How to Differentiate Math Problem Solving

Teachers ask me all the time how to differentiate math problem-solving when their students are all at different places. You want every student challenged in new and interesting ways, and you want all of them to benefit.

Here’s the real problem. What’s challenging for some students is way too tricky for others. Or you hand out a good task, and a third of the class is finished in minutes and asking what’s next while others have barely gotten started. (Tell me that wasn’t just my classroom!)

So I went looking for a way to get good tasks into all of my students’ hands, with room to expand and extend for the students who were ready. It took me nearly a year of mulling it over, and the result is a set of three-step problem solving tasks I call “Triple Threat”. If you all like this, I think I’ll make other versions as well–this one focuses on addition and subtraction.

Over time, I saw my students get better at thinking outside the box, talking to each other about math, and organizing their work. Here is what I was aiming for.

What I wanted these tasks to do

Get students thinking deeply and actually doing math, then talking about it.
Work for grades 3-5, knowing that students in that range have very different skill sets.
Build in differentiation. Not every student needs to do all three parts. For some tasks we only did the first part, and for others some students moved on.
I loved that I could introduce the task to everyone, but not all students needed to do all parts.
Fit into a full curriculum, as a whole class warm up or a small group task that runs 10 to 30 minutes and stretches longer when the talk is good.

That last one always interested me. A task I expected to be quick would sometimes take far longer, but when the discussion is good and students are engaged, it’s pretty hard to shut down the math.

What one task looks like

Every task I created has three parts, and the original problem stays in front of students the whole time (in other words, they don’t have to flip back and forth to refer back to it!). Here is one of the 12 tasks:

Getting started: Find three consecutive (in a row) numbers with a sum that is greater than 100 but less than 120.
Moving on: Now find four consecutive numbers with a sum that is greater than 100 but less than 120.
Even more: Write your own consecutive number problem. Make sure it works!

Everyone begins with the same problem. Some students stay with part one and dig into it. Others move on to parts two and three. There is plenty to talk about at every level.

How I used these tasks

I’ve had SO many teachers ask what a typical math class looked like in my room, I had to be honest: there wasn’t one answer to this. I ran things on a “menu” system. I had all these tasty options of how to organize my math class and served them up when it made the most sense. Here are a few ways I worked these tasks into the day.

Whole class warm up or bell ringer. The goal is not a correct answer. It is the work of problem solving. Each question has a starting point you can use with the whole class, and you choose how much modeling and help to give. Parts two and three can be used with everyone or just with the students who are ready.

The color slides are perfect to project. Click ahead to show parts two and three, and if students aren’t ready, no big deal, because the original problem appears on every slide.

Problem solving station. Print and laminate the half-page task cards. They are low ink and work well for math rotations, math workshop, and guided math. Having quality problems ready to go saves a lot of time.

Reproducible problem solving journal. The problems are typed up in a journal format, with a full page of work space for part one and parts two and three on the next page. The whole journal, all 36 problems, prints on 12 sheets of paper (without the cover) when you print double-sided.

Some of my students did only part of the collection, and others had the time and motivation to do much more. This is great if you are teaching whole class and want something for students to do if they finish early.

A little something extra. Open-ended tasks also work well for students who need a bit more. This is perfect whether you have one student or a handful. They can work together, practice accountable math talk, and push each other. Remember, students can partner up and work together–it’s a great way to push their math thinking!

Problem solving is not easy

These problems are not meant to be time fillers. They are meant to be rich, meaningful problem-solving experiences, and how you use them is up to you. I know we are all busy, but the time you invest in modeling some of the thinking and strategies really pays off as students become more independent.

When I used tasks like this with my students, the biggest thing I had to work on was saying less. Teachers tend to overteach. We tell too much, and we push our own strategies onto students before they are ready for them. Here’s an example of what that might look like.

Before I gave students the problem about Sam (he subtracts a 2-digit number from a 3-digit number, all the digits are different, and his answer is 85), I thought about how I would solve it as an adult.

I went straight to drawing boxes for the digits. Then I thought about what might get students off track. I did not want to show them my boxes, although I did coach a few students in that direction after they had worked for a while.

I did want to make sure they understood the task and the terms, like digits, so they didn’t waste time. That being said, I didn’t tell them what to do. Students worked in pairs to make sense of it, and then we came back together as a whole group to talk it through and get on the same page.

Three other things helped me build a culture for problem solving:

Process over solution.

Explain to students that there may be multiple answers, and they may not even get an answer. The process is far more important than the solution. A child can work diligently and truly work their brain even without a viable solution. That is a big shift for many students (and teachers).

For this reason, I didn’t make solutions available to students. Organizing work, working with precision, and explaining thinking are also key parts of the process, and students need to see them acknowledged. This kind of problem solving can take time, too. Students may need more than one class period to really dig in.

Build in reflection.

Problem solving is challenging and not black and white, so I liked students to get familiar with self-reflection and self-assessment. The set includes a student self-assessment checklist that you can use as part of the journal or on its own, to show students how important these math behaviors are to learning.

You will also see “prove it” in many of the tasks. We want students developing their critical reasoning and learning to defend their thinking.

Mix up the problem types.

You will notice a variety, from finding the “misfit” to “What are ALL the ways” to “What is the smallest.” These types get students thinking outside the box and making sense of the problem instead of filling in an answer blank. If this kind of problem solving is new for your students, plan on more scaffolded instruction and modeling at first. As students try more, you can take a less structured role.

Try the problems yourself first

For real. If you want to feel what students feel, try some challenging problems yourself. It helps you spot where students might struggle and prepares you to coach them better. Before I gave students a task, I spent a little time working it myself. It put me in that best teaching zone, and I challenge you to do the same.

Want to try the set?

The full resource includes 12 tasks (36 problems in all), a hint page for every task, half-page task cards, 36 slides to project, a printable journal, and a student self-assessment checklist. Take a look at these addition and subtraction problem solving tasks or click the image below.