# Introduction

## Overview

The lesson begins with a review of the foundational pieces of the lesson from the pre-assessment students did the day before: verbally describing and putting information into a table to determine when three plans for DVD rentals would cost the same amount. Students are then asked to state how they got started on their individual tables. After they share their strategies with their shoulder partners, students are given the objective of the day’s lesson. The focus of the lesson is to look at some different tabular representations. They are going to analyze each one to see if they can determine when the three different DVD plans cost the same, and they will look for similarities and differences between the tables. The order of the student work is purposeful. To make the lesson accessible to all students, the teacher chose student work that built upon the previous student to unfold a purposeful progression to tell the mathematical story about cost analysis.

## Teacher Commentary

This documented lesson on cost-analysis and comparison of plans depicted on tables is one of three lessons being developed around students’ misconceptions and understanding in our lesson study process this school year. This lesson is focusing on using tables to understand a cost analysis situation and will be followed by a lesson using graphs in a cost analysis situation and a lesson using algebraic equations in a different cost analysis situation. Our goal is to then have students make all three representations for a new and different cost analysis situation and discuss the merit of each representation in that particular situation. We will then give the students the MARS task "Picking Apples" for our third benchmark assessment to determine the effectiveness of our lesson study lessons. The majority of my regular math classes needed three days to complete the pre-re-engagement lesson and the re-engagement lesson focusing on Students H, A, E, and J.

Through these lessons we have been better able to understand the misconceptions that some students had when comparing the tables and/or reading tables in general. Some students noticed the multiplicative relationship and completed the table based on this understanding instead of looking at the relationship between variables which led them to then struggle to interpret the data that existed within the table that they had created.