[Looking for other grade levels? The button below allows you to download all of them or you can look here.]
If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth of Knowledge matrix. I’ll be releasing each grade level separately but if you want to see all of them now, you can download high quality, printable PDFs by clicking the button below.

It includes:

  • Elementary & Secondary matrix (a selection from 8 grade levels)
  • Elementary matrix (kindergarten through 5th)
  • Secondary matrix (6th grade through calculus)
  • 3rd, 4th, 5th, 6th, 7th, 8th, Algebra 1, Geometry, and Algebra 2 matrices (separate matrices for each grade level)


The pictures below give you a preview of what the front and back of the matrix looks like.  Each column explores one of eight topics: equation of a circle, central, inscribed, & circumscribed angles, perpendicular lines, area on a coordinate plane, geometric proofs, midpoint of a line segment, sector area, and transformations.

You’ll notice that the first problem in the column is traditional and familiar. It’s something you’d expect students in your class to eventually be able to figure out. Then look at the Open Middle problems at DOK 2 and DOK 3. You’ll notice that they’re on the same topic, yet are significantly more challenging. You may start to wonder whether or not your students can solve them, and what that may imply about how well they understand the concept.




Want answers or more Open Middle problems?
If you like these Open Middle problems and want to see the answers (I’m still working on getting them uploaded) or want to find more DOK 2 and DOK 3 problems, check out openmiddle.com.  Open Middle is a collaborative website where all problems are free and new submissions are welcome.  The more problems people submit, the more problems we all have access to.


Want more support?
If you’re looking for more support with implementing Open Middle problems in your classroom, I’ve got three options for you to consider:


One of the problems in this matrix was created by other people and I want to say thanks for their contribution.

  • The DOK 3 geometric proof problem was a collaborative effort of Jose De La Torre and Nanette Johnson answer by Ricardo Navarro with help from Robert Kaplinsky


I’m sure that there will need to be tweaks to this matrix, so please let me know if you have any questions, concerns, or suggestions in the comments below.

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