Unit 1 number patterns
- 1. Math 6: number patterns Unit 2
- 2. Number Patterns pg. 10 The first pattern is a shrinking pattern. The second pattern is an alternating pattern. The third pattern is an alternating growing pattern.
- 3. Explore pg. 10 1, 5, 13, 29, 61 How did you find the pattern rule for the first pattern? (I subtracted terms and got 4, 8, 16, 32, so I knew the rule was not multiplying each input number by the same number. I multiplied each term by 2, and got 2, 10, 26, 58,122, …. I noticed that if I then added 3 to each number, I got the pattern) The pattern rule is: Start at 1. Multiply by 2, then add 3 each time
- 4. Explore pg. 10 300, 298, 296, 294, 292 What is the rule for the third pattern? Pattern Rule: Start at 300. Subtract 2 each time What type of pattern is this? How do you know? It is a shrinking pattern; the terms get smaller.
- 5. Connect pg. 10 Recursive Pattern: Each term can be found by applying the pattern rule to the previous term. All above examples are recursive patterns.
- 6. Connect pg. 10 Write the 5 terms for a recursive pattern that starts at 7. The Pattern Rule is: Start at 7. Multiply by 2, then add 1 each time. 7x2+1 = 15 15x2+1=31 63x2+1=127 7, 15, 31, 63, 127
- 7. Connect pg. 11 We can write a pattern like this: 1, 6, 11, 16, 21 1 = 1x5 -4 6 = 2x5 -4 11 = 3x5-4 16 = 4x5– 4 21 = 5x5 -4 What would the 20th number be?
- 8. Connect pg. 11 Take: 1, 6, 11, 16, 21 Find the difference* -The difference is -5 Pattern rule: Start at 1. Add 5 each time
- 9. Connect pg. 11 1, 6, 11, 16, 21 How do we now extend the pattern? What number comes next? How do you know?
- 10. Lets try these 6, 13, 34, 97, 286 What do we do first? FIND THE DIFFERENCE 286 – 97 = 189 97-34 = 63 34 -13 = 21 13 – 6 = 7 What pattern do you see?
- 11. What’s the pattern? 6, 13, 34, 97, 286 Each difference is triple the previous difference! Therefore, this suggests that x3 is part of the pattern rule. LET’S TRY IT 6 x3 = 18 …. 18 - ? = 13…..5! 13 x 3 = 39…..39 – 5 = 34!! Continue with all of them! It matches! Therefore, The pattern rule is: Start at 6 then multiply by 3, then subtract 5.