Open Middle: Open-Ended Problems for K – 12

Nannette Johnson, Robert Kaplinsky, and Bryan Anderson have joined forces to create the site Open Middle .  Below is their blurb:

 Dan Meyer introduced us to the idea of “open middle” problems during his presentation on “Video Games & Making Math More Like Things Students Like” by explaining what makes them unique:

  • they have a “closed beginning” meaning that they all start with the same initial problem.
  • they have a “closed end” meaning that they all end with the same answer.
  • they have an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

Some additional characteristics of open middle problems include:

  • They often have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method. Example
  • They may involve optimization so that while it is easy to get an answer, it is more challenging to get the best or optimal answer. Example
  • They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it. Example
  • They are generally not as complex as a performance task which may require significant background context to complete. Example


I like that they are all short problems, so they would be easy to do as a warm-up or assign as a homework assignment.  I also like that there is not always one answer.  This can lead to rich discussions.

There are problems for Kindergarten through High School, all aligned to the Common Core. Below are some examples from Grade 3, Grade 8, and High School.  When a student starts the problem, only the problem is shown.  The “Hint” and “Answer” are accessed by clicking.

Grade 3:

Screen Shot 2015-02-06 at 1.48.51 PM

Grade 8:

Screen Shot 2015-02-06 at 2.01.44 PM Screen Shot 2015-02-06 at 2.02.24 PM


High School:

Screen Shot 2015-02-06 at 1.52.05 PM

Teachers can subscribe to the site to receive emails when new problems are added. Also, teachers are encouraged to submit their own problems.

Good stuff! Check it out!

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