My students have been working hard this year to improve as problem solvers. We consistently take time to talk about what makes effective problems solvers and practice the skill of problem solving. Last week I talked about the Three Reads strategy we use in our classroom.
Another strategy I like is giving students the answer and having them create the problem. Recently I gave my students three prompts:
- Write a division problem where the quotient would be 6r3.
- Write a division problem where the answer would be 5 1/3.
- Write a division problem where the quotient would be 7r3 but a mathematician would add one to the quotient to report the answer as 8.
Students had the option to brainstorm with a partner before writing. Each student had to create their own problem. My goal was to get students to think about the structure of math problems – narrative and expository text combined.
One of the first things I noticed was students struggled to create the complex narrative structure that exists in most fourth grade word problems. This made me wonder if one of the obstacles for young mathematicians is they struggle with the narrative component of a word problem.
Most of the problems students initially wrote for #2 were similar to this: There are are 16 cookies for 3 kids. How many cookies does each person get? These problems lacked the character names and any extraneous information that often appears in rigorous problems. They also lacked the need for multi-step problem solving.
The conversations with students after they wrote their problems was wonderful. I had some of the students go into their math books and look at similar division word problems. This helped them better understand the structure. Other students practiced writing some problems with me. In both cases, we talked about the “story” at the beginning of problems with characters and a scenario which creates the necessity to solve a math equation. One student actually said, “Ahhh!” The lightbulb went off.
This exercise made me realize the value of students looking at math problems to analyze the structure of how a problem is put together instead of trying to solve it. All of the problems we revisited had already been completed, so the student could focus on how the problem was written.
It’s another tool in the problem solving toolbox which I hope will continue to grow for me and my students.