The document summarizes key concepts about number patterns from a math textbook. It discusses three types of patterns: shrinking, alternating, and alternating growing. It provides examples of recursive patterns where each term is found by applying a rule to the previous term. Students are guided through exploring patterns, finding pattern rules, and extending patterns to additional terms. The document emphasizes that to identify a pattern rule, students should first find the differences between terms.

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.

12. Homework
PG 12 #1-6