Submitted by: Emily Bern
Grade Levels: 3-5, 6-8
In this lesson plan, which is adaptable for grades 4-8, students will experiment with slope and intercept using games, sports, and deduction.
- Conduct an experiment for slope and intercept.
- Computer with internet access for BrainPOP
- Chalkboard or whiteboard and markers
- Ramps or long pieces of wood of equal length
- Blocks of equal height (5 per group)
- 1 toy car per group
Slope, intercept, slope-intercept form, coordinates, coordinate plane, x-intercept, y-intercept
- PART ONE: Intercept: Introduce the concept of intercept by leading a brief discussion and playing the Slope and Intercept movie. Have students think about what intercept means and write it down in their notebooks while encouraging them to draw a picture or diagram.
- Have students discuss what intercept means and, if it isn't mentioned, prompt them by having them think about an interception in sports.
- Draw two lines on the board and have a student come up and circle where the two lines intercept.
- Then, have a student come up and circle where the x and y axis intercept on a coordinate plane.
- Draw a line on the coordinate plane and have a student circle where that line intercepts with the axis.
- Define intercept as “a point where a line intercepts or hits the x or y axis.”
- Have students spend some time circling and recording the intercepts of 4-6 examples. Ask them to make a note of any observations they notice.
- Go over the examples as a class and, if it isn't mentioned, point out the fact that the y value of the x-intercept is always zero and the x value of the y-intercept is always zero.
- PART TWO: Slope: Before going into the calculation of slope, it’s important for students to understand what slope is. To do this, students will participate in an activity in which they will compare the slopes of a ramp at various heights.
- This activity can be done in groups. Start by placing one block beneath a ramp and let a toy car go down the ramp. Record in a table the height of the ramp (one block, two blocks, etc.) and record how far from the base of the ramp the toy car traveled.
- Have students record how far the toy car goes for heights of one through five blocks.
- Then, ask them to compare the slopes based on the information they gathered by completing the following sentences:
_____ has the steepest slope.
_____ has the least steep slope.
_____ is steeper than 2 blocks high.
**Hint: if the toy car went farther the slope of the ramp was steeper
- Go over the answers as a class. Tell the students now that we have figured out how height can affect steepness of slope, we are going to use math to calculate the slope of our ramps.
- Have a student measure the length of the ramp and the height of one block. Ask the students, if we want to record this as points on a coordinate plane how would we do that? Answer- the length is on the x axis and the height is on the y axis.
- Record the points. Ex. (15,0) and (0,5)
- Explain that calculating the slope is finding out how steep the line is and using numbers to represent that. It’s a measure of how something changes vertically (up and down) compared to how much it changes horizontally (left and right). Introduce the equation: slope (m) = change in y/ change in x. It can be referred to as rise over run, or a vertical change over a horizontal change.
- Show that there are many points on this line but you only need two to figure out the slope. Model finding the slope of this line.
- Have students work in groups to find and record the slope of the remaining ramps using a coordinate plane. Go over the results as a class.
- PART THREE: Slope-Intercept form: Play the Slope and Intercept movie once again for a review.
- Tell the class that we are going to use what we’ve learned about slope and intercept and join them together to write an equation in slope-intercept form. By using the slope and one intercept, we can form this equation. It is expressed as y=m(slope)x+b (y-intercept). For our example, let’s find the slope of this line (draw a line on the coordinate plane). Ex: (5,6) and (0,1) is 6-1/5-0= 1
- Now we have the slope, -2. Now for slope-intercept form we write our equation as y= 1x+ 1 à x+1
- This formula is very helpful for forming more points on a line and graphing it.