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Lesson plan In this lesson, students learn how dynamic linear equations in algebra work by graphing them using Microsoft Math. They will learn how parameter changes affect graphs, understand the conditions that make two linear graphs parallel or perpendicular, use linear graphs to solve a real-life problem, and write two paragraphs explaining to their fellow students how linear graphs work. On This PageLesson plan information|
School level | | Curriculum areas | | Class time | | • | 2-3 hours, approximately |
| Software required | | Materials needed | |
Teacher guideGoals| • | Students will learn about dynamic linear equations by graphing them. | | • | Students will practice graphing algebraic functions using technology. |
Objectives| • | Students will understand the effects of parameter changes on the graph of y= mx + b, use them to solve problems, and explain them. | | • | Students will understand the conditions that make two linear graphs parallel or perpendicular, use them to solve problems, and explain them. |
Lesson procedureIntroductionIn this activity, you will use a technology tool to graph basic algebraic equations called dynamic linear equations. First you will investigate what happens on a linear equation graph when you change one of the parameters of the equation. After checking that you understand how graphing dynamic linear equations works, you will use your knowledge about graphing linear equations to solve a real-life problem and demonstrate your understanding of the conditions that make two linear graphs parallel. Finally, you will write two paragraphs explaining dynamic linear equations to your fellow students. I will guide you through each of these activities, but the goal is for you to figure out results on your own from your own investigations and practice. Main activitiesNOTE: Students who need more time to complete Activities 1-3 can omit Activity 4.
Software: Microsoft Math
What to do: Activity 1: Investigate dynamic linear equations by graphing them1. |
Graph y = mx +b in Microsoft Math. Animate b from -2 to 2.
For help graphing, read How to Graph a Function in Microsoft Math (.doc, 125 KB).
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Describe what happens to the graph when b = -2. Describe what happens to the graph when b=0. When b = +2.
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Animate m from -2 to 2. Describe what happens to the graph when m = -2. Describe what happens to the graph when m=0. When m = +2.
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Now graph y = -3x + 5 on the same axis. Set m and b for y = mx +b so that both graphs coincide. What are m and b when the graphs become the same line?
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Now set the controls so that the two lines are parallel. What are m and b when the lines are parallel? Is there more than one correct answer for m or b?
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Now set the controls so that the two lines appear to be perpendicular. (Be sure to click on the Proportional Display Button.) What are m and b when the lines appear to be perpendicular? Is there more than one correct answer for m or b?
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Activity 2: Check for understandingAnswer the following questions. Graph using Microsoft Math if you need to confirm your thinking. 1. | T or F The graph of y = 2x + 1 crosses the y axis at (0,2). | 2. | T or F The graphs of y = -x – 1 and y= -x+1 are parallel. | 3. | T or F The graph of y =3x -1 is rising from left to right. | 4. | T or F The graph of y = -3x + 1 is falling from left to right. | 5. | What has to be true of y = mx + b so that its graph will fall from left to right? | 6. | Write the equation for a line that is horizontal. | 7. | Where does y = -x -3 cross the y axis? [Teacher note: the closest you can get on m is .37.] | 8. | Write a function that has a graph that is steeper than the graph of y = x + 1. | 9. | Write a function that has a graph that is falling from left to right and crosses the y axis at (0, -4) | 10. | Write a function that has a graph that is parallel to y = x - 4. | 11. | Write a function that has a graph that is perpendicular to y = -2x + 1 |
Activity 3: Use a dynamic linear equation to solve a problem in real lifeRead the following scenario and answer the questions: Excellence Rental Car charges $35 per day + $0.19 mile for its Premier Plan. Excellence Rental Car has other rental plans that charge different amounts. To show customers the differences in the plans, the owner wanted to create a graph of her plans and run the graph as part of an advertisement in the newspaper. She started playing around with the Premier Plan charges on a graph. 1. | First, she reduced the amount of the per-day charges. What was the effect on the graph of the Premier Plan when she did this? | 2. | Next, she increased the cost per mile. What was the effect on the graph of the Premier Plan? When she looked at the graphs of her other car rental plans, one plan turned out to be parallel to the graph of the Premier Plan. | 3. | What can you conclude about this other plan? |
Activity 4: Explain the conditions and effects of graphing linear equations| • | Write a paragraph explaining what happens to the graph of y = mx + b when the parameters m and b are changed. Imagine you are explaining it to a classmate who was not at school today. | | • | Write a paragraph explaining the requirements on y = mx + b for two lines that are parallel or perpendicular. |
Conclusion| • | Observe students as they work individually and in groups. | | • | Evaluate the student work on the student handout. | | • | Prepare similar questions for quizzes and tests. |
Materials needed| • | Save the document How to Graph a Function in Microsoft Math (.doc, 125 KB) to your classroom computer and place it in a clearly marked folder so students can access it easily. To open this file, you might need to get Microsoft Office File Viewers. Adjust the directions as needed for your lesson.
| | • | Save the document Student Handout (.doc, 78 KB) to your classroom computer and place it in a clearly marked folder so students can access it easily. To open this file, you might need to get Microsoft Office File Viewers. Adjust the directions as needed for your lesson.
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