Transform Problem Solving: Push Them to Explain Their Thinking in One Simple Step

A few weeks ago it was time for our daily problem solving block in math class, and I looked over a few shoulders to find the most aggravating thing. The answers written (sometimes incorrectly) with nothing else.

So here was the problem (from Practice Problems for Multiplication and Division):

Jessie bakes cupcakes for her local business.  Six orders were called in on the phone. Each order included a half dozen cupcakes. How many cupcakes should she make?

Young learners are notorious for answering math problems like this:

Problem Solving Answer

That’s it. Granted it is the correct answer, but no explanation of their thinking or their strategy. SO aggravating for a teacher who is constantly pushing for students to explain their reasoning.  SO not in line with the math practice standards and what they are pushing students to do.

So I implemented a little game to help transform problem solving, specifically targeting how they are explaining their thinking. This poster is up hanging on my chalkboard:

Problem Solving Explanation

Here is how the “game” works:

1.  A student rolls the dice.

2.  Whatever we land on is the preferred method of communication for the day. The students must try to explain their strategy on their papers using:

  • words to describe the steps taken to solve the problem, including how you arrived at the answer.
  • a picture or a model of the problem.
  • a number sentence to show how the problem was solved.
  • tools (manipulatives) to act out the problem. We typically gather around a desk (each student has their own bag of tools) to see how they solved it.
  • FREE choice means just that, they can use their favorite way to solve the problem (maybe some other creative strategy beyond any of these four).
  • Teacher’s choice. This is kind of awesome because I can ask them to use number lines, graphs, skip counting or some other type of strategy that is appropriate to the problem type.

3.  The same student reads the problem out loud to the class (twice).

4.  The students solve the problem on their paper as many ways as they can (choosing their best way first), but when they explain it they should try to use the method of communication that was rolled.

5.  Two students are asked to come up to the board to show how they solved the problem, and explain their thinking. At least one of the students must have used the method of communication that was rolled.

Since I’ve started to use this, students have gotten better at showing their work, which in turn has made them better at explaining their thinking verbally. It also leads to awesome questions asked of the students who come up to explain their strategy.

Here is what that same problem looked like after we rolled the dice and asked that same student to use the strategy of a model/picture:

Problem Solving Explanation

Additionally, the other student who came up used a number sentence.

Problem Solving Explanation

Both great strategies!  I love that it encourages the use of different ways to explain, especially when some students get in a rut by only one strategy or one way to explain.  It has also been a big help to students who have trouble putting their picture into number sentences.

The best part? The kids think it’s like they are playing the lottery every day.


Manipulatives Aren’t Just for Kindergarteners

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In our classroom we’ve been working through the math practice standards. We just finished number 5 today: Use appropriate tools strategically. Last year I researched the math practice standards, re-wrote them to be kid friendly, and turned them into learning targets.

I can use the right tool for math, and explain why I chose it. 

We talked about the kinds of tools that mathematicians use, and they came up with a healthy list. After that, I read the problem, made sure to show them where to find the manipulatives, and turned them loose to work. I thought this math practice standard would be a breeze!

Some of the tools I put out:

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In the past I’ve always offered the appropriate math tool for them, taught them how to use it and that was that.  This is the first time I’ve ever asked THEM to choose a math tool from a bunch of options.

I learned today that math tools are much more complex than I expected. The result of today’s lesson was a total surprise.  (I LOVE that even after 8 years of teaching I can still be surprised.)  Every student in the room was comfortable with using the manipulatives, but only about 5 out of 25 were using them effectively.  Rather than thinking about what tool might help them solve the problem, many of them chose tools based on their shapes.  For example, the problem was about cookies, so they picked the fake money manipulatives because they were round and they could trace “cookies” on their paper.  They were using a math tool (clearly not the right one), they could explain why they were using it, but their use of it was not exactly accurate for the problem type.

I took this moment to reflect and think about how I can incorporate math tool use more intentionally. I think that there are many tools appropriate for third grade. I used to think that math manipulatives were just for kindergartners or the early primary grades, but I have realized quickly today that their complexity is vast and allows for deep thinking.  I am excited for the challenge of exploring each tool’s unique properties!

Don’t Be Scared of Those Math Practice Standards!

Don't Be Scared of Those Math Practice Standards!

I will never forget my first reaction when I read through the Standards for Mathematical Practice.


I think it took me another 5 reads to even scratch the surface of what they meant. The rest of the common core seemed like a piece of cake in comparison!

I really tried hard to understand them, but truth be told, I wasn’t sure how they fit in to my classroom. How were elementary students supposed to understand this stuff when I barely could?

As we began to implement the common core, I noticed my students struggling with the deeper problem solving concepts. I was so frustrated. I tried everything…I looked for strategies online to see if there was some kind of magic answer, I asked colleagues what they had tried and began to pull my hair out.

That was when it dawned on me…why don’t I try to incorporate the Standards for Mathematical Practice?  So I dug deep and did some research. One of my favorite things I found is from our friend Marilyn Burns (if you don’t know who this is, get to know her!). Her site is amazing, and the video series is really great.

All of the research allowed me to create a guide to introducing the standards for my students. I started with putting them into kid friendly I can statements. I added some sample problems and allowed the students to see each other’s work habits.

Voila! It was like a revolution was born. One of my students had the idea that we should post the standards on the wall, and get a point every time we had a question or gave a compliment with the language of the standard in our comment. Done! We had points like you wouldn’t believe by the end of the school year. (Incidentally the points counted toward absolutely nothing, they were just points for the sake of getting points!)

Intentionally putting the language of these math practices in our every day commentary did the trick. Students gained confidence, it was fun and best of all problem solving was no longer a stress in our classroom.