Principles of Mathematics 10 -
Number (Number Operations)

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

PRESCRIBED LEARNING OUTCOMES

It is expected that students will:

• use basic arithmetic operations on real numbers to solve problems.
• describe and apply arithmetic operations on tables to solve problems, using technology as required.
• use exact values, arithmetic operations and algebraic operations on real numbers to solve problems.

It is expected that students will:

• communicate a set of instructions used to solve an arithmetic problem
• perform arithmetic operations on irrational numbers, using appropriate decimal approximations
• create and modify tables from both recursive and nonrecursive situations
• use and modify a spreadsheet template to model recursive situations
• perform operations on irrational numbers of monomial and binomial form, using exact values
• explain and apply the exponent laws for powers of numbers and for variables with rational exponents

SUGGESTED INSTRUCTIONAL STRATEGIES

Many calculations in science, industry, and finance involve irrational numbers. Students need to be able to perform simple calculations with irrational numbers and properly interpret the results. Although many questions can be solved adequately using approximate values, students should be able to work with exact representations of irrational numbers where possible. Operations of radicals and exponents with rational exponents build on algebraic and exponential skills previously learned.

A table enables organized data to be recognized and facilitates calculations.

• Provide students with a descriptive paragraph or set of written instructions for guessing a secret number, and have them work out the series of mathematical steps required. Ask them to confirm their process with a partner to test its accuracy.
• Ask students to find the maximum length umbrella that can fit in a rectangular gift box, bottom corner to top corner, for a box with rational lengths and for one with irrational lengths.
• Provide students with a descriptive paragraph containing numeric data (e.g., mutual funds over a 10-year period) and ask them to organize the data into a table.
• Give students a collection of sale papers and have them comparison shop for specific items. Have them place the results of the comparison in a table and underline the best price.
• Provide students with a basic spreadsheet template for calculating the cost of building a house. Have them change the dimensions of the house and number of bathrooms and bedrooms to see how the construction, electrical, plumbing, and total costs change.
• Have students work in pairs to design a template to show balance owing on a sample credit card account at the end of one month after a payment has been made.
• Discuss with the class the historical necessity of operations on radicals (e.g., calculators not yet invented) and their place in the language of mathematics.
• Assign an activity sheet to parallel the operations on radicals with operations on variables (e.g., questions on both ).

SUGGESTED ASSESSMENT STRATEGIES

Number operations are the tools students use to solve problems. Students need to demonstrate a clear understanding of the processes involved in performing various operations involving irrational numbers and how the operations are used.

Observe

• Note students' abilities to use their calculators to approximate have them find and compare.
• Ask students to draw several regular polygons and have them count the number of sides, diagonals, and intersection points and prepare a table showing this data. Observe students' abilities to use the tables to describe how the values of each polygon can be predicted without counting.

Self/Peer Assessment

• Have each student create a question involving irrational numbers and submit the question and its solution. Display students' questions on the overhead for the class to answer. Ask the class to compare its solutions with those of the originators and determine whether students have correctly solved their own questions.
• Have students write out a description of how to produce Pascal's Triangle and have a classmate use their instructions to produce the first six rows.

Collect

• Ask students to create a spreadsheet that would show bills for a credit card account that would occur in a situation in which no payments are made. Assume the amount borrowed was $1000 and the annual interest rate is 18% compounded monthly. Have them extend the table to show 12 months of account balances. Ask students to write a letter from the bank explaining the table to the credit card holder.

Presentation

• Have students collect data from a school sports team (e.g., free-throw percentage, penalties or fouls vs. minutes played) and create a table that shows an analysis of calculated values. Have students present their results to the class.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Pure Mathematics 10 (Distance Learning Package)

Multi-Media

• The Learning Equation: Mathematics 10 Lessons 5 - 11
• Mathematics 10, Western Canadian Edition
  Ch. 1 (Sections 1.5 - 1.8)
  Ch. 2 (Sections 2.2 - 2.4, 2.6 - 2.10)
• MATHPOWER 10, Western Edition
  Ch. 1 (Sections 1.3 - 1.5, 1.7, 1.8)
  Ch. 2 (Sections 2.1)

Software

• Secondary Math Lab Toolkit
• Understanding Math Series

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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