Page 86 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• discuss real-life examples, such as fractals, to highlight the concept of infinity, and make connections to learning in geometry and measurement to illustrate this concept in a variety of ways;
• elaborate on the ways in which various cultures have understood the concept of infinity.
Teacher Prompts
• Explain how you know that there are an infinite number of fractions between 8 and 9 . 10 10
• How might a pattern continue if it begins with 1, 4, ...?
• Is the number set created from your pattern finite or infinite? Compare your number set with
that of a partner. Do they have the same density? Do they both have a limit?
• Are there more triangular numbers or more prime numbers between 1 and 100? How many
more?
• What do you observe about the size of each successive number in the set: 1, 1, 1 , 1 , ...?
3 9 27 81
Sample Tasks
1. Have students compare the densities of the set of even numbers between 0 and 100 (inclusive) and the set of real numbers between 0 and 100 (inclusive).
2. Have students create visuals or patterns of numbers that can be extended indefinitely.
3. Have students come up with a pattern of numbers in which each number gets progressively closer to the number 2.
4. Have students describe the pattern they observe in the coloured sections of the square below and make predictions about how much of the total square will eventually be coloured.
85