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:

• solve problems involving triangles, including those found in 3-D and 2-D applications.
• solve coordinate geometry problems involving lines and line segments, and justify the solutions.

It is expected that students will:

• solve problems involving ambiguous case triangles in 3-D and 2-D
• solve problems involving distances between points and lines
• verify and prove assertions in plane geometry, using coordinate geometry

SUGGESTED INSTRUCTIONAL STRATEGIES

Students are surrounded by geometric forms in nature, architecture, technology, science, and visual arts. In their study of geometry, students develop skills in deductive reasoning, problem solving, and the visual representation of ideas.

• Have students use trigonometry to calculate heights or lengths of items around the school (e.g., lamppost, flagpole, totem pole).
• Include numerous non-traditional learning opportunities such as;
  • participating in field studies (e.g., a construction site, airport)
  • interviewing guest speakers (e.g., engineers, surveyors)
  • investigating the operation of tools such as the commercial clinometer, or compass
  • researching projects involving real-life applications such as navigation, surveying, and astronomy
• Provide students with several examples of ambiguous case triangles and ask them to identify why the ambiguous case triangle has two possibilities. Have students describe the one situation where there is no ambiguity.
• Encourage students to develop an appreciation of the use of coordinate geometry in many real-world applications.
• Demonstrate the definition of a circle by using a student volunteer as the center and another as the locus point (x, y). As the student moves around the classroom, point out that the (x, y) values are constantly changing. Show the same effect using the trace feature on the graphing calculator.
• Encourage students to draw detailed diagrams whenever attempting geometry problems.
• Demonstrate concepts by using paper folding or other physical examples.
• Whenever possible, model inductive reasoning, and have students discover rules and theorems through experiments.

SUGGESTED ASSESSMENT STRATEGIES

Students apply their understanding of terms and procedures when solving problems using geometric properties of angles, lines, triangles, polygons, and the distance formula. Assessment in this area can focus on the importance of problem-solving skills.

Observe

• Observe the extent to which students communicate with each other using appropriate mathematical language and descriptions.
• Have students complete problems involving non-right triangles. Observe:
  • their ability to recognize the ambiguous case
  • how accurately students use mathematical language and symbols
  • the extent to which they demonstrate appropriate knowledge and understanding of concepts and procedures
  • the extent to which they persevere with assigned task
  • how accurately they complete diagrams and calculations

Question

• Ask groups or pairs of students to list as many applications of geometry as they can.

Collect

• Check students’ study sheets for accuracy, clarity, and the effectiveness of their illustrations.

Self-Assessment

• Have students make up a general marking rubric for geometry questions. Ask students to select a number of criteria that they need to improve.
• Give students a series of word problems and have them work in pairs. Ask pairs to compare their work with other pairs to verify their methods and solutions. Have them make individual action plans that include how they will overcome any weaknesses or how they will challenge themselves to learn more about the topic.

Presentation

• Have each students present an example of a problem from another discipline that requires a trigonometric solution. Examples could include physics (e.g., light refraction—Snell’s law), chemistry (e.g., bond angles), geography (e.g., map projections). Prior to the presentations, develop assessment criteria with students.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Mathematics 11, Western Canadian Edition
  Ch. 9 (Sections 9.1 - 9.3)
• MATHPOWER 11, Western Edition
  Ch. 8 (Section 8.7)

Software

• The Geometer’s Sketchpad

CD-ROM

• Geometry Blaster

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

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