Applications of Mathematics 11 -
Patterns and Relations (Relations and Functions)

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 represent and analyse quadratic, polynomial and rational functions, using technology as appropriate.

It is expected that students will:

• determine the following characteristics of the graph of a quadratic function:
  • vertex
  • domain and range
  • axis of symmetry
  • intercepts

SUGGESTED INSTRUCTIONAL STRATEGIES

In order to fully describe a function or relation, students need to be able to extract key data from either the graph of the function or the equation. Students should be able to describe, where appropriate the vertices, domain and range, symmetry, or intercepts of a relation.

• Provide real-life situations modeled by quadratic equations (e.g., parabolic sound reflectors in auditoriums, curves created by origami art, reflecting surfaces of search lights) and have students use graphing calculators to determine:
  • maximum (or minimum) value and its meaning in context
  • x-intercept(s) and its meaning in context
  • y-intercept(s) and its meaning in context
    Ask students to explain how these values relate to the real-life situations.
• Using visual aids such as flip cards, overhead projectors, or graphing calculators with overhead displays, present students with examples of several quadratic equations of varying levels of complexity and their corresponding graphs. For example: .
  Ask students to make generalizations about the relationship between the form of the equation and the shape of its corresponding graph. Repeat this process with the other types of functions.
• Work with science teachers to set up experiments to obtain parabolic data (e.g., use a Calculator Based Laboratory to obtain the heights of falling objects or projectiles and generate a model function to solve for roots, vertices, and time at a given height).
• Make BINGO Cards with the following setup:

  B	I	N	G	O
  max/min	x-int	y-int	axis of symmetry	domain & range

  
  

Provide a page with a number of options that students can fill in under each category. Using an overhead projector, display the graph or equation of a function. Students may mark under any category a correct feature of the graph or equation which appears on their card.

SUGGESTED ASSESSMENT STRATEGIES

Assessment strategies must emphasize the students’ ability to extract key descriptive information from parabolic graphs or equations.

Observe

• Parabola Aerobics: Students begin with their arms up in a parabola shape. Ask students to describe where the vertex is on their body; where the axis of symmetry is. Ask them to show you what the graph would look like if the x-intercepts (in this case the vertex) went from (0,0) to (-3,0) and (3,0). Observe that students make their parabola move down. Ask them to show you what would happen if the new axis of symmetry was . All students should move sideways, etc.
• As students use the BINGO Cards, keep track of possible correct solutions. As they play the game, observe the extent to which they can glean the graph or equation features from the given graph or equations.

Question

• Circulate and ask students:
  • how they select the window for their graphs
  • what happens when the TRACE feature is used
  • what the x and y values mean
  • why the y value changes when the x value changes
  • why a regression equation is used
  • what are its benefits

Collect

• Writing assignment: Given a particular problem or application, ask students to explain the importance and use of: - maximum or minimum points
  • x-intercepts
  • y-intercepts
  • the axis of symmetry
  • the domain
  • the range

  Assess student responses according to a previously developed set of criteria developed with the class.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Applied Mathematics 11, Western Canadian Edition
• Explore Quadratic Functions with the TI-83 or TI-82
• Exploring Functions with the TI-82 Graphics Calculator
• An Introduction to the TI-82 Graphing Calculator
• Modeling Motion: High School Math Activities with the CBR
• Using the TI-81 Graphics Calculator to Explore Functions
• What If ...?: The Straight Line: Investigations with the TI-81 Graphics Calculator
• What If ...?: The Straight Line: Investigations with the TI-82 Graphics Calculator

Software

• GrafEq (Macintosh & Windows Version 2.09)

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: January 11, 2001

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