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

## Overview

Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader) and Cecilio Dimas (7/8 math teacher) discuss the lesson on cost-analysis and the mathematical sense of student-created tables with and without errors. They want the students to make mathematical sense of the tables and discover the mathematical reasoning as well as to go beyond the notion that the table is either right or wrong. If the depiction is inaccurate, they want students to discover that the table could possess mathematical sense but not match the mathematical context of the original DVD plans and would therefore be an incorrect table for this context.

Another focus of the lesson is to allow students to have the opportunity to work collaboratively and observe how partner work may influence students’ understanding of tables. Their thought is that building in independent think time prior to partner time will allow students to formulate their own thoughts and not be influenced by others. Having to explain their thoughts to a partner will encourage all students to participate in explaining their thinking. Also, having students write on their own think paper will provide the teachers with an artifact to determine the effectiveness of the lesson and our prompts.

The educators also want to learn what types of mathematical statements students will come up with to describe and make comparisons of different tabular representations.

Students have been working with tables and graphs since elementary school. However, at the middle school level, we continue to see that students have not, yet, achieved a true understanding of how to make and read a table and graph. Through our observation and student work, we have noted that students are capable of creating tables and graphs within parameters such as: being given the labels for the x-axis and y-axis, the scale, column headings on tables, and sequential lists which provide opportunity for students to rely on multiples rather that identifying the relationships between the variables. Our goal has been to provide opportunities for our students to become fluent in reading graphical representations and to understand the data presented within the graph.