# Clip 6/11: Lesson - Part 5

## Overview

The teacher has a student share a conjecture with the class: If the rate is seconds per step, Alex wins; if the rate is steps per second, Joe wins. Students talk in groups to try to figure out how she got this conjecture and whether it makes sense. During class discussion a student talks about 20 seconds per step and 20 steps per second. The teacher has two different students demonstrate each rate. A final student concludes that the goals are different for each rate.

COACH LINDA FISHER: The research by Bell and Swan, Shell Centre at Nottingham, suggests that students benefit by looking at misconceptions. This is a good demonstration of how everyone benefits from exploring the thinking behind the different rates and how the goals of fastest is different depending on the rate chosen. The teacher takes the student thinking and uses it to pose a problem for the whole class to re-engage with the idea of the meaning of rates and how to compare them. Are the larger numbers faster or are the smaller numbers faster? Why?