My 5 Favorite “Open Middle” Problems
submitted by
Laura Wagenman
Chair, MCTM Communications Committee
I stumbled upon Open Middle in 2015 while looking for resources to be used as a warm up that would be easily differentiated for my fifth graders. Jumping in with a two-digit subtraction problem seemed like an easy way to introduce the format but I was taken aback by how difficult it was for many of my students. While we had discussed growth mindset, had been using visual representations, and had engaged in some productive struggle, many weren’t prepared for the level of flexible thinking Open Middle problems required. I was hooked!
Introduced by Dan Meyer, Open Middle problems have “multiple ways to approach and ultimately solve the problem.” Problems can be searched by grade level, DOK (Depth of Knowledge) level, as well as Common Core State Standard. While the site was started by Nanette Johnson, Robert Kaplinsky, Bryan Anderson, Dan Luevanos, and Zack Miller, many other educators have contributed as there is a link to submit a problem.
Whether you use a problem to introduce and gain insight into student knowledge, as practice, or as an assessment, you will find using Open Middle problems will promote flexible thinking, sense making, build number sense, increase use of strategies, and build student confidence as all students are able to enter into each problem.
My Favorites
This is a great problem to find out more about students’ ability with place value. As students tried various digits, I was able to see who was able to regroup as well as who was flexible in thinking. I initially told students to find the smallest difference and found many try four digits then stop. As I walked around asking if there was a smaller difference, students grudgingly tried other digits. It was exciting to see all students access this task, whether they got the smallest difference or not.
This problem was a game changer for me. Starting with the perimeter and working backwards to find side lengths allowed me to ask better questions of my students to increase their sense making and thinking. I reference this problem often when teachers ask about differentiating for students. This problem allowed me to see who knew the difference between perimeter and area and it challenged all students when they had to draw the rectangles that matched their side lengths.
After doing Open Middle problems since the first week of school, I shouldn’t have been surprised when I saw this student’s work. I posed this problem after a lot of work with decimal addition and subtraction. One of my favorite ways to use Open Middle was as an assessment to see who needed extra help. This student’s work showed me that she had knowledge and understanding with adding negative integers. While it was incorrect for this problem, I gained valuable insight.
I used this problem last summer with my daughter who had just finished first grade. As someone who had math come very easy to her, frustration set in right away when she saw addition on one side and subtraction on the other. It led to a very interesting conversation about equality and led to some teaching. We made number cards and she was able to solve it with the help of the Hint drop down next to each problem on the website. She even anticipated my inevitable, “Is there another way to solve this?” question and rearranged the numbers to find another possible solution.
This problem is a fantastic way to start a unit on fractions. As students start making fractions, I was able to see who understood equivalence, was able to compare using benchmarks, and who knew how to create fractions greater than 1. The best part was listening to students explain why they had placed each fraction where they had. If I were to do it again, I would use a clothesline so numbers could be easily moved.