Problem Solving Strategies

Problem solving is a huge component of my math instruction. I believe that problem solving should be consistently embedded within quality math tasks, rather than teaching problem solving as an isolated unit. However, I also believe that some problem solving strategies may need to be explicitly taught to students, especially students who lack a repertoire of problem solving skills. Toward the beginning of the school year, I like to introduce five different problem solving strategies using the printables from my Problem Solving Strategies pack in TpT. However, even if you don’t use the packet, you should still be able to gain some useful tips from this blog post!

1. Draw a Picture
2. Find a Pattern
3. Guess and Check
4. Work Backward
5. Make a List

I eventually add Write an Equation to the list, but I typically delay that strategy a bit until I focus on multiple representations in math problem solving. As I explicitly teach these strategies, I add them to a problem solving bulletin board. I’ll add the sixth Write an Equation poster later within that unit.

As I introduce each strategy, I give students a worksheet based specifically on that particular strategy. For example, on the day I introduce Word Backward, we will complete one Word Backward worksheet together, and then students will complete one with a partner or independently.

As students learn and practice the different problem solving strategies, they also add them to their math interactive notebooks. They can reference the examples any time throughout the year.

Occasionally, I’d rather use task cards than a traditional worksheet, so I also made a task card version of the problem solving worksheets. These are great for partner work or math stations.

Once students are more comfortable with the problem solving strategies, I will give them problems where they have to determine which strategy to use to best solve the problem. I’ve found that this is a good scaffolding step for students. Throughout the year, students have to apply the strategies to their math tasks within each unit, so there is constant reinforcement of each strategy.

Teaching these strategies at the beginning of the school year is a great way to prepare students for what I call “Struggle Time”. No matter what group I’m teaching, and no matter what topic I’m teaching the following scenario is inevitable: I explain a task with multiple modes of instruction; I model it; we practice a few problems together; students ask questions as needed; there is an anchor chart or reference somewhere in the room, and the second students start working someone raises their hand and tells me, “I don’t know what to do”. Have you been there before??? I always teach my students that the first five minutes of math workshop they must have “struggle time” before I will help them. I know that initially that sounds harsh, but it’s a great way to foster independence and problem solving. I’ve found that too many students begin to expect or rely on me telling them exactly what to do, rather than experimenting and applying strategies.

Of course, I do teach students what to do if they get stuck. We also talk a lot about having a growth mindset. Almost inevitably, students surprise themselves during that five minutes and they are able to get going on their own. If they are still stuck after five minutes, I try to guide them toward what to do, rather than to tell them what to do-which is definitely a weakness for me! My tendency is to take over, and I know that’s not helping anyone.