I’m blogging our fractions work daily–read Day 1.
Today kicked off with a quick review of yesterday’s homework. It was pretty simple, just comparing ten pairs of fractions using their fraction strips (no, I had no way to verify and no, I don’t care). Then there were two questions designed for Higher Order Thinking.
…and, close almost kills them. “Which is greater, 4/5 or 8/10? Using your strips, find the two fractions that are most near in value without being equal.” This was definitely a “but, what’s the answer?” moment. The instructions were perfectly clear, you need to fold the strips. But that concept of close really threw them for a loop. Estimation is a scary scary concept for them.
I did a quick overview of number lines, starting to introduce the idea of equal partitions, sequential v proportional reasoning (which number do you place first between 0 and 4? Most of my students place 1.)–but only for a quick couple minutes.
Moving on, we did a couple more comparison problems as a problem to get us warmed up and ready to go, and then they moved into groups and got a set of 10 comparisons. We didn’t want to get rid of context entirely, but we ultimately want them to classify these by type and didn’t want any groups mistakenly using things like, “these were all boys and these were all girls!” or, “these were about food!”
On the document above, they’re organized for teachers; I just made the questions only larger and printed one set per group of four. We gave them scissors to slice up the problems and then they solved these in their groups. I offered up the answers to anyone who was interested to emphasize how little I care about the answers and how much I care about their explanations. Most of the groups were trying really hard, which was awesome. (Side note: it should be missing piece–7/10 and 6/9 is super hard to explain!)
We ended up needing about half an hour to solve them, and then we gave them 10 minutes to sort them into groups of like problems. We brought it back together to generate categories–the students were having great conversations in their groups but were scared to speak up, but we got there eventually. After matching an example to each one, we assigned each group one category to write up for their peers. [This is where I say this was awesome, which I think it will be, but we have a shortened schedule for PSAT testing for sophomores and didn’t finish. Sadness.]
How do you prompt students to answer tough questions without giving them what you want to hear?
I developed this lesson with my team; the file was created by CC.