While I was participating in the Twitter #MSMathChat this week, we got onto the subject of having students write problems, which is a strategy I used while my students were working on adding and subtracting negative fractions and mixed numbers. @JustinAion and @J_Lanier strongly requested that I do a blog write-up of how I structured this activity, so here it is.
I have a full class set of individual-sized whiteboard that I find incredibly useful in situations like this. I gave every student a whiteboard, and I asked them to draw a line own the middle and label one side as addition and one side as subtraction. I then wrote a fraction or a mixed number on the board with the instructions “Write one expression for addition and one for subtraction that contain at least one negative fraction and have an answer of the number written on the board.” I also asked that they not write the answer, only the expression. I then collected the whiteboards and handed them back out so every had someone else’s expressions, and I asked them to make sure that the expression was equivalent to the number on the board. I then asked a few students to share. Sharing was very open, because if the written problem was wrong, no one had to know who wrote it because no one had their own board back. As they shared their equation, I asked if they thought it was a correct expression, and then had another student walk through how to get the answer.
I started with 1 2/5, and most students began writing 2 term expressions, but one student in particular wrote 1 2/5 + 1/5 + -1/5, which she thought was gaming the system, but actually gave me a great opportunity to review the inverse property of addition. Once she had written one with 3 terms, other students felt more free to write in more than two terms, and I got some pretty long equations. This made for some excellent expressions (I wish I had taken pictures), and forced a bunch of different students to think about complicated problems. After the students had figured out how to “game” the system by writing simple problems, I would throw a more difficult rule onto my instructions (For subtraction, one number must be a whole number, for addition, you had to use fractions or mixed number with different denominators, etc). As I added rules, it turned into a nice back-and-forth with them trying to fit their “easy” problems into my new rules and me trying to come up with new rules to push them,
Overall, I enjoyed this more than continually having to come up with my own problems for them to solve, and it offered them a different perspective on the operations. They seemed to like writing their own and solving other students’ problems. I can’t think of anything off the top of my head that I would change, outside of giving very specific instruction about them not doodling on the whiteboards. I actually just used a similar activity today where they were writing algebraic addition and subtraction equations with a specified value for X.