This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will classify conic sections, using their shapes and equations.

It is expected that students will:

• classify conic sections according to shape
• classify conic sections according to a given equation in general or standard (completed square) form (vertical or horizontal axis of symmetry only)
• convert a given equation of a conic section from general to standard form and vice versa

SUGGESTED INSTRUCTIONAL STRATEGIES

The study of quadratic relations helps students connect geometry and algebra. The theory of conic sections finds application in fields ranging from construction and telecommunications to aerospace and astronomy.

• Have students define quadratic relations in terms of their component functions so that they can use their graphing calculators. For example, a circle of radius 5 can be entered as:
  
  This allows students to explore domain, range, and limits as they relate to asymptotes.
• Ask students to collect examples of how quadratic relations are applied. Examples could include:
  • satellite dishes
  • jet engines
  • domed stadiums
  • car headlights
  • parabolic microphones
• Demonstrate, using a "take-apart" model, that conic sections result from the intersection of a plane and a cone.
• Discuss the advantages of writing equations in general or in standard form.

SUGGESTED ASSESSMENT STRATEGIES

As students explore problems involving quadratic functions and relations, they develop an understanding of how algebra and analytic geometry are applied in a real-world context. In assessing students’ abilities to use variables, graphing techniques, and algebraic representations, the focus is on the presentations (in words, symbols, and graphs) and explanations they use to illustrate their understanding of the concepts.

Observe

• To check students’ understanding of quadratic functions and relations, circulate through the classroom and note:
  • the extent to which students can analyse a particular quadratic relation given a graphing analysis outline
  • whether students can recognize the declining characteristics (locus) and properties of each type of quadratic relation, and can relate the type of conic to specific equations
  • whether students can explain the effect of an term in an equation — how does it affect the possible values of x (domain)? What about ?

Question

• Give students data or a list of measurements that describe various relationships or structures found in the real world. Have them develop an appropriate equation to describe each of these relationships. Ask students to predict other values, and answer associated questions based on their equations.

   

Collect

• Place a number of conics in graphic form or standard form and general form around the classroom. Have students sort them according to type and either
  • defend their choices
  • develop/present the criteria used in making their choices

Present

• Have students use a poster to summarize the characteristics of each conic as a subset of the general conic.

RECOMMENDED LEARNING RESOURCES

Multi-Media

• Mathematics 12, Western Canadian Edition
  Ch. 9 (Sections 9.1 - 9.3, 9.5, 9.6)
• MATHPOWER 12, Western Edition
  Ch. 3 (Sections 3.1, 3.3 - 3.6)

Software

• Secondary Math Lab Toolkit

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: December 4, 2000

Ministry of Education Home Page