[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: evaluating expressions, rounding decimals, multi-digit multiplication, multiplying decmials, subtracting mixed numbers, multiplying fractions, fraction division, and volume of rectangular prisms.

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 another person and I want to say thanks for his contribution:


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 am a assistant principal in the state of Tennessee and just found out about your resources through Twitter and really like what I am seeing! I do however want to ask if these DOK worksheets line up with the Tennessee Math Standards or could I share the standards with you and get more input as to how they line up? We are constantly looking for ways to help our teachers better our students and prepare them for end of course assessments. Thank you in advance for responding!

  2. Hi! I am so thankful for your Depth of Knowledge resources for 5th grade. I noticed there are questions from eight topics. Are the other topics available and I am not seeing them? Or, how were these eight topics chosen versus the others? Thank you in advance!

  3. Hello, I like what I am seeing, I am from Texas and we don’t do Common Core. Do your worksheets line up with Texas TEKS?

    • This is not meant to be a worksheet or something you would give to your students. This is meant to be a way to show how we can take a single concept and interact with it at increasingly deeper levels. If you don’t use Common Core, then I would pay more attention to the row labeled “Topic” and look for topics that align with what you teach.

  4. Mr. Kaplinsky, I’m working on a teaching assignment and your site has helped me tremendously. Thank you for making things so simplified!!

    Dawn F.

  5. Do you have the DOK matrix for whole number division and decimal division for fifth grade? This chart is very helpful. Will all the standards be added?

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