I had the exciting chance to do a Number Talk with a 1st grade class last week! Looking back to where these students ended the year, I was fairly comfortable starting with ten frames and entering into talking about teen numbers within this context.
I started with the same ten frame I did in 2nd grade, that I talked about here. Looking back, I wished I had started with a full row of 5 just to talk more about how they saw it or just knew it in relation to the 10. Next time:)
I then wanted to see how they thought and talked about a full ten frame and teen numbers. Did they count on from 10, just know 10 + 5, and/or talk about teen numbers as 10 and some more? So I posed these ten frames:
The students had some wonderful explanations of how they saw the dots and established how they just knew the ten if it was full. Some added on by ones to 15, some knew 10 and 5 was 15, some counted by 5’s to 15 and then one student some creative grouping vertically by 6,6,and 3. So I then pushed them a bit on how they recorded the equations and I was excited to quickly get 10+5= 15 and 5+5+5=15.
My brain right now is algebraic reasoning all they way so I could not pass up the opportunity to do this:
10 + 5 = 5 + 5 +5
I asked them if they thought their teacher would mark that right or wrong and why? I had them turn and talk to a partner and after a quick raise of hands, I could see the class was split on whether it was right or wrong. I asked those who said it was wrong why and got what I was expecting…
“After the equal sign can only be one number, no plusses. If you changed those lines (equal sign) to a plus, then maybe it would be right.” In reading Thinking Mathematically and Connecting Arithmetic to Algebra, I am finding this is a huge misconception that students build from K.
I asked the students who thought it was right to explain why and I got two uniquely different ways of thinking algebraically about this equation.
“They are the same because 10+5 is 15 and 5+5+5 is 15 so they are the same.” This student is looking for balance, this side equals that side so it is equal. I could assume that given 12 + 6 = _ + 5 + 6, this student would think they need 7 more in the blank to balance both sides.
The second student said this:
“The 10 is a 5 and a 5, so it is the same as the other side.” This seemed quite different to me. It felt like a symmetrical way of looking at equations. He decomposed the numbers to prove they were equal by the way it looked. I could assume that given 12 + 6 = __ + 5 + 6, this student may decompose the 12 to 5+7 to find 7 is the number that goes in the blank to make it look equal. A bit different and something I really hadn’t thought about until now.
Thanks to Michael Pershan to making me think (obsess) over the ways in which students think about these in such different ways 🙂
These were the last two in my talk that I did not get to because these 1st graders had so much to say about the first two and I had so much to learn!
Looking forward to working so much more with these kiddos!