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Lesson plan In this lesson, students learn basic coordinate geometry by graphing figures from equations and writing the equations of graphed figures. Using Microsoft Math, they first graph the equation of a circle and discover the effects of parameter changes on the graph. They then reinforce their understandings of circles and their equations by graphing more figures, working with equations that contain irrational numbers, and writing the equations for circles with a given radius and center. On This PageLesson plan information|
School level | | Curriculum areas | | Class time | | Software required | | Materials needed | |
Teacher guideGoals| • | Students will learn basic coordinate geometry by graphing figures from equations and writing the equations of graphed figures. | | • | Students will learn the effects of parameter changes on graphs. |
Objectives| • | Students will graph circles based on a given center and radius. | | • | Students will write the equation for figures shown in graphs. | | • | Students will write the equation for circles with an identified center and radius. |
Lesson procedureIntroductionIn this exercise in coordinate geometry we learn how to graph equations and discover the geometric figures those equations represent. We also learn how to write the equations for geometric figures for which you have certain information. You will do this exercise in two parts. First, using Student Handout #1, you will graph a mystery geometric figure from an equation and watch what happens to the graph when you change the parameters of the equation. Then, using Student Handout #2, you will graph more figures, work with equations that contain irrational numbers, and write the equations for circles with a given radius and center. [Give the students Student Handouts #1 (.doc, 50 KB) , which contains Activity 1. When they have completed it, give them Student Handout #2 (.doc, 34 KB). Make sure students know how to access the Help document How to Graph Equations in Microsoft Math. Students who need more time to complete the other activities can omit Activity 4.] Main activitiesSoftware: Microsoft Math
What to do: Activity 1: Graph the equation of a geometric figure and change its parameters on the graph.Note: If you need help graphing equations, graphing on a new set of axes, or animating the parameters on a graph, read the document How to Graph an Equation in Microsoft Math (.doc, 118 KB) that your teacher has saved to your classroom computer. 1. | Graph EQ 1: x2+ y2=1. (Be sure to select the proportional display button.) What kind of figure do you get? | 2. |
On the same axis, graph EQ 2: x2+ y2=4. How is the graph you derived from equation 2 different from the graph of equation 1? What do 1 and 4 seem to represent on the graph? Graph x2 + y2= r2. Animate r from 0 to 2. What happens as r increases?
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Graph EQ 3: x2 + (y-1) 2=1. How is equation 3 different from equation 1? What does this number appear to determine? Graph x2 + (y-a) 2 = 1. Animate a from 0 to 2. What happens as a increases? Now animate a from -2- +2. What happens as a goes from 0 to -2?
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Graph EQ 4: (x -1) 2+ (y) 2=1. How is equation 4 different from equation 1? What does this number appear to determine? Graph (x-a)2 + (y) 2 = 1. Animate a from 0 to 2. What happens to the graph as a increases? Now animate a from -2- +2. What happens to the graph as a goes from 0 to -2?
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Graph (x+1) 2 + (y-2) 2=25. Before you graph, can you predict what the figure will be, its size, and where it will be located.
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Note: For the following activities, if you need help graphing equations, graphing on a new set of axes, or animating the parameters on a graph , read the document How to Graph an Equation in Microsoft Math (.doc, 118 KB) that your teacher has saved to your classroom computer.
Activity 2: Graph more circles and write their equations1. | What is the radius of the circle with equation (x+1) 2 + y2=100? What is the center of the circle? Graph to verify. | 2. | Graph a circle that has a radius of 5 with a center of (-2, 2). What is its equation? |
Activity 3: Work with irrational numbers1. | What is the radius of the circle with equation (x+2) 2 + y2=40? What is the center of the circle? Graph to verify. | 2. | Graph a circle that has a radius of √5 with a center of (-2, 2). What is its equation? |
Activity 4: Write the formula or equation for a circle(x-h) 2 + (y-k)^2 =r2 is the equation of a circle where (h,k) is the center of the circle and r is the radius. 1. | In the equation x2 + y2=1, what is h, k, and r? | 2. | In the equation (x-2) 2 + (y+1) 2 = 9, what is h, k, and r? | 3. | Write the equation of a circle with a center at (-3, 1) and a radius of 5. |
Conclusion| • | Observe students as they complete each of the activities. | | • | Evaluate each student’s work on the student handouts. |
Materials needed| • | Save the document How to Graph an Equation in Microsoft Math (.doc, 118 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 documents Student Handouts #1 (.doc, 50 KB) and Student Handout #2 (.doc, 34 KB) to your classroom computer and place them in a clearly marked folder so students can access them 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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