So You Took Keywords Away – Now What?

Problem Solving Song
sung to Row, Row, Row Your Boat

“Problems come along in many different ways…
Follow these steps and you’ll find solutions all your days.
Understand the problem then choose a strategy,
Solve, then check your answer so it’s all that it should be.”

This song became the focal point of almost every demonstration lesson I presented as a coach. Every student on my campus, from kindergarteners through sixth graders, would belt it out. Sometimes we would whisper sing, sometimes caveman sing, and always with gusto. Then we would chant, “Understand, Plan, Solve, Check” three times.

This song captures Goerge Polya’s now-famous problem-solving process he wrote about in his 1945 classic, How to Solve It. This book has since become the centerpiece of school problem-solving strategies. Although some sub-divide the steps into 5-8 parts, almost every problem solving process out there is based on Polya’s “U-P-S-Check.”

A group of teachers I worked with a couple of weeks ago became enamored of the Problem-Solving Mat we were using to help children embrace the process and wanted something tangible for showing student work. The mat, linked below, walks students through the problem solving process and provides guidance and space to show work. This seems like a great follow-up for last week’s blog post, Don’t Fall Into the Keyword Trap!

Problem Solving Mat-U-P-S-Check

I’ve used this mat with students for years. Here are some simple guidelines:

1) Understand: Type the word problem in this space ahead of time. You may consider leaving the question off so students can interact with the situation first (see Target the Question in my previous post). Reveal the question only after students have spent time understanding the context, identifying the quantities and relationships, and anticipating possible questions.

2) Plan: Keep in mind that students often confuse representations and strategies when they identify their plans. Help them understand that strategies are the ideas they bring to bear on the problem, while representations are the means they use to show their thinking. For example, a student may use a skip-counting strategy to think about a solution and then use a number line to represent that thinking. In this case, a solid plan would include both the thinking strategy (skip counting) and the representation (number line).

Also note that the planning phase of this process may be not be sequential. Students may identify the plan up-front, or they may start working and “discover” their just-right plan during the process or even after they’re done. You need not insist that they create the plan and stick to it prior to doing anything.

3) Solve: Young children often use manipulatives to help them think through their solution. The Solve section on the mat is large enough for them to use manipulatives directly on the mat and then translate their representations into drawings. Students may also use this section to show their thinking by using numbers, pictures/diagrams, and/or words to convey their thoughts. You may want older students to sub-divide this section vertically so they can record the steps they used on the left and provide justification on the right.

4) Check: Finally, in the bottom row, students record the “simple” answer, typically a number with a unit label. They re-read the original question and answer the question in a complete sentence. Although there are many other ways to “check” a solution, this way reinforces the notion that the solution should make sense as an answer to the question posed at the beginning.

The format on this Problem-Solving Mat has been used with literally hundreds of students with great results. It’s even a focal point for problem solving in The Amazing Ten Frame Series by KP Mathematics. Try it out…and let us know what you think in the comments section below.

Happy Problem Solving!!!!

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

PS – Remember that the Beyond Math Blocks Teacher Institute is coming up in Phoenix, AZ, on October 25-26. My colleagues and I will be sharing this process and many others as teachers reimagine mathematics teaching and learning in grades K-5. We’d love to have you join us! Check it out by clicking here.

PPS – One more thing: Don’t miss Peggy’s latest journal entry on the amazing properties of KP Ten-Frame Tiles this week. It’s about place value. You may be surprised to see that there’s such a concept as the “infinite ten-frame.” Click here to view.