Mathematics 8 -
Patterns and Relations (Variables and Equations)

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

In order to prepare students to solve and verify one-step linear equations with rational number solutions, it is expected that students will:

• illustrate the solution process for a one-step, single-variable, first-degree equation, using concrete materials or diagrams
• solve and verify one-step, first-degree equations of the form:
  • x + a = b
  • ax = b
  • 
  where a and b are integers

• solve problems involving one-step, first-degree equations
  

SUGGESTED EXTENSIONS

To extend students' understanding of variables and equations, they could:

• illustrate the solution process for a two-step, single-variable, first-degree equation, using concrete materials or diagrams
• solve and verify two-step, first-degree equations of the form:
  • ax + b = c
  • 
    where a, b, and c are integers
• solve problems involving two-step, first-degree equations

SUGGESTED INSTRUCTIONAL STRATEGIES

Variables and equations provide students with the mathematical tools needed to solve complex, real-world problems. Learning is facilitated when students are given opportunities to use manipulatives and to describe equations in their own words.

• Have students use manipulatives or models to explore the concept of balance or equality, using examples such as:
  • a weight balance
  • a function machine
  • algebra tiles
• Give students opportunities to solve equations in various ways (e.g., manipulatives, computer software, games).
• Suggest that students work in pairs to construct flow charts of equation-solving procedures, then switch with other pairs and attempt to apply the steps to a given problem. Is there more than one way to solve the problem? Discuss as a class.
• Discuss with students the value of algebraic operations for solving problems. Have them consider longer, more complicated equations that can be solved easily and quickly using algebra but would take much longer to solve using arithmetic.
• Use student research (e.g., from the Internet) to create a timeline of events in the history of the use and development of algebra.
  

SUGGESTED ASSESSMENT STRATEGIES

Assessment focuses on students' understanding of the basics of solving equations: demonstrating an understanding of the solution processes, maintaining the equality of both sides of algebraic expressions, and verifying solutions.

Observe

• Review students' work as they solve first-degree equations. Look for common misconceptions and present them to the class for discussion.

Question

• Ask students to explain or demonstrate the processes they use to verify their solutions.

Collect

• Have students create flow charts showing the processes used to solve and verify the listed forms of first-degree equations. Evaluate students' work using criteria such as the following:
  • defines the processes clearly, logically, and accurately
  • shows all necessary steps in the processes
  • maintains equality throughout the solution process
  • accurately illustrates the process for verifying solutions
  • method of display effectively communicates information
  Give students the feedback necessary to correct their work.
• Ask students to solve two-step linear equations, explaining in writing how to do each step in the process and showing their work. Note the level of understanding demonstrated by students' explanations. Do they maintain the equality of expressions on both sides of the equations?

Peer Assessment

• Have students solve equations, showing all their work. Ask them to exchange solutions with other students and use keys to mark each other' s work. Students can identify the errors in their peers' solutions, explain how to fix them, and use partners' feedback to correct their own work.
  

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

CD-ROM

• Mathville VIP
  

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

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