Deriving the Equation of a Parabola Lesson Plan
Course: Analytic Geometry
Class Length: 90 minutes
CCGPS Standard:
Mathematical Goals:
Vocabularly:
Previous knowledge:
Materials Needed:
Classroom set-up:
Opener (7-10 Minutes)
Activity 2 (30-35 minutes):
Activity 3 (20-25 minutes):
Whole Class Discussion (5-10 minutes):
Class Length: 90 minutes
CCGPS Standard:
- MCC9-12.G.GPE.2 Derive the equation of a parabola given a focus and directrix
Mathematical Goals:
- Understand the definition and construction of a parabola
- Understand how the parameter "a" (when the parabola is in vertex form) affects the distance between the focus and directrix.
- Understand how to write the equation of a parabola given a focus and a directrix.
Vocabularly:
- Focus
- Directrix
- Parabola
- Perpendicular Bisector
- Parameter
Previous knowledge:
- Definition of a quadratic function
- The shape of a parabola
- Vertex form of a quadratic
Materials Needed:
- See each individual activity for a list of needed materials
Classroom set-up:
- This lesson is designed so that each student should have access to a computer. Therefore, students either need to have their own individual laptops, or the teacher should reserve the computer lab for this lesson.
- Have the desks facing so that the teacher can see the computer screens at all times in order to ensure that students are on topic.
- Before students arrive, the teacher should have prearranged partners for the class. Choose partners based on who works well together, can stay on topic, and make sure each pair has someone who is good at articulating mathematical ideas (or at least try to make sure each pair has someone. This way, "good" math conversations can take place.) If a student is absent that you weren't expecting, put the "leftover" student with another pair to form a group of three.
Opener (7-10 Minutes)
- Students should come in and pull out their worksheet that they should have completed for homework last night from Activity 1
- If you want to grade/check this assignment, do this as the students are coming in. It is not recommended that you collect the homework sheet, because students will probably want to use it as a reference during today's activities.
- Anticipated student responses as well as questions to ask students can be found here. Make sure to pose the listed questions to the students so that students can hear what others took away from the activity.
- In order to make sure everyone is on the same page, ask one student to come to the board and draw the construction of a parabola (up to the point where the locus is created) so that everyone can, again, see which distances are equal in the construction.
Activity 2 (30-35 minutes):
- After the opener is completed, tell the students who their partners will be for the class period. If the students need to be moved to a computer lab, make this transition now. If not, ask them to partner up and pull out their laptops.
- Pass out copies of the worksheet "Exploration of Parameter a" and tell the students to begin working.
- Circulate around the room so that students know you are available for questions.
- For more information on implementing this activity, please click here.
- Ask the students to let you know when they have completed the worksheet. At that time, check #10 on the worksheet for understanding and correctness (Answer Key can be found in the link above). If they have completed #10 correctly, introduce that pair to Activity 3.
Activity 3 (20-25 minutes):
- Again, the students should be working in pairs or groups of three (the same as before).
- Make sure the students are on the correct applet. For this activity, only one computer is needed per group, but try to observe and make sure that each group member is operating the computer at some point.
- For more information on implementing this activity, please click here.
- Once all groups finish the activity, pull the class back together for a whole class discussion. The first groups that finish can go ahead and start Activity 4.
Whole Class Discussion (5-10 minutes):
- Ask the students to reflect on the two activities they did today. What went well? What was hard/challenging? Was it the material that was hard, or just using the technology?
- Ask the students how the focus relates to the vertex "Is the focus always 'inside' the curve of the parabola?"
- Ask how the directrix relates to the parabola. "Will the directrix ever touch the parabola?"
- Ask the students to explain what "p" represents. If p is the distance between the focus and vertex, how much is the distance between the focus and directrix?
- Ask the students how they would write an equation for a parabola if they were only given the focus and directrix.
- Work an example on the board, but let the students tell you what to write.
- For this activity, students should be working alone so that the teacher can clearly see how well each individual student understands the material.
- For information on how to implement this activity, click here.
- Khan Academy keeps track of students correct and incorrect answers, and suggests that they get 3 correct answers in a row. In order to show the teacher that the student really did get three correct answers in a row, The student should take a screenshot of their screen so that the teacher can see the three check marks. Then the student should email this photo in.