Lesson

# Clip 5/11: Lesson - Part 4

## Overview

The teacher refers to strategies for comparing rates: If the number of seconds is the same, you can compare beans, if the number of beans is the same you can compare seconds. I want you to use these strategies with new data. Joe, 16 steps, 10 seconds; Sarah, 32 steps, 20 seconds; Alex, 15 seconds, 21 steps. Who is the fastest?

Students first think on their own, then share in groups before class discussion.

## Teacher Commentary

COACH LINDA FISHER: I was surprised by some of the challenges this task caused for students. The first student uses the rate 20 seconds for 32 steps, which seems uncomfortable to me. But the structure of the data allows the ratio to make sense either way. I think the format of the data allows a greater range of strategies for students. One student struggled with making common units. He used 40 seconds for Sarah and Joe, but 60 seconds for Alex. Another student talks about doubling Alex, but then describes a different process. I like that the discussion in group and now familiar context of rate allows students to self-correct as they talk. I worry that sometimes we, as teachers, jump in to quickly to "fix" mistakes. This may actually stop learning, because the students aren't the sense-makers. One student is still looking at absolute differences, how far apart are the two numbers, rather than a proportional strategy. I think during the learning process students naturally go in and out of understanding.

Many students took the idea of common multiple to convert time to 60 seconds, which again I found fascinating. I didn't hear students using 30 seconds, which would have been easy. I was thinking because Alex's time was 15 seconds, I might be tempted to change everything to 5 seconds. The design of the numbers for both time and steps opens up many possibilities. So I like the thought behind the choice of numbers and variation in data presentation. I think this is an important part of the lesson design process. We often think and discuss what is the "activity" or problem, without giving enough attention to how it's worded or the numbers used. We underestimate the importance of this in the types of thinking students engage in.