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 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 Kaplinsky, Bryan Anderson, Dan Luevanos, and Zack Miller.

Hello,

First of all, thank you for this wonderful resource! I have been teaching math for 10+ years and always been looking for great task ideas. Now, I am teaching AP Calculus and serving as the Mathematics Program Coordinator at iLearn Schools in NJ. I encourage my teachers to use open middle problems.

Second, are you planning to add any problems for calculus? I think calculus content is a good fit for one middle idea. I looked at the problem submission form and realized that the problem has to be linked to CCSS. If I come across any good open middle problems for calculus, how can I share them with you?

Thank you again for doing this.

Gurkan

We would love some Calculus problems. We just haven’t had any Calculus submissions. Please submit away!