math, Number Sense & Numeration, Number Talks

What you see isn’t what I see

For Number Talks this past week I made some arrays on Smart Notebook and projected them on the board. We spent time each day talking about what we noticed and thought. Early on the fact families emerged. I’m glad because we’ve just finished up some multiplication and division learning and I was glad to see this being put into practice.

On Friday I displayed the picture below:

As you can see there were multiple ways to see this picture. Immediately people saw the array of 4 rows with 3 bikes in each.

One child kept insisting it was 2 groups of 6. It took a minute for him to convince his peers, and I had to help by circling the 2 groups. I’m glad we took the time to let him explain! He was clearly showing some beginning “partial products” thinking and I wouldn’t have known this if I hadn’t probed for an explanation.

Finally someone started talking about the bike tires. I don’t have a photo of that annotation, but it was interesting to see how the students went in to figure out that 12 groups of 2 = 12+12 = 24. Of course they were able to complete the fact family. At this point very few were counting by one’s. I was quite happy about that for sure!

It took me very little time to use the tools in Smart Notebook to make these arrays. I’ve definitely used Mathies for this as well, but the pictures in Smart Notebook led to a deeper conversation. This week I need to find some cars with 4 wheels to expand on our conversation.

This work also builds on the “Eyes on Math” number talks and picture-based number talks we’ve been doing all year. Tomorrow we are going on an array hunt around the school with our iPads. That activity has been preempted a few times but I think it will end up being a better activity now that we’ve discussed the picture arrays a few times.

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