PD: A Math Task for Teachers

I’m planning a PD for a group of elementary math teachers that I’ve never met before. This makes things difficult because I don’t know anything about what they know or what their experiences are.

I was told that one of the sessions should be about engaging students in doing mathematics–which is what I think all PD sessions should be about:).  I’m trying to use a math task to engage teachers in doing math before we talk about how to engage students. My goal is to use the task to build some content knowledge around fractions and to have a shared learning experience that we can generalize from. Here’s the task I’m planning on using during the session:

I used the guidelines I posted last time to help me select and modify this task.  Here’s what I was thinking as I planned:

1. The task starts by asking for a prediction or estimate of the final answer:  I added this in because I wanted to get a quick read of the group and to make sure that everyone understood the task. I’m debating about using notice/wonder instead.

2. Knowing the formula is not enough to complete the task: It’s not enough to know the procedure to find equivalent fractions to complete all parts of the task.

3. I can provoke an interesting discussion based on a common misconception. The numbers in the task allow me to pose the following misconception: “The first three situations are equivalent since there is always 1 sandwich fewer than the number of people.”  I’m hoping this will lead to an interesting conversation about why this thinking doesn’t work and what you might do with students that think it does.

4. They have to prove WHY something is true. I like the idea of having them create a poster with convincing evidence that supports their solution. The discussion that comes out of comparing different posters will allow us to discuss what it means to convince or prove in math.  I’m going to encourage using diagrams and I also plan on handing out connecting cubes that they can use to work through the problem.

5. It can be used with students with minor tweaks. The task will need to be modified based on the level of students it’s used with, but I think it could be used across grades 3 to 5.

After we complete the task as a group, I’m planning on using these prompts as a reflection:

  • Doing mathematics: Write a about the activity from the perspective of a learner. Think about the learning processes. What helped you as a learner? What helped you sort out the mathematics
  • Teaching mathematics: Write about the activity from the perspective of a teacher. How is this activity different than other lessons on fractions? What do you like about it? What are some concerns?


The comments you all left last time were so helpful. You pushed me to think about now about how I will decide what warm up task I’ll use, what type of reflection prompts might be helpful and to keep in mind that some teachers that might be uncomfortable with the content.

I’m excited to hear your feedback on this task and any suggestions on how you might change things before I actually try it out.

6 thoughts on “PD: A Math Task for Teachers

  1. Cleargrace

    I am planning a couple of pd activities for the math teachers at our high school. I want to help them learn to use productive struggle, multiple entry points, and questioning to help students who need the extra push, without giving away the answers. I like this task, along with your three stages. The poster is a great way to show the thinking as the ‘proof’. I think you could even use a form of talking points within each group of teachers as they evaluate each of the other groups’ posters.
    I am also using your previous post to make my PD better.
    I am teaching alg 1 and geom this year.

  2. goldenoj

    Your prompts don’t show up for me – I see a Google message that I need permission.

    I LOVE this task, and have used it in several different situations with preservice and inservice teachers. Do you show the video of the teacher? There’s so much for inservice teachers to notice about her class management, questioning and introduction of the problem. Plus, for teachers, seeing students do this stuff is fascinating. Are you going to ask them to do it with any restrictions?

    Great series, Nicora!

  3. Nicora Placa Post author

    Thanks for letting me know about the prompts. It should be fixed now. I’m so glad to hear that you’ve had success with the task. I think it’s such an interesting task for teachers to work through. I really want to show the video but I don’t think I’ll have enough time.

    Also, I’m not sure about what restrictions to place on the task. I wish I had a sense of where the teachers are at in terms of both their understanding of math and beliefs about teaching. What restrictions do you use?

    1. goldenoj

      Depending on context, I ask them something like to perform it without any fraction operations, but instead try to imagine students who have just been introduced to fractions and understand unit fractions. What I want to avoid is 5/6 and 3/4, cross multiply and 5/6 was bigger. For teachers who are as new to me as you’re saying, I might instead just ask them to estimate the order, and try to draw pictures to evaluate their estimates.

      1. Nicora Placa Post author

        That makes sense. I like the idea of having them draw pictures because it might help avoid them going the cross multiply route. Although it might be interesting to see if they can explain why that works. Thanks for the help!

  4. Pingback: Summer PD: The Fair Share Task - Bridging The Gap