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.
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.