Principles of Mathematics 10 -
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:

• examine the nature of relations with an emphasis on functions
• represent data, using linear function models

It is expected that students will:

• plot linear and nonlinear data, using appropriate scales
• represent data, using function models
• use a graphing tool to draw the graph of a function from its equation
• describe a function in terms of:
  • ordered pairs
  • a rule, in word or equation form
  • a graph
• use function notation to evaluate and represent functions
• determine the domain and range of a relation from its graph
• determine the following characteristics of the graph of a linear function, given its equation:
  • intercepts
  • slope
  • domain
  • range
• use partial variation and arithmetic sequences as applications of linear functions

SUGGESTED INSTRUCTIONAL STRATEGIES

Describing functional relationships is essential to interpreting and predicting the behavior of the world around us. Students will explore ways to translate between algebraic and graphical representations and use these skills to make inferences and solve problems.

• Ask students to explore non-linear functions with graphing technology such as calculators or computer software programs. Discuss the similarities and differences in the graphs and equations with the class.
• Have students use graphing calculators or computers to graph and investigate the graphic changes as a number is added (e.g., ) and when is multiplied by a constant to develop the concept . Have them record their findings in their journals, using their own words.
• Ask students to work in groups to determine techniques that will generate linear equations, given information other than slope and intercept.
• To explore the relationship of linear equations in computer programming, have students work in co-operative groups to generate short programs that produce linear drawings, then share these with the class.
• Organize a carousel activity in which students move in groups around various stations set up with activities to generate data. Students decide as a group how best to graph or display the data. Discuss as a class the similarities and differences in the solutions.
• Use a bakery model (ingredients in pastry out) or a sawmill/pulp model (log in lumber pulp/paper out) to illustrate the concept of domain and range.
• Have students use a function machine to calculate the range of a function from its domain.
• Have students generate two data points in a linear function (e.g., kilometers driven and car rental cost) and graph them. Ask them to generate model functions to answer questions about the intercepts (fixed costs) and slope) variable costs).
• Ask students to use maps and scale diagrams to calculate distances and sizes.

SUGGESTED ASSESSMENT STRATEGIES

Plotting data, and the subsequent analysis of relations and functions,a re key to student understanding of patterns. Assessment in this area should focus on students' ability to perform individual outcomes (such as graphing and analyzing functions derived from the physical world), and reflect students' understanding of the uses of graphs.

Collect

• Have students collect data on relations between pizza costs and diameters. This data could be represented as a list of ordered pairs, expressed as a rule, described in equation form, as a hand sketched graph, and finally drawn using a graphing calculator. Check particularly for students' ability to select scale, find slope in appropriate units, and select window parameters.

Question

• As students work on using function notation, evaluating functions and determining domain, range, intercepts and slope, check for their ability to work competently using both sketches and graphing tools. Note students' abilities to translate their graphing skills to understand the real-world implications of the data.

Presentation

• Have students conduct research into the cost of video rentals over time and present the data as a list of ordered pairs and the graph of the function. Note students' understanding of the use of the graph they have created (e.g., At what point has the rental cost exceeded purchase price?).

Peer Assessment

• Ask students to work in pairs using graphing calculators. Students can display graphs o their calculators, then challenge their partners to reproduce the graphs on their own calculators.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Exploring Functions with the TI-82 Graphics Calculator
• Graphing Calculator Activities for Enriching Middle School Mathematics
• An Introduction to the TI-82 Graphing Calculator
• Modeling Motion: High School Math Activities with the CBR
• Pure Mathematics 10 (Distance Learning package)
• Using the TI-81 Graphics Calculator to Explore Functions
• A Visual Approach to Algebra
• What If...?: The Straight Line: Investigations with the TI-81 Graphics Calculator
• What If...?: The Straight Line: Investigations with the TI-82 Graphics Calculator

Multi-Media

• The Learning Equation: Mathematics 10 Lessons 34 - 42
• Mathematics 10, Western Canadian Edition
  Ch. 5 (Sections 5.1 - 5.7)
• MATHPOWER 10, Western Edition
  Ch. 5 (Sections 5.1 - 5.6)
  Ch. 6 (Sections 6.5 - 6.8)

Software

• GraphEq (Macintosh & Windows Version 2.09)
• Green Globs & Graphing Equations
• Secondary Math Lab Toolkit

Games/Manipulatives

• Radical Math: Math Games Using Cards and Dice (Volume VII)

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 30, 2000

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