry with these problems. We then spent time learning about proofs of angles and segments until we could start talking about Euclid’s Parallel Postulate. I started off talking about proofs by looking at Elon Musk arguing that we are living in a game. We analyzed the argument, wrote two column “proofs” to synthesize it. It has been a wild ride and we are wrapping it all up with the lesson we did the other day, and the project we are finishing now. The lesson comes from this one I wrote a while ago where they blow up balloons and do some geometry on them. Here are the questions they needed to answer for this.

Wrapping up With Some Social Justice

After doing our project on the X Games, and then doing some statistics lessons like our paper airplane competition, I had my students do a final project on whatever they wanted. I asked them to pick a topic and create a survey. We talked about topics related to social issues, topics for changing the school, fun topics, whatever. But giving freedom to algebra students isn’t always easy. My students have had a hard time with math, and school in general and when they are given the chance to say what they really think, it can get a little unruly. Many of them wanted to talk about immigration issues and I had to listen to some loud rants about racism, which is not normal ground for classroom discussions in math, and can be pretty dicey.

Ramping Up the Inquiry

Is real inquiry-based learning possible in a ninth grade algebra class full of struggling learners? If so, what does it look like? Is it rigorous? Can you cover the content?

Here are my quick answers to the respective questions: Of course it is; See below; Yes and schools don’t understand the meaning of rigor (more on that in a future post); Don’t care.

For the past 5 or 6 weeks my algebra 1 kids and I have been working on a project about the X-Games. Specifically we have looked at skateboarding and mega ramps. I chose this project because I currently teach in a school that has a set curriculum and I have to teach quadratics right now. Since the real world application for quadratics has to do with things being launched in the air, I thought the kids could explore ramps and think about what it would mean to bring the X-Games to our town.

What Tony Hawk Has to do With Factoring Trinomials

My freshman algebra kids and I are starting a new trimester and our first project is going to be about the X-Games. On Monday, we kicked it off with this video of Tony Hawk riding a new kind of corkscrew ramp. We talked about it and then I had them inventing a new structure for the X-Games to bring up ratings, and then building their structures with paper. They also needed to brainstorm some problems that would need to be solved in the construction or riding of their structures. We are going to focus on projectile motion in this project but to build up to that we are learning the stuff about polynomials and factoring.

How Food Trucks Will Save Civilization

This trimester, I am doing a project on food trucks in my algebra 1 class. We started off talking about pancakes thanks to a friend of mine, Vanessa Svihla from the University of New Mexico, who gave me a problem to pose, “How many pancakes can fit in my car?” Kids have been working on this problem and other pancake math problems such as “How many people would the biggest pancake in the world feed?” But things were too “mathy” and my classes are kids who have not been successful with math. At all. So I felt like what I was doing wasn’t really going to help them in the end and needed a place to land. It was really bothering me.

I am usually OK with these kinds of existential crisis where I feel like I’m not grounded and everything is falling apart because it usually means that I’m about to learn something great. In this case, I’m just went back to what I already knew, which is that we needed to end this three weeks with a deliverable related to our project at the end of the trimester. I had committed to have one of these every three or four weeks so before Christmas break, so I decided I want to have my kids have a business plan sketch for a pancake stand. That will give us a focus and a way to feel like we aren’t just floating around in pancake batter. So I had them design and start building custom to-go containers with a memorable logo, a menu, and a budget for a crowd.

Absolute Value Inequalities, a Release Valve

I hate teaching absolute value inequalities. Hate it. Like my kids hate kale. I taught it anyway, and my freshman loathed it even more. I could connect inequalities to our project but absolute value was kind of a stretch. “Some anarchist,” I hear you saying. But I’m new at this school and am trying to work with my department as much as possible. So I did it. I did some human number line graphs, an idea I got from Bob Lochel’s blog. I also used this conceptual approach from this NCTM article which helped. But I hate the idea of having a standard that you just “have to teach” but you can’t explain to your students why. That is generally the idea behind “good math teaching” though. You have a list of stuff you need to cover, and the best teachers find the best ways of getting that information across, as if your students were a class of willing receptacles eager to learn anything you have for them because they trust you and just need the best explanation. But if you have been teaching teenagers longer than say, a week, you probably realize that isn’t exactly the case. But still, sometimes you find yourself in that situation even when you don’t want to be. It’s what you get for teaching a subject that most people despise.

Transformations

My students are killing it right now in Geometry. We spent some time learning about rigid motions so that I can use them as the basis for their proofs on congruence. This will save us about 150 pages in the textbook, which I wasn’t really using anyway.

Bare Bones Lesson: Marionettes!

This was apparently a math problem given to a third-grade class either for test-prep or an actual test. It came up on a Facebook group that I belong to:

Jessica has a 45-inch-long piece of yarn. She cuts it into a number of 4-inch pieces. She has 13 inches of yarn left. How many 4-inch pieces does she cut?

Which equation can be used to solve the problem?

a) 45 – 13xn = 4     b) 45xn – 13 = 4     c) 45 + 13×4 = n     d) 45 – nx4 = 13

Give to Cesar the Things That are Cesar’s …

I wrote this letter to a teacher at my previous school who was having trouble reconciling what she was taught about implementing grades and standards and tests into instruction, and what the school does as an innovative project-based learning school. The principal at the school, referred to as Tanya, tells the staff that grades are based on mastery of content, not amount of work turned in, or extra credit, or effort. This was confusing to Kristen because she was having a hard time identifying where this was happening in practice. I wrote this letter to try and help.

Being More Like Malcom X and Saving Babies From Burning Buildings

Here are a couple of letters I sent to a new project based learning teacher. She is teaching at a school that focuses on the health care industry and had some questions about a project on epidemics and math content. Specifically she asked how to get the content into the project and then how to teach it without using direct instruction.