Solving Math Problems in Three Simple Steps

Last year, I introduced this graphic to students to teach problem solving techniques:


As with any acronym, mnemonic, or organizational concept, this guide, while, comprehensive, didn’t apply to all problem situations. Students were also resistant because they saw it as “so much work” and something I was making them do as opposed to a helpful system for approaching problem-solving.

They would ask me, “Do we have to do the five fingers”?

As the year went on, we discovered a way to condense the method to three steps (the 4th was implied).

This was somehow easier for them to embrace and still covered the essentials.

1. Draw/Visualize
This step is important because there are so many times a student sees a problem as too complicated or has too many elements to begin. They stall out before they get started. I encourage them to draw simple pictures, tables, number lines, etc. to definitively show their understanding. It’s amazing how a simple drawing will help a child interpret a problem. The drawing forces them to read each part and retell it in a different way. This ensures understanding of what the problem is asking from the beginning.

2. Solve
Once they know what is being asked, they usually have an idea of how to solve, in what steps and what operations. Showing each step with numbers is important so that both student and teacher can track how they arrived at their answer. In this way it’s easy to spot misunderstandings of how to solve the problem versus simple calculations errors.

3. Explain (the answer)!
I used to have students explain their process, and I got a lot of, “I carried the ten, then I added the tens, then I…” It was difficult to help them understand what explaining the process really meant, probably because I didn’t have a very good idea either. In addition, the excessive writing felt pointless to them because they had already shown how they solved it. Instead we started explaining the answer, “14.5 dogs fit into each kennel, but because you can’t have half a dog, it’s really 14 that fit…” Again, they’re demonstrating their understanding of the problem. This also gave them an opportunity to evaluate the reasonableness of their answer.

The fourth “implied” step was to reread the problem and their work. Since this is a practice in all subjects, we refer to it, but it’s no longer a discreet part the process.

I’ve come across lots of problem-solving guides, and they all have helpful strategies like”highlight important information” or “use math words”. Students want a system that’s simple, effective and doesn’t feel like busy work. We found that this 3-step system works. Additional strategies like “highlighting important information” may need to be taught to struggling students. Focus lessons on including relevant vocabulary may also be needed if students aren’t being specific enough. In other words, this is a great place to start and then you can fill in the gaps according to what your students need rather than starting with a cumbersome mnemonic or acronym.


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