Open Middle provides higher critical thinking math problems for students. DOK 2 and DOK 3 level math problems require students to strategize and figure out how they would solve the problem rather than being expected to know what the first step is. Oftentimes Open Middle uses a style of question where students can only use certain digits that need to fit a pattern.

Multiple Attempts

It should be expected that when students tackle a higher critical thinking math problem that it will take them multiple attempts. Notice in this paper version (intended to be printed) it provides room for 6 attempts. Personally, it took me more than 6 attempts to solve this problem. Additional paper was needed. However, providing students a structure where it is clearly conveyed that they are expected to make multiple attempts helps students understand that this is part of the process of tackling a higher critical thinking problem.

Digital Version

For students tackling the problem digitally or collaboratively, Google Jamboard is a nice option. Adding the digits allowable for the Open Middle problem helps students to keep track of which digits they used and helps prevent them from accidentally reusing a digit. In my Jamboard template I have added images for the students to use with the Open Middle problem. They can then drag them from the bottom of the frame up into the empty boxes of the Open Middle problem.

Explain Your Strategy

Instead of “Show your work” we ask students to “share their strategy.” The initial strategy is to simply drag the numbers into the boxes and see what happens. Students add a sticky note to the Jam to explain why they put the numbers where they did.

Duplicate the Frame

Students may want to duplicate the frame using the Frame Bar in Google Jamboard. This allows them to build on their strategy and explain their thinking. Students will click on the rectangles icon at the top of the frame, this is the Frame bar. Hovering over the frame thumbnail, 3 dots will appear. This more options menu allows for the frame to be duplicated.

Duplicate the frame in Jamboard

At Least 3 Attempts

Share with students they should have at least 3 attempts, probably more. Google Jamboard allows students to have up to 20 frames. If they need more than this to show their attempts they will need to continue in a 2nd Jamboard.

Discount Example

I also created a Google Jamboard sample Jam for discount.

Solution Spreadsheet

Many Open Middle problems have more than one possible solution. Using a spreadsheet I went through multiple attempts to find one possible solution to the sample problem.

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