Number talk today:
Got a lot of great ideas. A few that struck either me or my students:
- Several students doubled, and then doubled again to make multiplying by 4 easier
- Using the distributive property to break apart 10 and the half seems like common sense, but it was a big hit in two classes. I’m beginning to think that a flexible understanding of the distributive property is a huge part of number sense
- Among students who prefer to operate with improper fractions, there is a divide between students who see the opportunity to simplify the fraction first (21/2 * 4/1 = 21/1 * 2/1) rather than multiplying (one student converted to a common denominator of 4, for 84/4, then multiplied 84 * 4 and divided by 4*1). These are the valuable shortcuts that a) make calculation easier, but b), and more importantly, show an understanding of algebraic structure, in particular the critical importance of the commutative and associative properties when working with fractions.
On this note, I’ve been thinking more about the longitudinal structure of number talks. I’m structuring them day by day pretty randomly — whatever I think will be meaningful is what we think about. I’m curious if grouping them by structures I want students to see would be valuable. On the one hand, sustained practice with a mathematical idea could help solidify that idea, especially in lower-skilled students. On the flip side, math is math, and number talks as mixed practice have a lot of value in messaging math for math’s sake. On top of that, I’m not sure students could keep track of a weekly theme for number talks, the unit we’re in for the rest of class, and then a range of topics for warm-ups and the rest of their classes in a meaningful way. But maybe it’s something to think about.
I wonder if any of the students read this as “How many quarters in ten and a half?”, and got the answer in a jiffy.
I did have two students who said they converted to decimals because that made the most sense to them, but none shared the strategy of thinking of it using money which surprised me.
Being from England I didn’t think of quarters as money, just as quarters, like halves and thirds !!!
I bow down humbly in the presence of such gretsneas.
Interesting. Many of the strategies were clever ways of multiplying 10 1/2 by 4, because students love to multiply by the reciprocal for division. But I’d love students to be able to think like you are as well — considering how many pieces fit into the whole, even with fractions. I wonder if dividing using two mixed numbers could promote this type of thinking.
May I ask what grade this is?
8th
You might really like this book http://www.heinemann.com/products/E02662.aspx
I am a true believer in being deliberate with every “move” I make in my classroom. So your thoughts about a “longitudinal structure” is (in my opinion) a good idea. I would often ask my students if they understood why I set it up a certain way. And sometimes the strategies they are using build of each other.
Just some thoughts 🙂
That book looks interesting — I like the cover!
I wonder how many different themes I could come up with for number talks — whether to divide by operations, by representation, fractions vs decimals, estimation vs precision… lots to think about!