I've talked about Number Talks before. Recently I've had the chance to do a couple of number talks in a local sixth grade teacher (thanks so much to the teacher and kids for welcoming me!).
Since I didn't know the kids at all I did a couple of dot cards for the first number talk.
Here are some of the students' strategies (hexagon on left and triangle on right):
"An Honest Mistake" as an Opportunity for Deeper Thinking
One student initially said there were 12 dots in the triangular arrangement. After a few people shared their strategies she said her answer "was an honest mistake." I asked her if she would explain what she was thinking. She saw the triangle as split into two halves: She saw 6 solid dots on the left half, then doubled that to get 12.
Of course, when doing this she's double counting the two middle dots as shown below.
It would be perfectly fine to stop here after the student had explained her thinking, but instead I asked the class to talk to the people next to them and see if they could start with this kid's thinking but adapt it to make it work. Take a minute to think about how you would do this...
3...
2...
1...
My first thought was to subtract out the dots that were double counted, so it would be "6 + 6 – 2" because there's 6 on each side, but 2 of them were double counted. But one student came up with another strategy: "2 × (4 + ½ + ½)" which looked like this:
I love seeing new strategies that I hadn't thought of! Also, I was so excited that we could take "an honest mistake" and come up with a new idea out of it. I thanked the student for being willing to share their strategy that didn't work and pointed out how we were able to use it as an opportunity to do some interesting math thinking. Teaching moves like this treat mistakes as normal and as opportunities for everyone to learn more.
Leave a Comment
Short Link for this Post: https://goo.gl/VYH3vF