Mathematics 9-
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 use a scientific calculator or a computer to solve problems involving rational numbers, it is expected that students will:

• document and explain the calculator keying sequences used to perform calculations involving rational numbers
• solve problems, using rational numbers in meaningful contexts
• evaluate exponential expressions with numerical bases

SUGGESTED EXTENSIONS

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

• use the exponent laws to simplify expressions with variable bases
• use a calculator to perform calculations involving scientific notation and exponent laws
  calculate combined percents in a variety of meaningful contexts

SUGGESTED INSTRUCTIONAL STRATEGIES

Proficiency and efficiency in number operations is an important skill for the workplace, further education, and informed citizenship. Students can improve number operation skills and fluency through estimation, pencil-and-paper calculations, and appropriate calculator use.

• Create an activity sheet of questions that demonstrate the limitations of the calculator. Include questions that require the use of brackets and calculator memory buttons. For example:
  • 5 x 3²
  • 2¹⁰⁰⁰
  • -3² and (-3)²
  Ask students to develop their own questions that can test the appropriate use of their calculators.
• Have students use spreadsheet software to:
  • automate a chequebook
  • track homework time versus TV-watching time
  • keep sports statistics on school teams or individual student athletes.
• Ask students to identify resource people in the community who might use formulae with exponents in their work (e.g., foresters, plumbers, engineers, farmers). Have students interview a resource person about a formula they use and then return to the class to teach their peers about the formula, what the values are, and what information it provides to the person interviewed. Discuss as a class how real-life problems can be explained using formulae.
• Use mathematics games to give students practice in working with exponents (e.g., a game in which students are dealt a single card each, with numbers expressed in exponents). Have students hold their cards face out, so that they can see everyone else's but not their own, and bid based on how big they think their numbers are.
• Calculate with examples from the natural and social sciences for practice in scientific notation (e.g., number of micro-organisms in a sample population, distance between stars).
• Have students estimate some large numbers for use in operations (e.g., number of seconds since the "big bang" divided by the number of words ever spoken). Have them attempt to perform the operation using both long division and scientific notation, and discuss the relative merits of each.
  

SUGGESTED ASSESSMENT STRATEGIES

Number operations are the tools students use to solve problems. Assessment focusses on students' ability to use these tools accurately and appropriately in various contexts.

Collect

• Make up fraction "twisters" and have students determine whether they are true. For example: If a fifth of a fifth is less than a fourth of a fourth, then a fourth of a fifth must be less than a fifth of a fourth, of course. Is a third of a third more than a third and a third or is a third of a third less that a third cut in a third, or is it all absurd? Ask students to create their own twisters and challenge each other. Check for accuracy and understanding.
• At the start of instruction, identify outcomes that students are expected to achieve at the end of instruction. Have students organize examples of their own work into portfolios as evidence that they have attained the desired outcomes. Examples might include homework assignments, graded quizzes, personal summary sheets of learning, or anything else that shows students have acquired the intended learning.

Observe

• Examine students' work as they use the exponent laws to simplify and evaluate expressions. Watch to see that they are performing the appropriate operations. Provide feedback to help students identify and correct their errors.

Question

• To what extent can students:
  • estimate solutions to teacher-supplied problems
  • use their calculators or other appropriate technology to solve the problems
  • compare their estimates to the solutions they obtain using their calculators
  • determine possible reasons for any large differences between their estimates and calculator solutions.

Peer Assessment

• Have students work in pairs to make up questions to challenge their partners' skills with a calculator. Look for use of brackets, exponents, and negative coefficients. Confirm that the authors of the questions can solve them and explain the solutions to their partners.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 9)
• MATHPOWER 9, Western Edition
  

• The Learning Equation Mathematics 9 (TLE)
• Math Tools
• Mathematics 9 (Distance Education Package)
• Minds on Math 9, Revised Edition
• Understanding Math Series
  

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

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