I'm reading The Problem With Math Is English and the author says “How many times does half go into 10?” is the only question most teachers have. Which is a problem since that has very little meaning to most students. I posed the question to Twitter and offered “How many half units fit into ten whole units?” as the only context free alternative I could come up with. Luckily, my tweeps came through with plenty more!
Bridget Dunbar: how many groups of 1/2 are in l0?And then there were the people who offered a context to explain the abstract question:
Teresa Ryan: Yes. I like using the groups idea.
Tina C: but what is a group of 1/2?
Teresa Ryan: Yeah, guess I should have thought about that longer. I was picturing groups of numbers, and 1/2 doesn't quite work. I guess what I'm thinking is breaking the 10 into individual pieces, then counting how many 1/2's there are
Tina C: that’s exactly what this book is about. Falling back on our ingrained language which doesn’t always help kids.
Kathryn Freed: how many groups of 1/2 an orange could be made from 10 oranges?
Tina C: ooh An orange is interesting. This reminds me of @TriangIemancsd's post on partitioning
Teresa Ryan: I guess I’m struggling with students seeing 1/2 of something as a group
Tina C: I agree-I don’t see half of anything as a group. But we could translate into group language via an orange
Bridget Dunbar: I picture a number line and marking off the number of halves in 10 wholes.
Justin Lanier: "How many halves are there in 10?" There’s also the other interpretation: “If 10 make a half of a pile, how big is a pile’?”
Tina C: I like this question because I find it easier to answer. No one has used that interpretation yet.
Justin Lanier: People tend to avoid this interpretation with fractions. I have shed this prejudice :)
Math Minds: or you could start with 10 divided by 2 ask for multiplication prob u could use to solve?
Paul F: You’re making bread, and your only clean measuring scoop is a half cup. How many scoops do you need to make 10 cups?
Zach Schultz: how many "half Oreos" go into 10 Oreos. ( if we had more half dollar coins laying around I'd say how many of these go into $10)
Jen Silverman: I need to serve each GI 1/2 pound of home-style potatoes How many servings can I get from a 10-pound bag?
Jen Silverman: I had a 10 c. bowl of popcorn. When I split it evenly btwn the Ss in my class, each S got 1/2 c How many Ss?
There were a few people who agreed that "How many halves are there in 10?" would be their go to question. What question comes to your mind first? Which approaches best help students understand the computation?