Unit 3, Lesson 7
Representations of Linear Relationships
Grade 8
Preparation
Lesson Narrative
In this lesson, students develop an equation for a linear relationship in context by expressing regularity in repeated calculations (MP8). Students measure volume using a graduated cylinder. Identical objects are added to the cylinder, increasing the volume in the cylinder by the same amount with each object. Students graph the relationship, interpreting the initial water volume as the vertical intercept and the slope as the rate of change, or the amount by which the volume increases when one object is added.
In this lesson, students also continue to strengthen their understanding of how the slope and vertical intercept are connected in equations that represent a linear context by both interpreting an equation in context and creating a context to match an equation (MP2). This lesson continues to focus on positive slopes.
- Create an equation that represents a linear relationship.
- Generalize (orally and in writing) a method for calculating slope based on coordinates of two points.
- Interpret the slope and $y$-intercept of the graph of a line in context.
Let’s write equations from real situations.
Required Materials
Required Preparation
If doing the 20 minute version with a physical teacher demonstration or the 40 minute version with students collecting data, partially fill a graduated cylinder with water and immerse identical solid objects into the cylinder. Record the resulting volume in the cylinder after adding different numbers of objects and verify that the increase in volume is approximately linear and determine a good initial water volume so that there is enough water and room in the graduated cylinder to immerse 10 to 15 objects.
For the digital version of the activity, acquire devices that can run the applet.