To start the lesson, ask students what they already know about slope. They may know terms such as
rate of change and
rise over run. Often, students have recollection of these terms but don't remember or understand what they mean or how they relate to
slope.
Ask students what it means to have positive or negative slope. Encourage a student to come to the front of the room and draw a line with positive slope. Ask classmates if they agree that the line has positive slope, and then ask how they can tell.
A line with positive slope is pointing upward as you look to the right. You always want to see if the line is pointing upward or downward on the right side of the graph, just as we read to the right.
Sketch these two lines with positive slope for students to see.
Ask students to tell you all they can about the two graphs. What's the same? What's different? Emphasize that although both lines have positive slope, there is something different about the direction in which they point. Explain that this description of how
slanted a line is can be described by a number called its
slope.
Now, draw a third line that has the same slope as the first line, but a different y-intercept. Ask students again for comparisons.
Students should eventually recognize that the third line has the same slope as the first line. Once they do, they are ready to think about the slope number as a description of how slanted a line is.
Use the activity sheet for practice and enforcement.
The activity sheet guides students through a process for finding the slope of a given line. Page 1 is meant to be completed as a class, so having an overhead slide of this page will be helpful.
Distribute the activity sheets and make sure each student has 1 or 2 colored pencils. Many students enjoy using a colored pencil to draw and shade the slope triangle, and doing so makes the lesson more memorable. You might ask students to use one color when they're drawing the triangle for a line with positive slope, and another color for triangles representing negative slope.
Shade in the slope triangles with students as shown below.
Encourage students to simplify their fractions on page 1 of the activity sheet. Point out that for each line, the simplified forms of the fractions are equivalent — no matter which two points on the line you student use, or how large the triangle is, you get the correct slope.
On page 2, students are given the slope triangle in the first 3 examples (the top row). In the next 3 examples (middle row), they are given only the points to use to draw the triangle. In the last 3 examples (bottom row), students have to find the points themselves before drawing the triangle and determining the slope. The idea here is to gradually get students comfortable with finding the slope.
While students work on page 2, be sure that they:
- Simplify all fractions
- Determine which lines have negative slope and use a negative fraction to represent the slope of these lines.
This exercise provides students with the skill of finding the slope of a line from a graph. This skill can be applied to less abstract examples using real data from a table or a graph.
