C1.4 Create and describe patterns to illustrate relationships among rational numbers.
Activity 1: Talking Numbers (Using Patterning to Discover Number Properties)
Present an incomplete table which shows enough information to be able to search for a pattern. Have students individually analyze the information on the table and lead a class discussion on possible patterns. Next, have students complete the table and be prepared to explain their thinking.
Example of number tables
- What do you notice?
| \(2 \times 4 = 8\) |
| \(2 \times 3 = 6 \) |
| \(2 \times 2 = 4\) |
| \(2 \times 1 = 2\) |
| \(2 \times 0 = 0\) |
| \(2 \times (-1) \ = \ ?\) |
| \(2 \times (-2) \ = \ ?\) |
| \(2 \times (-3) \ = \ ?\) |
| \(2 \times (-4) \ = \ ?\) |
- Can you predict the next values in this pattern? Explain.
- What would be the value of (2 times (-100)) Why?
- How would you show that (-2) times (-4) = 8 from a table of numbers like the one above?
Activity 2: The Chessboard (Making Conjectures and Generalization From a Number Pattern)
Materials
- Chessboard reproduced on a grid sheet or on a paper
- Non-permanent felt-tip pen
- Calculator
Divide the students into teams. Present the scenario to them. Each team must answer the questions. Discuss the proposed strategies in a debriefing session.
Situation
Anastasia is fascinated by the patterns of squares on a chessboard. Using her chess board and a non-permanent felt-tip pen, she creates a sequence of numbers.
She writes numbers on the boxes. In square A1 she writes the number 100 000 000, in square B1 the number 10 000 000, in square C1 the number 1 000 000, in square D1 the number 100 000 and so on.
She would like to identify the 64 squares of the chessboard with a number.
- What number will be written in box H1? How do you know? (last square of the first row)
- Can you explain the rule for finding the number assigned to each box? Is there a more efficient way to write your number?
- What number will be written on the 64th square of the chessboard? Describe the number pattern you would use to find this answer.