## Overview

Antoinette Villarin teaches middle school mathematics at Westborough Middle School in South San Francisco, California, and at the time of this 2016 recording had been teaching for 15 years. Antoinette has also collaborated with Patty Ferrant in a lesson on perimeter and area recorded for Inside Mathematics.

In this lesson, Antoinette’s students are asked to compare a graph and an equation to a real-life situation in which liquid flows out of a container that has a top prism and a bottom prism. The lesson is part of a larger unit in which students look at rate of change, interpret slope, and write an algebraic equation in slope intercept form.

In interpreting slope as rate of change, Antoinette’s students show their abilities to justify and build a mathematical argument based on a real-life situation. In their prior learning, the students had converted other real-life situations — such as a plant growing or a family saving money — into numerical tabular and graphical representations, as well as algebraic representations. The lesson primarily addresses rate of change: as one quantity changes, a second quantity also changes. This lesson, Comparing Lines and Linear Equations, was created by the Mathematics Assessment Project.

Antoinette also engages in substantive pre- and post-lesson coaching conversations with colleague, mathematics coach, and Inside Mathematics featured educator Cecilio Dimas.

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