## Overview

In fall of 2008, Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader) and Cecilio Dimas (7/8 math teacher) developed our first lesson on cost-analysis. By the end of fall 2008, all eleven 7th grade classes, regular and accelerated, had been taught the DVD Plan lesson. The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students had been given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. Using this idea as an anchor problem taken from our original pre-assessment with the MARS task "Gym," we were devising avenues for our students to explore and understand specific multiple representations of breaking points. We believe that being able to understand multiple representations for the breaking even points in a written explanation, a table, a graph, and an algebraic rule is critical to success in algebra. The design of our year-long lesson study is to address each of these multiple representations: verbal, tabular, graphical, and algebraic generalization. Our perception is that students tend to see the graph as the “last thing” with no real connection to the mathematics of the situation or to other representations and that was our reason to put it after the verbal and tabular representations.

Lesson Goals

-Comparisons of different deals: do these representations make mathematical sense and do they match the mathematics of the three plans?

-Verbal descriptions

-Tables graphs

-Algebraic rules

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