Math Memos

The Handshake Problem

I first came across this problem in Marilyn Burns’ book, About Teaching Mathematics. That book was really instrumental for me as I started to realize I wanted my math class to center around rich problems, that valued student sense-making.

I like this problem because it seems incredibly easy, but isn’t. I also really like that there are many different approaches/problem-solving strategies that students can use here. I often use it at the beginning of a semester to engage student in a conversation about how multiple approaches that come from them are both valuable and mathematical. Continue reading how Mark Trushkowsky used The Handshake Problem in class »

The Painted Cube


The first time I saw this problem I had my student hat on. As a participant in in group setting at one of the NYSED/CUNY Teacher Leader of Mathematics Institutes I attended, my fellow group members and I were tasked with solving a version of The Painted Cube.

Note: If this is your first time seeing this problem, you may want to stop here and spend some time working on a solution before continuing.

Continue reading how Patricia Helmuth used The Painted Cube in class »

The Paycheck Problem

Update: I wrote another version of the Paycheck Problem that may be more appropriate for pre-HSE classes. The hourly rate is a whole number and the practice test question does not use f(x) notation. Please let me know what you think in the comments below or in the Google Doc --> Paycheck Problem (pre-HSE version)

I don’t have my own class these days, so I’m always grateful to teachers who let me visit as a guest teacher. Angelo Ditta and Will Croxton from LaGuardia Community College in Long Island City, Queens generously allowed me to teach a combined class at their campus on the last day of class so that I could try out this new problem. The students were at a high school equivalency level, but with different levels of math abilities, as is typical of most adult education classes. The students at La Guardia are a wonderful mix of native New Yorkers and people from around the world. It’s an amazing place. Continue reading how Eric Appleton used The Paycheck Problem in class »

Mowing the Lawn: Let Students Ask the Questions

A couple months ago, one of my favorite math Tweeters and bloggers, Fawn Nguyen, posted this, which I promptly liked and retweeted:

Continue reading how Tyler Holzer used Mowing the Lawn: Let Students Ask the Questions in class »

Writing about Math: Solving Equations

Not long ago, I read an article by Marilyn Burns in which she explained how she used to view math and writing as “oil and water.” She thought that the two subjects had nothing to do with one another, and “writing played no role in [her] math classroom.” But now, she says, she “can no longer imagine teaching math without making writing an integral aspect of students’ learning.” In this article, Burns goes on to offer a number of suggestions for how teachers can incorporate writing into their math classes. This article really stuck with me, and so now, at least once each week, I like to ask my students to write about the math that we have been doing in class.

Continue reading how Tyler Holzer used Writing about Math: Solving Equations in class »