Mathematics 8 -
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 use patterns, variables and expressions, and graphs to solve problems, it is expected that students will:

• substitute numbers for variables in expressions and graph and analyse the relation
• translate between an oral or written expression and an equivalent algebraic expression
• generalize a pattern from a problem-solving context

SUGGESTED EXTENSIONS

To extend students' understanding of patterns, they could:

• represent a pattern using mathematical expressions and equations, and verify by substitution

SUGGESTED INSTRUCTIONAL STRATEGIES

Looking for patterns and making generalizations from them are mathematical skills useful in investigating and solving real-world problems. The variables, expressions, and equations used to describe patterns and relationships are the basis of students' study of algebra.

• Have students work individually or collaboratively to explore patterns by:
• working at concrete activities using simple cases (e.g., dividing a circle by lines to create patterns)
• developing a pattern using, for example, two or more shapes, colours, or textures
  
• differentiating between growing and repeating patterns
  
• changing a growing pattern to a repeating pattern
  
• changing a given pattern to a new one
  
• determining the formula to extend the pattern

Encourage students to use concrete materials where possible (e.g., algebra tiles, algebra lab gear, two-colour counters). Remind them that there are many possible ways of describing patterns.

• Ask students to bring in examples or pictures of patterns from their surroundings (e.g., flower petals, architecture, needles on a tree, ploughed fields). Invite them to make conjectures about the patterns. Ask students:
  • How did these patterns occur?
  • How would you go about finding or creating a pattern?
• Display a table of ordered pairs. Have students work with partners to determine the rule that was used to generate each pair. Students could then create patterns using their own rules and challenge their partners to generate the rules from the patterns.
• Have students work in groups to examine graphs from a variety of sources and attempt to interpret their meaning.
• Brainstorm terms that have the same meaning, such as sum, difference, product, and quotient. Have students develop posters of these terms, which can be put up in the classroom.
• Ask students to suggest one number each, and respond to their numbers with others based on a pattern or equation. Ask students to plot each pair of numbers. Continue until students can guess what the pattern is.
  

SUGGESTED ASSESSMENT STRATEGIES

Students use higher-order thinking skills to identify patterns and to generalize. Assessment should provide opportunities for students to demonstrate their problem-solving skills.

Question

• As students solve problems using patterns, variables, expressions, equations, and graphs, ask them to explain the methods and processes they are using. Provide feedback to students concerning their application of problem-solving approaches.

Collect

• Ask students to annotate their work to describe the processes they use to solve problems. Alternatively, students could provide brief descriptions of which processes did and did not work.

Self-Assessment

• Work with students to generate a set of criteria that can be used to evaluate problem-solving skills. Use the criteria to create a rating scale that students can use to evaluate their own skills. Criteria should demonstrate:
  • a willingness to persevere to solve difficult problems
  • flexibility in trying different approaches<br>
  
  
• Note: Refer to Suggested Assessment Strategies In Problem Solving section.
  

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 8)
• MATHPOWER 8, Western Edition

Multimedia

• The Learning Equation Mathematics 8 (TLE)
  
• Math Tools
  
• Mathematics 8 (Distance Education Package)
  
• Minds on Math 8, Revised Edition
  
• Understanding Math Series
  

• Mathville VIP

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

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