Clip 5/13: Lesson Fraction Multiplication Part 2A

Overview

As her students work to describe and classify their problems, identifying which are more like Jesus’s problem (multiplying fractional quantities) and which are more like Camila’s problem (finding a fraction of a whole), Erika circulates around the classroom questioning her students and probing their thinking.

Two of the problems she has given her students do not have visual representations, so she invites them to create drawings of those problems if it would be helpful to their process.

Teacher Commentary

ERIKA ISOMURA: When I was doing this, the planning and the stories and all of those things, I really wanted to give them an opportunity to really experience. Some multiplication is this amount that we're taking a part of and it does feel often a bit like division, even though it's actually a multiplication problem.

Then other times, it's very intuitive that this is a multiplication, I'm repeating, and repeating, and repeating. If it's repeating then I've got all the parts, and I just repeat them a certain number of times then I get that final quantity, versus I have something and I'm taking the fraction of it, which means I'm taking the smaller bit which is going to feel more like division.

After they had decided what kind of problem, they had the option of starting to just play with it on their own. I told one student, "That really does, to me, show that you’re really thinking about what's happening in the problem as far as the quantities.”

What I asked her was, "Now, let's actually be in real life. If you had that box of 8 crayons, it makes sense that you could take half of each crayon, but would you? Would you walk around snapping crayons in half and have all these broken crayons?" Her response was, “No."

Then we talked about in the real world, if you've got this box and I said, "You're only going to take out half of the crayons, what would you do?" She said, "I'd take out 4." Then we said, "That's so interesting because the answer you got by snapping crayons in half was also 4.” I told her specifically that there are 2 different ways that we could be thinking about those numbers, but when we go back to the actual problem, the story, maybe one of them makes a little more sense.