[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: markup & discount, unit rates with fractions, adding and subtracting rational numbers, multiplying and dividing rational numbers, probability, solving two-step equations, circles, and complementary & supplementary angels.

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:


Some of the problems in this matrix were created by other people and I want to say thanks for their contribution. Those problems include:


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.


  1. I attended your seminar in Nebraska recently. You had mentioned you would soon be releasing more DOK Matrices; however, I’m unsure if that means a more comprehensive set for each grade level, or if that meant you would release 2-page sets for more grade levels.

    I value these and would love to use them frequently. This is a product I would invest time and my own money to implement for my students on a regular basis.

    • I’m not sure if I understand your question Carina. So, here’s what I have (and they’re all free):

      – My first DOK matrix covered topics from all over elementary and secondary
      – Then I made ones that were specifically for elementary (K-5) and another for secondary (6 to Calculus)
      – Now I’ve made ones that are specific to 3rd, 4th, 5th, 6th, 7th, 8th, Algebra, Geometry, and Algebra 2.

      With the grade level specific matrices, you can download them all right now by clicking on the button above. I’ll be blogging about each one separately over the coming months. Let me know if you have more questions.

      • I was wondering if you were going to eventually go more in-depth for each grade level and cover more of the standards.

        • Right now, my only goal is to make matrices for K, 1, and 2. Other than that, I would go to openmiddle.com and get lots of problems on lots of standards.

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