# Clip 8/14: Problem 2 - Part A Comparing Linear Functions

## Overview

The lesson study team had imagined that some correct mathematical statements about Student A’s work would be made and that some concern about zero would be raised. The team also had foreseen that students might forget the mathematical purpose of these tabular representations, specifically when the three plans would cost the same. Student A had created one vertical table depicting all three plans. The table did not match the plans, but was mathematically correct. Additionally, Student A did include zero in their table which provided the class the opportunity to think about the insight that is gained by including zero in a table. For this investigation, zero provided the students with the information on whether or not there was a monthly fee.

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.