Mathematics 8 -
Number (Number Operations)

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 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

SUGGESTED EXTENSIONS

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

• calculate combined percents in a variety of meaningful contexts
• estimate, compute (using a calculator), and verify approximate square roots of decimals
  

SUGGESTED INSTRUCTIONAL STRATEGIES

Students' understanding of the number system is expanded to include rational numbers. They practise familiar arithmetic operations in new contexts.

• Ask students to solve basic operations with fractions using student-constructed or commercially available manipulatives (e.g., fraction tiles, Cuisenaire rods, attribute blocks, grid paper).
• Invite students to play games and to create their own games that incorporate operations with rational numbers (e.g., mathematics crossword or "cross-number" puzzles, mathematics bingo, Who Am I?)
• Demonstrate an iteration strategy (e.g., guess, check, modify) by having students develop methods of finding an accurate square root approximation to a number that is not a perfect square (e.g., Newton' s method).
  Newton' s method: is between 4 and 5 since is between and
• Have students consider open-ended problems using the context of "consumers." Then ask students to display solutions to the following types of questions and, if appropriate, substitute figures for those in the newspaper ads:
  • Compare newspaper ads or create examples where the same product is advertised "on sale" at more than one location (e.g., 20% off, 15% off with more free options, $5 off). Which is the best deal?
  • What is the final price of a $5 item marked 30% off?
  • What is the percent discount of a $10 item reduced by $2?
  • Compare similar products to determine which is the best buy.
• Pose, or have students pose, problems involving ratio, rate, proportion, or percent selected from
  the media. Discuss the mathematical validity of each example and the message it communicates to the reader.
  

SUGGESTED ASSESSMENT STRATEGIES

Students demonstrate their understanding of new number concepts by performing arithmetic operations using these numbers. Assessment focuses on students' understanding of the processes, as well as their accuracy in performing the operations.

Observe

• Watch students as they interact with other students to play mathematics games.
  • Does a lack of participation indicate a need for additional instruction?
  • Do the games students create reflect an understanding of concepts?
• Observe students' work with manipulatives. Have them explain how they use manipulatives to represent various operations.
  • Do they use correct terminology?
• When students solve problems, look for evidence that they understand the operations they are using by:
  • correctly performing calculations
  • identifying the correct ratios
  • performing calculations in the correct order
• Ask questions like:
  • Why did you use this operation?
  • What would happen if you changed the order of calculations?

Question

• Ask students to explain the steps involved in calculating a percent of a number.
• Have students describe two different ways they can verify their work.
• Ask students to explain the processes they use to estimate and verify square roots.

Collect

• Have students develop written or oral descriptions of the steps they follow to add, subtract, multiply, and divide rational numbers, providing examples that illustrate each step. Check their work to determine where students are having problems.

Peer Assessment

• Ask students to develop numerical examples of operations and challenge other students to represent them using manipulatives. Have students identify and correct errors in each other's representations.

RECOMMENDED LEARNING RESOURCES

Print Materials

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

• 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
  

• Mathville VIP

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

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