Open-Ended Math

I've been using a blog for math since December. I'm finding it pretty successful on many levels and wasn't aure that it would be this successful. With my background in Responsive Classroom I like to incorporate academic choice and challenge by choice. I try to make it a point that the children have a choice in how they solve the problem and where they enter the problem at. Does that sound tricky, making a math problem do those things while also ensuring that they are working cooperatively?

I spend time introducing math materials to my students. Base-ten blocks, counters, fraction rods, rulers, etc. Anything they need to use in math I make sure we take the time to learn how to use and care for it. I find this important to do because I want my students to use them if they need them. As new materials are introduced, they are added to their math tool kits. I also make sure that we have plenty of grid paper handy of various sizes in case it is needed. Having the materials out and handy makes a big difference when it comes time to solve problems.

When I first started to create open-ended math problems I began simply. At the time I began we were learning multiplication and division. A post looked something like this:
My four friends came over for lunch the other day. One of them brought brownies for our
dessert. When she cut the brownies, there was enough for each of us to have the same
amount. How many brownies could each of us have and how many did she cut? Explain how
you found your answer.
This was one of many problems we used for the children to learn the fives facts.

By this time the children had identified a strategy that worked for them: equal groups, repeated addition, arrays, or skip counting. They also identified the materials that worked best for them: dry-erase boards, counters, or graph paper. These two choices building Academic Choice because the children were able to choose the how.

As you can see from the problem, it is designed to be Open-ended, allowing the children to choose how to challenge themselves. For some of my students, discovering that we each had two, 2x5=10, was challenging for them. Whereas for others, discovering that we each ate 12, 5x12=60, was challenging. And all of them took the time to find multiple solutions to the problem.

Now that we are working with money, I have made the posts much more complex. I still want the children to practice their multiplication facts, paticularly the 6,7,8, and 9's while at the same time subtracting money amounts. One of the posts the children will be doing in the next couple of days requires them to choose a number of friends (over 5) to take to the movies. They then have to choose which movie they will see (Pirates of the Carribbean or Kung Fu Panda) ANd how they will see it (2-D, 3-D, or IMAX). Then they have to determine which snacks they will buy, all while staying under a $100 budget. This problem still builds in all of the choices of the earlier problems, but are now learning some ways to organize a lot of information using graphics.

And all the while the children are required to work cooperatively, with a partner to solve the problem. They post their solution together, and if they have time they provide feedback to their classmates on their response. And of course, we come back together to talk strategy. I think we all enjoy this because the children have the opportunity to share their expertise. It may sound like something like this will take a lot of time, but it takes anywhere from 45-60 minutes a day. On most days, the children have ample time to hop on an online game that allows them to practice math skills. Every mow and then we spend a couple of days on a problem, but that's usually to provide the children with an opportunity to find a new solution to the problem.


  1. Thank you so much for writing this. I am meeting tomorrow with my grade level partner, and we are planning math instruction for next year. I plan to show this to him. We do lots of problem solving, and we struggle to make it meaningful to students. I really like this idea.


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