Mathematics 8 -
Number (Number Concepts)

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 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

SUGGESTED EXTENSIONS

To extend students' understanding of number concepts, they could:

• express three-term ratios in equivalent forms
• demonstrate and explain the meaning of a negative exponent, using patterns (limit to base 10)
• demonstrate concretely, pictorially, and symbolically that the product of reciprocals is equal to 1
  

SUGGESTED INSTRUCTIONAL STRATEGIES

The development of students' number sense requires that they incorporate new types of numbers, including common fractions, integers, and whole numbers, into their understanding of the number system. Linking new concepts to prior understanding and working from concrete to abstract representations are essential in developing numeracy.

• Invite students to work in pairs to examine problems requiring operations with very large or very small numbers. Demonstrate how to represent these numbers in decimal ("normal") notation and in scientific notation. Discuss the benefits of each method.
• Ask students to consider the following strategies:
  • divide any number by numbers progressing closer to zero and record the results
  • divide by zero and use multiplication to check the solutions.
  • Example:
• Ask students to represent the same number (e.g., 5) in as many ways as possible (e.g., ratio, fraction, percent, decimal). Have them identify and label the form for each representation.
• Bring in examples of ratios, percents, decimals, and fractions from newspapers or trade magazines or by searching the Internet. Discuss with the class why the form might have been chosen in each case. Does one form tend to be used more often in particular types of media?
• Give groups of students the same set of rational numbers to order on a number line. As each group presents their number lines to the class, have them justify the placement of each number.
• Have students calculate the square root of a number using a calculator and round the results to:
  • no decimal places
  • one decimal place
  • two decimal places, etc.
• Have students explain in writing how their results differ in each situation and how their results may affect further calculations.
  

SUGGESTED ASSESSMENT STRATEGIES

By demonstrating an understanding of the rational number system, students can show they possess the basic knowledge needed to use mathematics to solve problems. Assessment focusses on determining students' abilities to work with rational numbers.

Observe

• To what extent are students able to represent a simple number (e.g., a percent, a decimal, a fraction)? Determine the degree of accuracy in the labeling.

Collect

• Give students lists of fractions and decimals to arrange in numerical order and place on a number line. Have students develop lists of rules based on their work.
  • Can students correctly order and place numbers?
  • Do they make conversions correctly?
  • Do the rules they identify accurately reflect the process?

Print Materials

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

Multimedia

• Hot Dog Stand: The Works
• 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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