Stage 4 Years 7 8 Number Patterns Press

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 2

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

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. 4 - 2 = 8 - 4 = 16 - 8 = 2 4 8 4

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

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

Number Patterns 3 Many patterns are made by adding or multiplying the previous term by a given number. Example 128, 64, 32, 16, 8, . . 4. . Try dividing consecutive terms. 64 ÷ 128 = 0. 5 32 ÷ 64 = 0. 5 16 ÷ 32 = 0. 5 Rule: Multiply by 0. 5 The next two numbers are: End of Slide 7

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, 1, 2, 3, 5, 8, 13, … Prime Numbers 2, 3, 5, 7, 11, 13, 17, … Rule: Start with 1 and add two. Rule: Start with 1 & add next counting number. Rule: Start with 2 and add two. Rule: Square each term. Rule: Start with 0, 1 and Rule: only two factors, End of add last two numbers. itself and 1. Show 8