Principles of Mathematics 10 -
Patterns and Relations (Patterns)

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 generate and analyse number patterns.

It is expected that students will:

• generate number patterns exhibiting arithmetic growth
• use expressions to represent general terms and sums for arithmetic growth, and apply these expressions to solve problems
• relate arithmetic sequences to linear functions defined over the natural numbers

SUGGESTED INSTRUCTIONAL STRATEGIES

Many natural phenomena and man-made processes grow and shrink according to easily defined mathematical rules. An understanding of arithmetic and geometric growth helps students to better understand how the world around them changes.

• Give students a collection of arithmetic or geometric sequences with blanks either between the numbers or at the end of the sequence for students to fill in. Have them state the common difference or ratio and give a word-based rule describing how one term is calculated from the previous term.
• Have students find three examples of arithmetic or geometric sequences found in nature or used by people in their day-to-day lives.
• Ask students to match a column of linear equations to a column of arithmetic sequences.
• Have students describe or model natural phenomena that incorporate geometric sequences in their structure (e.g., flowers, spiral shells, paper folding).
• Give students numerical and non-numerical patterns and ask them to define the rule(s) for each pattern. Have them use the rules to make predictions and classify the patterns.
• Have students use concepts of arithmetic and geometric growth to solve problems such as:
  • If $1000 is deposited each year into an account that earns 12% compounded annually, how much money will have accumulated after 25 years?

  Then have them:

  • generate a model of this situation
• identify it as geometric or arithmetic
• discuss the answer (Is it surprising? Reasonable?)

SUGGESTED ASSESSMENT STRATEGIES

Assessment strategies should demonstrate algebraic skills as well as holistic pattern recognition. Students should also be able to articulate methods to aid in pattern discovery.

Observe

• How quickly do students see the patterns in partially completed sequences:
  • with no hints (2, 5, 8…)
  • with hints (2, _, _, 16, _… - geometric)
• Can students develop a mathematical equation from a sequence?

Question

• Can students articulate what to look for in determining whether a collection of numbers is an arithmetic sequence, geometric sequence, or neither?

Collect

• Have students collect five arithmetic, five geometric, and five other sequences. Provide them with equations or descriptions of how to generate each sequence.

Peer/Self Assessment

• Have each student develop a connect-the-dots puzzle using a combination of sequences and linear equations. Ask them to have another student do the puzzle and check it for accuracy.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Exploring Advanced Algebra with the TI-83
• An Introduction to the TI-82 Graphing Calculator
• Modeling Motion: High School Math Activities with the CBR
• Pure Mathematics 10 (Distance Learning Package)
• A Visual Approach to Algebra

Multi-Media

• The Learning Equation: Mathematics 10 Lessons 22 - 24
• Mathematics 10, Western Canadian Edition
  Ch. 1 (Sections 1.1, 1.2, 1.4)
  Ch. 5 (Section 5.5)
• MATHPOWER 10, Western Edition
  Ch. 2 (Sections 2.3, 2.5, 2.7)

Software

• Secondary Math Lab Toolkit
• Understanding Math Series

Games/Manipulatives

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

CD-ROM

• Geometry Blaster

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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