Review: “Building Equations Using M&M’s”

The article describes an activity to support using algebraic techniques to solve linear equations in one variable, intended to directly follow instruction in equation-solving techniques. The author claims that the activity “actively involves students in identifying the variable, formulating an equation, and then solving the equation.” (Borlaug, 1997)

To begin, the teacher distributes small bags of M&M’s to each student and keeps a bag to use for him or herself. The teacher counts each color in his or her own bag and draws and completes a table on the board listing each color and the number of that color found in the bag. The students count their own M&M’s and make their own tables, but they keep their results secret.

The students then receive a list of questions, designed to be set up as equations and solved. The list begins with easy questions that the student will be inclined to “just answer” without algebra; the questions get progressively more difficult, encouraging the students to use algebra to solve them. The teacher selects a student and asks that student to complete one of the questions and then pose the question to the class for their consideration. For example, “I would have to add (or eat) ____ red candies to have the same number of red candies as the teacher. How many red candies do I have?”

The rest of the class works on a solution to this problem. As the questions become more complicated – “If I tripled the number of yellow candies I have, I would have ____ more candies than the teacher. How many yellow candies do I have?” – many students will decide that the algebra techniques they’ve been studying are – surprise, surprise! – useful for solving these problems. For those who don’t gravitate to algebra but who are stuck, the teacher provides friendly nudging. So, the next phase is to build and solve the appropriate equations. A side effect of this effort is that students sometimes discover that there is more than one appropriate equation, depending primarily on what color they choose for the variable x.

The author finds that after the main activity, some classes will be comfortable moving on and inventing their own problems. Here’s one actual example from the article:

I have a total of 61 candies in my bag. I have 9 more brown candies than orange candies. If I eat all my brown and orange candies, I will have 32 candies left. How many brown candies did I eat? How many orange candies did I eat?

This example represents an impressive level of involvement with the material; however, a number of issues come to mind as I consider the realities of using this activity in my own classroom. I would be concerned about my students just eating the M&M’s. I’m thinking of one student in particular, who has no self-control and who is frequently out on suspension for various discipline incidents. He has learned almost none of the algebra techniques that the rest of the class has picked up and so would not naturally be able to participate in this activity without hand-holding. An obvious approach would be to have students work in small groups; however, in this case I can’t imagine him contributing to a group larger than two. Even in pairs, it’s hard to imagine this student not just eating the materials. (I’ve seen him eat paper. Could he resist M&M’s?)

Another drawback I envision in a high-school classroom would be the non-traditional math student who prides himself on creative ways not to do the assigned work. If this student has access to the Internet, he could easily look up the distribution of colors in an average bag of M&M’s and use that to “cheat.” Of course, this would be more complicated than just doing the work and would only lead to approximate answers (due to the actual randomness of filling an M&M’s bag at the factory), but the student would have found another distracting way to avoid learning the material. This scenario is unlikely in most classrooms, especially a middle-school classroom such as mine.

Also, I’m not comfortable with giving candy to kids. Is that what the parents want? What about the teachers who have these kids later in the day? And do I want to fight the trash battle? But are there alternative manipulatives? They need to be similar in size and shape to each other and randomly distributed with a limited number of colors. I’ve seen little plastic colored circular pieces, like transparent tiddly-winks, that are made for overheads. Maybe the simplest solution is colored construction paper cut into one-inch squares and mixed together.

References

1. Borlaug, Victoria. (1997, February). Building Equations Using M&M’s. Mathematics Teaching in the Middle School, 2(4), 290-292.

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