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

- match header and descriptor
- place in the order that students learn number

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.

**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!

## About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!

Thank you for the reminder to go back and read Doug Clements’ and Julie Sarama’s book. In the past, I have had teachers work with the ideas–definitions and examples of these big concepts–but never did it as a card sort and poster. Appreciate the idea–and if you don’t mind, will share it with some groups over the summer.

Absolutely! Please share as you see fit (it’s kinda the reason I posted it).

It was an amazing shift for me and it’s been such an eye opener for teachers when they see that children can subitize without counting and cardinality. But then that also bring to light the difference between the conceptual and perceptual subitizer.

Please share how it goes!

I think the cut-n-sort cards are great. I put the book on my Amazon wishlist!

Thanks! Will put the book on my list to read. I love a good math book!

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Hi Graham

I am following all your work and activities. I do have a question based on your trajectory summary. My understanding is that kiddies may not learn these in a specific sequence (not linear). Am I incorrect or is it more linear as you suggest?

Thanks,

Debbie

Hi Debbie,

My understanding is that students work through this progression as if it’s linear although some students may skip stages. I This work is heavily influenced by the work of Doug Clements and Julie Sarama. If you’re not familiar with their work you definitely want to check it out. Great stuff!