Mathematics 9 -
Patterns and Relations (Patterns)

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

In order to prepare students to generalize, design, and justify mathematical procedures using appropriate patterns, models, and technology, it is expected that students will:

• model situations that can be represented by first-degree expressions
• write equivalent forms of algebraic expressions, or equations, with integral coefficients

SUGGESTED EXTENSIONS

To extend students' understanding of patterns, they could:

• use logic to present mathematical arguments in solving problems
• write equivalent forms of algebraic expressions, or equations, with rational coefficients.

SUGGESTED INSTRUCTIONAL STRATEGIES

By searching for patterns, describing them in various ways (including algebraically), and recreating them, students are able to extend patterns as a part of their personal expression.

• Demonstrate to the class problem-solving techniques that may be employed to solve difficult problems. For example:
  • Using dots to represent the triangular numbers (1,3,6,10,...) predict the 20th, 100th, and nth term.
  • Find the total number of squares on a chessboard (all squares, not just 1 x 1), and extend the pattern to an n x n board.
• Have students collect graphs and formulae from science, social studies, and other subjects, and categorize each as either linear or non-linear
• Give students an algebraic expression followed by four choices (a, b, c, and d). Have students select which of the four choices are equivalent to the original and explain their selections. This activity can be repeated until most of the students are able to select correctly.
• Have students work in pairs to measure two variables (e.g., length of their arms and their height or the circumference and diameter of circular objects). Then have students post their measures on the board as pairs of numbers. Challenge students to search for relationships between the numbers.
• Challenge students to determine an algebraic expression for the sum of n consecutive natural numbers and the sum of n consecutive square numbers. Have students share results and discuss them as a class. Did they find more than one method?
• Present an open-ended question such as the handshake model (i.e., given n people in the room, how many handshakes can take place?). In groups, students could determine solutions and then record and report their methods. Encourage them to use hands-on equations, algebra tiles, and diagrams to model the problem. Discuss each method.
  • How well would it work if there were 50 people in the room? 100?
  • Are all methods equally powerful?
    

SUGGESTED ASSESSMENT STRATEGIES

Assessment of this suborganizer focusses on students' understanding of skills related to the introduction of algebra: accuracy and the use of appropriate procedures.

Question

• As students work independently and in small groups to find equivalent forms, ask them to explain the processes they are using. Note the clarity of students' explanations and their reasoning. Provide feedback to students concerning their clarity and reasoning.

Collect

• From the strategies students develop for searching for relationships, have them generate and verify formulae. Check the accuracy of students' work and provide feedback.
  o On selected problems, have students annotate their work to describe the processes they used to solve the problems. Alternatively, have students provide brief descriptions of what worked and what did not work as they attempted to solve particular problems.

Peer Assessment

• Have students justify to classmates their methods for determining whether equations are linear. Work with students to develop criteria to use to help them decide whether the justifications are convincing.
• Having discussed with the class what generally constitutes a good problem (e.g., clarity, is solvable by peers), ask students to work in small groups to generate problems for other groups to solve. Note the complexity of the problems generated as well as the success of the groups in solving them.
  

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 9)
• MATHPOWER 9, Western Edition

Multimedia

• The Learning Equation Mathematics 9 (TLE)
  
• Math Tools
  
• Mathematics 9 (Distance Education Package)
  
• Minds on Math 9, Revised Edition
  
• Understanding Math Series

© Copyright 2001. All Rights Reserved. BC MOE Standards Department.
Maintained by: Mathematics Coordinator
Revised: September 1, 2001

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