Clip 4/13: Lesson Fraction Multiplication Part 1

Overview

Erika begins her lesson by engaging her students in a conversation about the terms whole and part, activating their prior knowledge with mentor “string” problems, and asking the students to identify the parts and wholes in each scenario.

Her students then work with new problems, sorting and describing differences and similarities between the new problems and the ones they’d done before: “Are any of these problems a lot like Jesus's problem, where he already knows his pieces or his parts, but he needs the whole amount? And are any of these problems like Camila’s, where she needs the pieces because she already has the whole?”

Teacher Commentary

ERIKA ISOMURA: Here, I asked my students to recall two mentor problems they’d worked with before:

1. “Jesus is inventing a math game. He needs ___ pieces of string. Each piece needs to measure ___ feet long. How much string will he need in total?” Where would we find whole and parts in this problem?

2. “Camila is also inventing a math game. She has ___ feet of string. She decides that she only needs ___ of that length for her project. How long will that piece of string be?” What was going on with wholes and parts for Camila's string problem?”

I then asked my students to work with novel problems, identifying how these novel problems were like the problems we’d worked with previously, sorting the problems into groups.

When we’d worked with these problems before (with Jesus having 7 lengths of string that were each 2/3 feet long, and Camila needing 2/3 of a total length of 7 feet, for example) my students found that somehow these were coming out the same.

Which was really provoking because, one student for example kept saying, "I don't understand why that's happening, I'm dividing.” He didn’t see that as a multiplication, so he was really agitated by the fact that he feels like this is a division problem and yet, it's producing the same result with the same numbers as a multiplication problem.

In his view, Jesus' problem of the repeated 2/3's, that’s clearly multiplication, but the other one seems to be giving the same answer and yet it's clearly, in his brain, not a multiplication problem.