Student activity
Follow the steps below to guide your students through this lesson plan.
Note teachers: Please download the student activity handouts located in the sidebar under Software and Materials Needed, for additional details about the main activities for this lesson plan.
Activity 1: Graph the equation of a geometric figure and change its parameters on the graph.
Note students: 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" that your teacher has saved to your classroom computer.
- Graph EQ 1: x2+ y2=1. Be sure to select the proportional display button. What kind of figure do you get?
- On the same axis, graph EQ 2: x2+ y2=4. How is the graph you derived from equation 2 different from the graph from 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?
- 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?
- 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?
- Graph (x+1) 2 + (y-2) 2=25. Before you graph, can you predict what the figure will be, what its size will be, and where it will be located?
Note students: 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" that your teacher has saved to your classroom computer.
Activity 2: Graph more circles and write their equations.
- What is the radius of the circle with the equation (x+1) 2 + y2=100? What is the center of the circle? Graph to verify.
- Graph a circle that has a radius of 5 with a center of (-2, 2). What is its equation?
Activity 3: Work with irrational numbers.
- What is the radius of the circle with equation (x+2) 2 + y2=40? What is the center of the circle? Graph to verify.
- 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.
- In the equation x2 + y2=1, what is h, k, and r?
- In the equation (x-2) 2 + (y+1) 2 = 9, what is h, k, and r?
- Write the equation for 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 in the student handouts.