1 NumberPatterns Press Ctrl-A ©2009 G Dear – Not to be sold/Free to use Stage 4 Years 7 & 8

2 Number Patterns 1 A number pattern is a series of numbers that obeys a rule. Example 1 Rule: Start at 3: Add 5 3,8,13,18,23,28, Example 2 Rule: Start at 2: Add 1 & Multiply by 2 2,6,14,30,62,126, End of Slide

3 Finding the Rule 1 Many patterns are made by adding or multiplying the previous term by a given number. Example 2, 5, 8, 11,... Try subtracting consecutive terms. 5 – 2 = – 5 = – 8 = + 3 Rule: Add 3 The next two numbers are: End of Slide 14, 17.

4 Finding the Rule 2 Many patterns are made by adding or multiplying the previous term by a given number. Example 2, 4, 8, 16,... Try subtracting consecutive terms = = = 8

5 Finding the Rule 2 Many patterns are made by adding or multiplying the previous term my a given number. Example 2, 4, 8, 16,... 4 ÷ 2 = 2 8 ÷ 4 = 2 16 ÷ 8 = 2 Rule: Multiply by 2 The next two numbers are: Try dividing consecutive terms. End of Slide 32, 64.

6 Finding the Rule 3 Many patterns are made by adding or multiplying the previous term by a given number. Example 128, 64, 32, 16,... Try subtracting consecutive terms = = = -16 No!

7 Number Patterns 3 Many patterns are made by adding or multiplying the previous term by a given number. Example 128, 64, 32, 16, ÷ 128 = ÷ 64 = ÷ 32 = 0.5 Rule: Multiply by 0.5 The next two numbers are: Try dividing consecutive terms. End of Slide 8, 4.

8 Special Patterns (Rules) Odd Numbers 1, 3, 5, 7, 9, 11, 13, … Even Numbers 2, 4, 6, 8, 10, 12, 14, … Triangular Numbers 1, 3, 6, 10, 15, 21, … Square Numbers 1, 4, 9, 16, 25, 36, … Fibonacci Numbers 1, 2, 3, 5, 8, 13, … Prime Numbers 2, 3, 5, 7, 11, 13, 17, … Rule: Start with 0, 1 and add last two numbers. Rule: only two factors, itself and 1. Rule: Start with 1 & add next counting number. Rule: Square each term. Rule: Start with 1 and add two. Rule: Start with 2 and add two. End of Show