Open Middle© Math

Open Middle© problems are challenging, fun problems for students of any age. The idea behind Open Middle© problems is that there are multiple solutions for finding the answer. To solve these and to prove that you have a valid solution, you need to find different possible solutions. Here’s one that I tried:

I tried Multiplying Two-Digit Numbers – Closest to 7,000. For my first attempt, I tried using the digits 1, 2, 3, and 4. I was not really thinking about the impact of place value. I was just wanting to see what happened. On my next attempt, I knew I had to have a significantly larger number so I tried 91 x 52. While that was better, it was still a bit away. My last attempt was 91 x 82. It was closer but I am wondering if I could get closer.

These Open Middle© problems are available by grade level and by different domains, in different languages. Each problem has a hint and a solution. With each of these problems, student can record their different attempts in finding solutions. The Open Middle worksheet provides opportunities for students to record their thinking and ideas for their next attempt.

Where’s the math? For these problems, you can choose the math that you want students to focus on. The Open Middle© problems encourage students to make multiple attempts to find the best solution for the problem, so students are making sense of problems and persevering in solving them.

What grade levels? With all the choices, you can do K through 12+. Adults even have fun with these.

Ideas for Remote Teaching

  • Synchronous Technology – If you are wanting to attempt these with synchronous technology, I would suggest using a template from Alice Keeler. She has created one for equivalent fractions to give you an idea. Each student would be assigned a slide to enter in their attempt. You can find her template here.
  • Asynchronous Technology – Students could fill out the Open Middle worksheet showing their attempts and then share what they came up with for their final attempt.
  • Paper– Students could fill out the Open Middle worksheet and submit that.
  • Homework – Give students one of these to attempt at home and have their family members try to solve it. Have them interview their family members as to why they used the numbers they did. And then ask the students what did they learn from interviewing their family members.

Did you try this activity? What happened? We would love to hear how it went.


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