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Open Middle Math Depth of Knowledge Matrices by @robertkaplinsky

Open Middle Math Depth of Knowledge Matrices by @robertkaplinsky

Guest Blog post by Robert Kaplinsky

Ready for a problem that will make you rethink how we teach students mathematics?  Try solving the fourth grade problem below in less than three attempts.

Using the digits 1 to 9 at most one time each, place a digit in each box to create a fraction that’s as close to one as possible.  

For example, you could use the 1, 2, 3, and 4 to make the fraction 12/34.  Is that as close to one as you can get?  Also, this is not the Price is Right so a little over 1 and a little under 1 are both great.  Good luck!

Open Middle Problems

We call these kinds of problem Open Middle problems and there are hundreds of them available for you to use for free on openmiddle.com.  Below you’ll see matrices that compare traditionally used problems to Open Middle problems.  Use the button below to download high quality, printable PDFs of all of them or preview what you’ll get by scrolling below.


Elementary & Secondary Matrix

Elementary Matrix (K-5)

Secondary Matrix (6 – Calculus)

Third Grade Matrix

Fourth Grade Matrix

Fifth Grade Matrix

Sixth Grade Matrix

Seventh Grade Matrix

Eighth Grade Matrix

Algebra 1 Matrix

Geometry Matrix

Algebra 2 Matrix

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