Unit 2, Lesson 10
Meet Slope
Grade 8
Preparation
Lesson Narrative
In this lesson, students use dilations and triangle similarity to understand why the slope of a line can be calculated by dividing the vertical change by the horizontal change for any two points on the line. Students also see that this ratio determines how steep the line is.
Students begin by finding dilations of a triangle with one vertical side and one horizontal side. All the dilations use the same center but different scale factors. Students observe that regardless of the scale factor used, all the resulting triangles are similar, and their longest sides all lie on the same line. They are slope triangles. By analyzing examples, students see that all slope triangles for a given line are similar, and so any slope triangle can be used to find the slope of a line. The quotient of the vertical side length and the horizontal side length will always be the same (MP7).
Students then use slope triangles to draw lines with a given slope. They determine that lines with the same slope are parallel and that as the slope increases from 0, the lines look steeper (from left to right).
- Comprehend the term “slope” to mean a number that tells how steep a line is. To find the slope, divide the vertical change by the horizontal change for any two points on the line.
- Draw a line on a grid given its slope and describe (orally) observations about lines with the same slope.
- Justify (orally) that all “slope triangles” on one line are similar.
Let’s learn about the slope of a line.
Required Preparation
Provide access to geometry toolkits, making sure tracing paper is available for each student.
Provide access to straightedges.
Slope is a number that describes how steep a line is. To find the slope, divide the vertical change by the horizontal change for any 2 points on the line.
The slope of this line is 2 divided by 3, or .