It’s Thursday, which means at 2:00, I’m off to Mrs. Quick’s class to play math with the first graders. Hooboy, they were wound up today. This was going to be fun.

While scanning through the Math Forum’s problems of the week, I came across this one about puppies. And who doesn’t like puppies?! Puppies and math! Double win.

Being new at this whole elementary classroom thing, I naively thought that maybe this problem would be too easy. But trusting my pedagogical prowess (and the expertise of the Math Forum’s problem-writing team) , I was confident I could extend the problem if necessary.

Again, we were in rotations with groups of 4 – 5 students each. I had a student read the problem out loud (note to self: In the future, have copies for the other children to follow along.) The next thing ABSOLUTELY BLEW MY MIND, again, because of my initial thought that the problem would be too easy. Out of the 20 students I worked with, exactly 2 of them got the right answer the first time they approached the problem. And the other 18 all did the same thing: 4 + 2 = 6. I was so delighted with this, I might have actually let out an audible squeal. Their explanations all revolved around the same main theme: *There are 4 of something, 2 of something, and the questions says ‘altogether.’ Therefore, 4 + 2 = 6. *

I asked them what we knew about the problem. We knew we had 4 crates and 2 puppies in each crate. I then prompted them for how we could model the 4 crates. We love drawing on whiteboards. So we drew 4 crates. Then the wheels really started churning. Puppies, in crates. We got this.

Then we had to make sure we were convinced that the answer was truly 8 and not 6. A few groups had time to tackle the “extra” question: Can there be 9 puppies? Why or why not? One thing was clear: we were absolutely certain there could NOT be 9 puppies altogether.

My favorite “why nots”:

*There are two puppies in each crate and the answer has to be an even number.**The answer is 8. There can’t be 9 because we just convinced ourselves that the answer was 8.**If we had three crates with 3 puppies in each crate then there could be 9.*

What I love about these 1st graders is all of their thinking and reasoning relies on their own sense-making. Very little of their explaining involves a reliance on algorithms and memorized processes.

I’m marking today’s experience solidly in the win column. All of us learned today. I learned more about how to facilitate problem solving with first graders, and each and every student shared their mathematical thinking today on a non-routine problem. Moreover, we were convinced that there are 8 puppies and not 6. And we all know that 8 puppies are much better than 6.