Conic Sections: 4 week unit plan
SOL’s covered: AII.8, AII.18
Circles and Parabolas (2 weeks)
Distance and Midpoint Formulas (1 day)
Show how the pythagorean theorem is used to derive the distance formula.
Describe the midpoint formula.
Have them do some problems to determine the distance and mid-point of two points.
Circles (2 days)
Objective: To learn the relationship between the center and radius of a circle and the equation of the circle.
Give the students the general equation for all circles.
Show how this equation is a translation of the equation for circles centered at the origin.
Give students problems requiring them to use midpoint and distance formulas to find the center and radius of a circle and give the equation of that circle.
Discuss how to find equation of a circle given lines tangent to circle and radius.
Show how to find equation for circle given endpoints of diameter.
Review (2 days)
Spend time working in groups on several review problems. Teacher can walk around and help individual students.
Spend time going over the review problems with the whole class. Have students put the problems on the board and explain them to each other.
Quiz (1 day)
Give a quiz to see how everyone is coming along.
Computer lab worksheet (1 day)
Objective: For students to see the relationship between the equations for different conic sections. To be able to understand what each element of the equation does to the graph.
Parabolas (1 day)
Define and label a graph of a parabola and all of it's components.
Describe how to set up the equation so that the graph can be easily drawn from the equation and vice versa.
Give students problems requiring them to graph parabolas.
Review (2 days)
Go over how to complete the square in order to put equations into standard form.
Give them several problems to put into standard form. If time allows let them work in groups.
Conic Sections: Ellipses and Hyperbolas (1.5 weeks)
Ellipses (1 day)
Give definition of ellipse and it's components.
Show students what the equation of an ellipse looks like and how changing different components adjusts the graph.
Explain the difference between equation of ellipse and circle.
Give some problems for them to work on.
Hyperbolas (1 day)
Explain the difference between the equation of an ellipse and a hyperbola.
Also, explain the difference in the definition.
Have them do a few problems.
More on Central Conics (2 days)
Explain the difference between equations of ellipses and hyperbolas not centered about the origin.
Give them problems that require them to complete the square twice in order to put into standard form.
Quiz (1 day)
Give a quiz on ellipses and hyperbolas.
Solving Systems of Equations (2 days)
Explain that the solution of a system of equations is where the graphs of the equations intersect.
Show them how to solve a system by graphing the equations. Use graphing calculators to solve using this method.
Show them how to solve using the algebraic method and substitution method.
Review and Test (0.5 weeks)
Review (2 days)
Give the students several review problems to work on in groups. Walk around and help those who have questions.
Spend a day going over all of the review problems with the whole class. Get students to put some on the board and discuss them with their classmates.
Test (1 day)
Time to see if you're earning your money.