Math Memos
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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:

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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.

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The Movie Theater Problem

I wanted to share some feedback on this problem because it’s so similar to the Goats and Chickens Problem that Daphne Carter-McKnight wrote about recently. You can read her fantastic writeup of the problem here. I like to use the Movie Theater Problem to assess how well students are able to make connections between the two problems and to see if they’re able to try some new approaches that maybe they didn’t try the first time around.

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The Goats and Chickens Problem

I chose to write about this problem because I love it! I love:

  • the variety of possible solution methods: arithmetic, algebraic, pictorial, mathematical, and representational;
  • the humor inherent in the problem;
  • the potential fun for students and their joy in working it out;
  • the gender switch on Farmer Montague;
  • seeing the different ways students draw the chickens and goats;
  • being surprised at who solves the problem and how;
  • seeing the light come on in students’ eyes when they arrive at the solution.

This problem pushes students to think outside the box. It is non-discriminatory in that I can, have, and did give this and a similar problem to students learning at the most basic level and those taking the HSE exam in the same week.

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The Ice Cream Combinations Problem

With this problem, I hope to observe how students will organize data and if they are able to recognize patterns. I also wanted to see what counting techniques the students might use to find all of the possible outcomes. Some of my students have experience developing harts and graphs, while others are new to these concepts. I was interested in seeing which students would figure out different solutions and help others to formulate solutions if they were having difficulty. My class is composed of students with math grade equivalents between 5.0 to 11.0 on the TABE.

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