Principles of Mathematics 10 - Number (Number Concepts)

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:

• analyse the numerical data in a table for trends, patterns and interrelationships.
• explain and illustrate the structure and the interrelationship of the sets of numbers within the real number system.

It is expected that students will:

• use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are not related recursively (not calculated from previous data)
• use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are related recursively (calculated from previous data)
• classify numbers as natural, whole, integer, rational or irrational, and show that these number sets are "nested" within the real number system

SUGGESTED INSTRUCTIONAL STRATEGIES

Using tables enhances students’ ability to see data in a compact and easily readable format. Students can extract specific information from tables, and use them to do general comparisons and find relationships.

• Distribute single newspapers to groups of three or four students and have them browse through the paper to find the sections that contain the most tables. Ask the groups to give two reasons why those particular sections use tables extensively.
• Have each student find three specific pieces of information in a table from a newspaper, magazine, or the Internet and share with a partner. Have pairs share their findings with the rest of the class.
• Place a multi-column, non-recursive table (e.g., hockey standings/stock market data) on an overhead. In a class discussion, encourage students to compare and contrast the data in the table. As a class, produce a word list of connections between the rows and columns of data.
• Provide students with a recursive table (e.g., mortgage, credit card account, savings account). Point out that the closing balance for any month is the opening balance of the next month. Ask students to analyse the repetitive nature of the calculations. Have them calculate the balance after three payments, given an opening balance, a monthly rate of interest, and the payment amount.
• Discuss the definitions of the various number systems. Use a set of nested measuring cups with appropriate labels to illustrate how the number systems fit inside one another. Illustrate the anomaly of irrational numbers by slipping a piece of paper between the rational-number cup and the real-number cup. Have students transfer these concepts to Venn diagrams in their notebooks.
• Draw a number line on the board and have students place rational numbers in appropriate places, then ask them to place irrational numbers on the line. Point out that a decimal approximation of the number is necessary to allow for the proper placement and that more decimal places lead to greater accuracy.

SUGGESTED ASSESSMENT STRATEGIES

Tables are commonly used to represent real life data. Assess students’ ability to use tables in a practical way. Students demonstrate their understanding of the structure and interrelationship within the number system when they explain the processes they use as they experiment with and manipulate numbers.

Observe

• While students are drawing meaning from tabular representations of data, note their ability to:
  • use words to describe data
  • identify specific facts from tables
  • determine trends where they exist
  • develop recursive tables in the form of spreadsheets
• Provide students with a nested Venn Diagram and have them place numbers appropriately. Observe students’ abilities to place numbers in such a way that they fit all the appropriate numbers systems.

Collect

• Give students multi-column tables such as sports standings, and note the extent to which students are able to glean information. Have students write a newspaper article based on the information and note the extent to which they are able to interpret data.

Question

• Ask students to suppose that they are responsible for adding 10 new items to the inventory of a clothing store. Have them create a spreadsheet that shows price, GST, PST, and cost. Ask them to explain how the value for each cell in their spreadsheet is calculated.

Self/Peer Assessment

• Work with students to develop criteria they can use to assess their posters. Criteria might include:
  • it is easy to use for classifying numbers
  • it makes sense to others
  • it gives accurate examples

  Students can use these criteria to assess their work, then compare their assessment to the teacher’s assessment.

Presentation

• Have students gather similar information on each of five scientists and present it in tabular form to another student or class.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Pure Mathematics 10 (Distance Learning Package)

Multi-Media

• The Learning Equation: Mathematics 10 Lessons 1 - 4
• Mathematics 10, Western Canadian Edition
  Ch. 1 (Sections 1.6, 1.7)
  Ch. 2 (Sections 2.1, 2.5)
• MATHPOWER 10, Western Edition
  Ch. 1 (Sections 1.1, 1.3)
  Ch. 2 (Sections 2.1, 2,2)

Software

• Understanding Math Series

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Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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