It’s often better to have students explore concepts and identify patterns themselves through investigation. Thats why I prefer to introduce the gradient-intercept form of a line with the following Desmos activity.
I start the lesson by showing students a collection of different lines with their equations on them and ask pairs to establish patterns in the shape and equations of lines. I then ask my pairs to pair up to discuss competing theories before the groups of four share the findings with the class. This is called “Think-Pair-Share” and it helps students communicate their ideas in a non-threatening way. It often helps the discussion as students don’t feel like their ideas are “too silly to share” because they have been bounced off three peers before being shared with the class. It also opens up some interesting vocabulary debates which consolidate understanding of terminology and general mathematical ideas.
Once the theories are “chalked” up on the whiteboard, I get the students to open Desmos and type “y=mx+b” into the input bar on the left hand side. Desmos will then ask you “Add sliders”? Choose the blue “all” button.
Desmos will draw the line with the sliders for the gradient and intercept set at one.
Now you can choose the animate icon to the left of m and b to see the sliders move smoothly to illustrate the affect of changing the gradient and the y-intercept.
I end the lesson by a matching activity between the equations and their graphs to consolidate student understanding.
How do you teach the Gradient-Intercept formula? Share your tips and techniques in the comments below.