# Graphing Proportional Relationships - Fluency Practice

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## Objective

Students will be able to identify the constant of proportionality and equation for the graph of a proportional relationship.

#### Big Idea

Y over x or x over y? It takes practice to keep that straight!

## Launch

10 minutes

OpenerAs students enter the room, they will immediately pick up and begin working on the opener –Instructional Strategy - Process for openers. This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3

Learning Target:  After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended target is, “I can graph proportional relationshipos and I can identify the equation for a proportional relationship.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

## Explore

45 minutes

White Board Practice:  Graphing Practice Explore Video This lesson incorporates several of the mathematical practices.  First and foremost, students have to pay close attention to detail - are they setting up the ratio of y to x, or are they reversing it (mathematical practice 6).  Additionally, students are having to look at problems in a variety of ways - words, graphs, tables, equations - this requires versatility and a good conceptual understanding (mathematical practice 4).  Though not explicity a tool in terms of technology, students will need to use certain tools to present information - via tables and graphing on the coordinate plane (mathematical practice 5). As with all proportional relationships, students will be looking for patterns, constants, that let them know that a relationship is proportional and thus they can write an equation or identify a constant of proportionality (mathematical practice 7).  Since students are working in groups, they will need to not only reason with one another, but also persevere through problems (mathematical practices 1 and 3).

## Summary

5 minutes

Instructional Strategy - Table Discussion: As a summary to the lesson, I am going to ask students to have a discussion on how to determine the constant of proportionality given a graph.  This was a key error made in the previous lesson, so I want to see which students are able to correctly identify it now!