Appendix A: Mathematics 8 Prescribed Learning Outcomes

The organizers for Mathematics 8 are as follows:

Problem Solving
Number (Number Concepts)
Number (Number Operations)
Patterns and Relations (Patterns)
Patterns and Relations (Variables and Equations)
Shape and Space (Measurement)
Shape and Space (3-D Objects and 2-D Shapes)
Shape and Space (Transformations)
Statistics and Probability (Data and Analysis)
Statistics and Probability (Chance and Uncertainty)

In order to prepare students to use a variety of methods to solve real-life, practical, technical, and theoretical problems, it is expected that students will:

• solve problems that involve a specific content area (e.g., geometry, algebra, statistics, probability)
• solve problems that involve more than one content area within mathematics
• solve problems that involve mathematics within other disciplines
• analyse problems and identify the significant elements
• develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following:
  
  • guess and check
    
  • identify patterns and use a systematic list
    
  • make and use a drawing or model
    
  • eliminate possibilities
    
  • work backward
    
  • simplify the original problem
    
  • select and use appropriate technology to assist in problem solving
    
  • analyse keywords
• solve problems individually and co-operatively
• determine that solutions to problems are correct and reasonable
• clearly and logically communicate a solution to a problem and the process used to solve it
• evaluate the efficiency of the processes used
• use appropriate technology to assist in problem solving

Number (Number Concepts)

In order to prepare students to demonstrate a number sense for rational numbers, including common fractions, integers, and whole numbers, it is expected that students will:

• define, identify, compare, and order any rational numbers
• express two-term ratios in equivalent forms
• represent and apply fractional percents and percents greater than 100 in fraction or decimal form and vice versa
• represent square roots concretely, pictorially, and symbolically
• distinguish between a square root and its decimal approximation as it appears on a calculator
• express rates in equivalent forms
• represent any number in scientific notation

Number (Number Operations)

In order to prepare students to apply arithmetic operations on rational numbers to solve problems and apply the concepts of rate, ratio, percent, and proportion to solve problems in meaningful contexts, it is expected that students will:

• add, subtract, multiply, and divide fractions concretely, pictorially, and symbolically
• estimate, compute, and verify the sum, difference, product, and quotient of rational numbers
• estimate, compute (using a calculator), and verify approximate square roots of whole numbers
• use concepts of rate, ratio, proportion, and percent to solve problems in meaningful contexts
• derive and apply unit rates
• express rates and ratios in equivalent forms

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

Patterns and Relations (Variables and Equations)

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

Shape and Space (Measurement)

In order to prepare students to apply indirect measurement procedures to solve problems
generalize measurement patterns and procedures and solve problems involving area and perimeter, it is expected that students will:

• use the Pythagorean relationship to calculate the measure of the third side of a right triangle, given the other two sides in 2-D applications
• describe patterns and generalize the relationships by determining the areas and perimeters of quadrilaterals and the areas and circumferences of circles
• estimate and calculate the area of composite figures

Shape and Space (3-D Objects and 2-D Shapes)

In order to prepare students to link angle measures and the properties of parallel lines to the classification and properties of quadrilaterals, it is expected that students will:

• identify, investigate, and classify quadrilaterals, regular polygons, and circles according to their properties

Shape and Space (Transformations)

In order to prepare students to analyse design problems and architectural drawings using the properties of scaling and proportion, it is expected that students will:

• represent, analyse, and describe enlargements and reductions
• draw and interpret scale diagrams

Statistics and Probability (Data Analysis)

In order to prepare students to develop and implement a plan for the collection, display and analysis of data, using technology as required and to evaluate and use measures of central tendency and variability, it is expected that students will:

• formulate questions for investigation, using existing data
• select, defend, and use appropriate methods of collecting data:
  • designing and using surveys
  • research, using electronic media
• display data by hand or by computer in a variety of ways
• determine and use the most appropriate measure of central tendency in a given context

Statistics and Probability (Chance and Uncertainty)

In order to prepare students to compare theoretical and experimental probability of independent events, it is expected that students will:

• use various data-collection techniques (including computers) to simulate and solve probability problems
• recognize that if n events are equally likely, the probability of any one of them occurring is
• determine the probability of two independent events where the combined sample space has 52 or fewer elements
• predict population characteristics from sample data

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

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