# Clip 4/14: Problem 1 - Part A Comparing Linear Functions

## Overview

The lesson study team had anticipated that students would make correct mathematical statements about Student H’s work and have some concern regarding the third table. Additionally, the team had expected that some students would present the argument that table #3 is about months and cumulative costs for that particular DVD plan. The team had agreed that any incorrect responses would be managed by asking the class if we were all in agreement by using hand signaling and ask if someone would be willing to defend a particular answer to provide further clarification. Student H had created three different horizontal tables that were all mathematically correct. However, the third table did not match the DVD plans. Additionally, Student H did not label all three of the tables, thereby allowing room for confusion and an inability to accurately respond to the original prompt. The notion that mathematical comparisons in this situation can only be made with like units is a big mathematical idea in this particular case or context. Likewise, the notion that just because there is a correct mathematical pattern doesn’t mean that the table is correct for this context. This too, is a big mathematical idea for our students.

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.