Unit 5, Lesson 2
Representing Proportional Relationships
Accelerated 7
Preparation
Lesson Narrative
The purpose of this lesson is for students to understand that while there are many ways to scale axes when graphing a proportional relationship, certain ranges for the axes are helpful for seeing specific information.
Students begin by considering a claim that the graph of one line is steeper than the graph of a second line. While one graph looks like a steeper line, by noticing the scale of the axes of each graph, it can be determined that the two lines actually have the same slope. In an optional activity, students sort graphs on cards based on what proportional relationship they represent (MP7). Each graph has a different scale, with some scales purposefully quite different, pressing the need to pay attention to scale and rely on mathematical definitions of steepness, not just visual ones.
Next students create a graphical representation of a proportional relationship when given a table and a description to start from. They learn that the rate of change in a proportional relationship is the same as the constant of proportionality: the amount one variable changes by when the other variable increases by 1. An optional Info Gap activity allows students to graph a proportional relationship on an empty pair of axes that includes a specific point.
- Compare graphs that represent the same proportional relationship using differently scaled axes.
- Create an equation and a graph to represent proportional relationships, including an appropriate scale and axes.
Let's graph proportional relationships.
Required Preparation
None
The rate of change is the amount changes when increases by 1. On a graph, the rate of change is the slope of the line.
In this graph, increases by 15 dollars when increases by 1 hour. The rate of change is 15 dollars per hour.
Graph, horizontal axis, x, amount earned in hours. vertical axis, y, amount earned in dollars. line starting at 0 comma 10, passing through 2 comma 40 and 60 comma 100.