Technology Lesson Plan
Katie Schaible
An Exploration of the Slope of a Line, and How it can be Used
Algebra 1
Objective: The student should be able to:
 Define the slope of a line.
 Explain the meaning of slope.
 Use the slope – intercept form of a line as a prediction tool.
 Find the slope of perpendicular lines.
 Find the slope of parallel lines.
Materials: Internet, Geometer’s Sketchpad, Fathom, lab materials, pencil, paper, graph paper…….and an inquisitive mind!!
Activity:
Day 1
1.
Hand out review worksheet. Review with students how to graph a line using points.
Complete examples.
2.
Discuss aspects of the line, including the slope of the line.
3.
Show examples on www.exploremath.com
4.
Students will complete the exploration worksheet on Geometer’s Sketchpad.
5.
Return as a class, and discuss what the students have discovered in their exploration.
Assignment: Textbook, p. 363-364 #1-30
Day 2
1.
Review key concepts about slope that students previously explored.
2.
Students are to complete “Bungee Jump” lab.
Assignment: Complete Lab write up

X
Slope Review Worksheet /Internet Exploration
NAME ___________________________

Recall graphing an equation of a line using points. Create an x,y chart. Substitute a value for x and solve for y.
Try to graph this line: y = 3x + 4
Y

List one aspect of the line you can easily tell from the equation. Hint: It involves an intercept!
___________________________________________________________________

Describe the slant or SLOPE of the line.
___________________________________________________________________

Go to the website www.exploremath.com
, click on the link for lines/linear equations under the gizmos by category sections (right side of screen). Look at both the slope calculation and slope intercept form activities. Answer the following questions. BE
SURE TO MOVE AROUND THE POINTS AND LINES…..remember this is a
DYNAMIC website!!!
1. What is the de finition of slope….in your own words?
2. What is the formula for slope?
3. What is the slope intercept form of a line?
4. Describe the various components of the equation of a line in slope intercept form.
5. Describe how you can graph a line from the slope intercept form.

2.
3.
4.
5.
1.
Geometer’s Sketchpad Exploration of Slope
NAME
Directions: Follow the instructions below as your work through Geometer’s Sketchpad.
Answer all questions that are listed.
 Open Geometer’s Sketchpad from the desktop. Make sure the CD is in the disc drive.
 From the GRAPH menu, select DEFINE COORDINATE SYSTEM.

From the GRAPH menu, select PLOT NEW FUNCTION.
 Click on EQUATION in the pop-up box, be sure y = f(x) is selected.
 Enter in the equation 3x+4 using the keypad in the pop-up box.

You can change the axis by clicking on them with the mouse and dragging in or out.
 Now, you know how to graph an equation of a line.
 Pick 5 of your own equation to graph. Keep all of your equations in the form y=mx+b. Pick different values for m….make the values be fractions, and positive and negative numbers. Also pick both positive and negative numbers for b.
I GRAPHED THESE 5 EQUATIONS, Sketch each graph next to the equation:
 After you graph your equations, answer the following questions.
1. What does the value for m indicate? How can you tell this from your graphs?
2. What does the value for b indicate? How can you tell this from your graphs?

3. How would you describe the line when m (the value for slope) is positive?
4. How would you describe the line when m (the value for slope) is negative?
5. What happens to the line when m (slope) is a very large number?
6. What happens to the line when m (slope) is a very small number?
 Open a new document in Geometer’s Sketchpad. Again, select DEFINE
COORDINATE SYSTEM from the GRAPH menu.
 Select PLOT NEW FUNCTION from the GRAPH menu.
 Plot the following lines: y=3, y=-5, y=10.

Answer the following questions.
7. What do you notice about these lines? How would you describe these lines?
8. How would you describe the slope of these lines? (hint: think rise over run)
9. You can now complete the statement, “The slope of all horizontal lines is ……”
 Open a new document in Geometer’s Sketchpad. Again, select DEFINE
COORDINATE SYSTEM from the GRAPH menu.

Select PLOT NEW FUNCTION from the GRAPH menu.
 Plot the following lines: x=3, x=-5, x=10. To get this into x = mode, you will need to click on equation in the dialog box, and select x = f(y)
 Answer the following questions.
10. What do you notice about these lines? How would you describe these lines?
11. How would you describe the slope of these lines? (hint: think rise over run)
12. You can now complete the statement, “The slope of all vertical lines is ……”
 Open a new document in Geometer’s Sketchpad.

Using the line tool, draw a line anywhere in the screen.

 Select the point tool, plot a point not on the line.
 Using the arrow tool, select both the point and the line.
 From the CONSTRUCT menu, select PARALLEL LINE. Geometer’s Sketchpad will draw a line parallel to the first line through that given point.
 Using the arrow tool select only one of the lines.
 From the MEASURE menu, select SLOPE. Notice the slope of the line is calculated, and a grid will appear.
 Deselect the line and the slope value. Using the arrow tool, select the other line, and from the MEASURE menu, select SLOPE. Notice the slope of that line appears.

Repeat the above procedure with a few different lines.
 Answer the following questions.
13. What do you notice about the slopes of parallel lines? How do they relate with each other?
14. You can now complete the statement, “The slope of parallel lines are the…..”
 Open a new document in Geometer’s Sketchpad.
 Using the line tool, draw a line anywhere in the screen.
 Select the point tool, plot a point not on the line.
 Using the arrow tool, select both the point and the line.
 From the CONSTRUCT menu, select PERPENDICULAR LINE. Geometer’s
Sketchpad will draw a line perpendicular to the first line through that given point.
 Using the arrow tool select only one of the lines.

From the MEASURE menu, select SLOPE. Notice the slope of the line is calculated, and a grid will appear.
 Deselect the line and the slope value. Using the arrow tool, select the other line, and from the MEASURE menu, select SLOPE. Notice the slope of that line appears.
 Repeat the above procedure with a few different lines.
 Answer the following questions.
15. What do you notice about the slopes of perpendicular lines? How do they relate with each other?
16. You can now com plete the statement, “The slope of perpendicular lines are the…..”

NAME __________________________
BUNGEE LAB
– Slope, Algebra 1
The purpose of this lab is to gather data, analyze it, and make predictions. To do this you will be using your knowledge of the equation of a line. You will be able to use Fathom, and your graphing calculator as tools. Follow all directions.
A water bottle will serve as your person bungee jumping. Rubber band will serve as the bungee line. You will also need a ruler, and pen and paper to keep track of your results.
Secure the first rubber band around the top of the water bottle. Fill the water bottle about 1/3 full with water. Hold the rubber band and measure how far the water bottle stretched once it was dropped. Measure from your hand holding the rubber band, to the end of the water bottle. Take your measurements in centimeters. Continue tying on rubber bands to the previous one, and continue to take measurements for each rubber band. Keep track of your data in the table below.
Number of Rubber Bands
Centimeter’s that Water Bottle Dropped
Now, you will enter your data into Fathom to look for a line of best fit. It might also help for you to hand graph the data to get a general idea of your line of best fit first.
FATHOM

Open Fathom from your desktop

 Drag a box from the toolbar for your collection into the screen. Label the box Bungee
Jump Data.

Drag a chart from the toolbar for your collection into the screen. Label the first column of data “Number of Rubber Bands.” Enter your data into this column.
 Label the second column of data “Length of Fall”. Enter your data into this column.
 Drag a graph from the toolbar for your collection into the screen.
 Drag the number column to the x-axis of the graph, and the length column to the y-axis of the graph.
 Right click on the graph. Select MOVABLE LINE. Use the arrow tool to move the line around. Try to find the best fit line. You could also right click on the graph, and select
MAKE RESIDUAL PLOT to help with your accuracy. Selecting SUM OF SQUARES will also help with this.
What do you think the best fit line is? ___________________________________
 Once you think you have found the best line, right click on the graph, and select
LEAST SQUARES LINE. The line of best fit will be displayed along with its equation.
What is the equation of the line of best fit? ________________________________
How accurate was your approximation?
_____________________________________________________________________
Now, your person wants to be more daring. They want to bungee jump from the top of the second flight of stairs in our building. This distance has already been measured and is 10 meters. You now have to determine the number of rubber bands needed for the jump.
Remember, your person wants to be safe, yet have the biggest thrill. So, get them as close as possible to the floor without allowing them to crash!!!
Explain how you are going to determine the number of rubber bands needed?
What is your estimate of the number of rubber bands needed?
Tie the number of rubber bands you think you will need to the bottle. Now, as a class, we will go to the staircase and complete the jumps!

What was the result of your jump?
If you determined the number of rubber bands correctly, explain how your calculated this. If something went wrong, explain where you think the error resulted.
How did mathematics, and the knowledge of slope, and the slope intercept equation of a line, help you with your prediction?