Before I travelled to NCTM I was finishing up some district PL with K-1 teachers. As part of the workshop, teachers were asked to engage in a Number Sense Trajectory Cut-N-Sort

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  • place in the order that students learn number

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Easy enough right?

Of all the times I’ve used this activity only a handful of teachers have correctly ordered the trajectory.  FWIW-I had no idea number sense started with subitizing and comparison either.

Personally, it’s a favorite activity because it helps identify teacher misconceptions, which in turn helps move students through the learning progression.  Even though it shines a light on misconceptions, teachers really like it and that has to count for something.


If you have the chance, do this with your grade level or teachers in your district.

After teachers completed their poster we shared and discussed using the K-1 Learning Trajectory document below.

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Let me be clear… this is by no means my work.

I created this document to be included in the Georgia Frameworks 5 years ago.  This work is a mash-up from 3 of the most respected people in K-2 mathematics and they are educators that have drastically influenced the teacher I am today; John Van de Walle, Doug Clements, and Julie Sarama (who I just realized are on twitter…score!).

I shared this with some teachers after Christina’s session at NCTM.  She did an amazing job explaining the importance of number relationships as mentioned by Van de Walle. Since then I’ve received some emails asking me to share this trajectory, so I figured I’d share here as well.

Be sure to include this book on your summer reading list.  It changed the way I interact with students in the primary grades and I keep referring back to it 5 years later.  Thanks Doug and Julie for making us all smarter!

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