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About

The name “Open Middle” might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:

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

Open middle problems generally 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 generally 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 such that it is easy to get an answer but 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

We hope you enjoy these problems.  Please be sure to send us any ideas for problems we can add.

Nanette Johnson, Robert KaplinskyBryan Anderson, Dan Luevanos, and Zack Miller.