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A Discovery Activity for the Algebra Classroom Using the Transform Application
Elizabeth OBrien
VA Standards of Learning: A.6 and A.7
Objectives: Using the line y=x as a reference, generalize the effect of changes in the equation to the graph of the line. Use the graphing calculator to facilitate development of this concept.
The teacher must have the Transform Application loaded onto their calculator and then select the application from the APPS menu.
2. The teacher will begin by going to the settings mode in the Transform Application and setting the calculator to the following:
3. Then the teacher will go to the graph screen and begin with a discussion of the line y = x. Then the teacher will use the right arrow key and left arrow key to change the slope, keeping it a positive slope. Have the students discuss the changes to the graph.
Key Questions:
How are the lines the same?
How are they different?
Which graph appears the steepest?
Where does each graph cross the y- axis?
What causes the differences to occur?
4. The teacher will the go to the settings mode in the Transform Application and set the calculator to the following:
5. Then the teacher will go to the graph screen and begin with a discussion of the line y = - x. Then the teacher will use the right arrow key and left arrow key to change the slope, keeping it negative slope. Have the students discuss the changes to the graph.
Key Questions:
How are the lines different?
Which line appears the steepest?
What causes the lines to change?
How can we get a very steep line, a flatter line?
6. Next the teacher will the go to the settings mode in the Transform Application and set the calculator to the following:
7. Then the teacher will go to the graph screen and use the right arrow key and left arrow key to change the y- intercept. Remember you must first use the up and down arrow keys to toggle to the B. Have the students discuss the changes to the graph.
Key Questions:
How are the lines the same?
What is different about the lines?
Where does each line cross the y-axis?
What happens to the graph when a constant is added to y=x?
8. Summary: Have the students write a paragraph describing the effect of m and b in the equation y=mx+b.
9. Assessment: To determine students level of understanding there is a worksheet attached that can be used as practice, or as a quiz to allow students to demonstrate their level of understanding.
Graphing Equations in the slope-intercept form: y = mx + b Name: _________________
1. Compare the two graphs:
Which of these two graphs has a larger slope? ______________________________
Explain how you determined your answer:
2. Compare the two graphs:
How are these two graphs similar? ______________________________________________
What is the difference between these two graphs? _____________________________________
What caused the change to take place? ______________________________________________
3. Examine the graph:
Describe two things you can determine about the graph just by looking at it and not doing any
calculations. ________________________________________________________________
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