The idea of a number talk is fairly simple: you give students a problem, and give them time to work the problem mentally....no pencil, no paper, no calculator. Then have a discussion about different ways that students solved the problem.
I was eager to try this idea in my classroom, but somewhat reluctant to give up the time (isn't it always about time!). After attending a session on number talks in middle school, I was convinced that I wanted to make this part of my classroom. It seemed like a fairly easy idea to implement and one that could really be the center of lots of good discussion.
The session that I went to for math talks was a good introduction. We watched some video clips of the instructor doing number talks in a classroom and analyzed them. One of the most helpful things that we did was practice recording the thinking of our partners. Some of the ideas were easy to record, but others were a bit challenging. It was definitely helpful to spend some time thinking ahead about some of the best ways to record strategies to help students understand abstract representations.
So this week, I actually tried out a number talk for my warm up the last two days, and it was awesome! I will definitely be incorporating number talks into my warm ups a couple of days a week from now on. The conversations we had around different ideas was phenomenal. My first piece of excitement came from the wide variety of hands that I had in the air of students eager to share their strategies....and some of them were kids that definitely do NOT make a habit of raising their hand. I have one kid that has been completely disengaged since spring break....like this kid's goal for state assessment was "To try and stay awake".....and he has had his hand in the air the last two days, sharing his ideas. Is that not amazing???!! :)
The other thing that was so exciting was the huge variety of strategies. The first problem I picked was 18 x 5, which I think was a suggestion I got from the session. It was a great problem and it led to lots of different strategies. Our discussion has included some of the following strategies:
- 10*5 + 8*5 = 50 + 40 = 90
- 20*5 - 2*5 = 100 - 10 = 90
- (2*9)(5) = (2)(9*5) = 2(45) = 90
- (9*2)(5) = (9)(2*5) = 9(10) = 90
- 18 + 18 + 18 + 18 + 18 = 90
- 18 + 18 = 36, 36 + 36 = 72, 72 + 18 = 90
- counting up by multiples of 5
- counting up by multiples of 5, starting at 60 since they knew that 5 x 12 -= 60
I was very pleased with this many strategies coming to the surface on our very first attempt! And this one number talk brough up important ideas and vocabulary such as distributive property, associative property and commutative property.
So on day 2, I chose the problem 15 x 8. I intentionally chose a problem that had an even number and a multiple of 5, hoping to encourage rearrangement of factors to get to a multiple of 10. Again, I had tons of hands in the air, and a wide variety of strategies. As with the first problem, I had a variety of strategies used. The most common ones were probably these:
- 10*8 + 5*8 = 80 + 40 = 120
- 15 * 2 = 30, 30 x 2 = 60, 60 x 2 = 120
- 15 + 15 = 30, and there are four groups of 2 15s, so you would have 30 x 4 = 120
My favorite one, however, was the very last one of the day. It came from a student that had already shared one strategy, and as he looked as the wall, he said, "Or you could use a clock. The 15 is like 15 minutes, and there is 4 of those in an hour. So it would take 2 hours to have 8 sets of 15 minutes, and I know that 2 hours is 120 minutes." I mean seriously.....could I have asked for anything more! What awesome, creative reasoning!
So, after 2 short days, I am quickly a believer in number talks in the middle school classroom. I can definitely see a ton of advantages to making these a part of my classroom from day 1 next year.