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One Size Fits Most: Open Middle Math Tasks

Open Middle Math Tasks are a hidden gem within the transformation of math education. For generations, math classes purely focused on a procedure directed to getting the correct answer. However, there is currently a big shift in mindset from memorization of procedural fluency to an added emphasis on understanding concepts and building mathematical reasoning. This shift birthed the genius concept of “Open Middle Math Tasks”.


Caution!!!

It’s important to explicitly note: procedural fluency is still extremely important. However, now more attention is designated towards reasoning to help learners identify and correct their own mistakes to become independent learners. As well as, give credit where it’s due to learners who need a structured path to do it their own way with justified mathematical reasoning.


To my knowledge, these tasks were coined by Math Educator, Robert Kaplinsky. Open Middle Tasks simultaneously broadens and intertwines procedural math fluency skills with mathematical reasoning. The fluency comes into play as students complete the same exercise numerous times to construct true mathematical statements. Reasoning builds from adjusting the values with each trial to both fit within given parameters and create numerous correct mathematical statements.


Here you’ll see an example of a 5th grade level open middle math task.



Using an Open Middle Task…


I recommend introducing an open middle task AFTER students have already practiced the procedure with direct instruction. While there are parameters set to use the digits 1 to 9 at most one time each, I find it the most useful to not set limitations on digits when introducing an open middle task the first time. This allows students to bridge their understanding from procedural fluency to mathematical reasoning with less limitations by widening the scope of mathematically accurate responses.


Be sure to emphasize that answers do not have to be identical to be correct and there are multiple, sometimes even infinite correct responses. In fact, greatly encourage learner and challenge learners to find the most correct responses. Initially modeling two or three different correct responses for learners helps them to begin envisioning all of the possibilities before setting them off on their own.





This task will likely engage students in the productive struggle so mentally prepare learners in advance that by nature this task is designed to involve multiple trials and errors so they understand it’s part of the learning task and not a sign that they are failing but rather engaging with the activity. Holding discussions or turn and talks after a trial and error gives the opportunity for students to reason and explain how to improve their response. Additionally, use your discretion from knowing your learners, but I recommend after at least three to five successful completions without digit limitations leveling up the activity to include set parameters. Be sure to display and share the variety of correct responses your learners compose!


To learn more about Open Middle Math Tasks, I encourage you to review resources and materials from Robert Kaplinsky or click here to get a free link to downloadable open middle math tasks for grades k-12. Share any thoughts or questions you have below! If you found this helpful share this story!


Here's a sample of an Open Middle Task completed in collaborative groups from my 8th grade students!





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