Number Patterns and Rules

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Concept Review

Number Patterns and Rules: The Math Detective's Secret

Imagine you're a detective who just discovered a mysterious sequence of numbers: 3, 6, 9, 12, 15... What comes next? How do you crack the code? The answer lies in discovering the hidden rule that creates the pattern.

Every number pattern follows a secret rule — like a recipe that tells you exactly how to get from one number to the next. Once you discover this rule, you can predict what comes next, just like a mathematical fortune teller!

Cracking the Pattern Code

Let's solve our mystery sequence step by step. Look at what happens between each number:

Aha! The rule is "add 3 each time." This means the next number would be 15 + 3 = 18.

🔍 Detective's Discovery

Here's the surprising part: You can generate an infinite number sequence from just one simple rule! Start with 2 and use the rule "multiply by 2":

2 → 4 → 8 → 16 → 32 → 64 → 128...

That tiny rule can create numbers bigger than the population of your entire city!

Rules Come in Many Flavors

Number patterns can follow different types of rules:

➕ Addition Rules

5, 8, 11, 14... (add 3)

✖️ Multiplication Rules

3, 6, 12, 24... (multiply by 2)

Think of it like a vending machine for numbers. You put in one number, the rule processes it, and out comes the next number in the sequence. The rule is your mathematical recipe that works every single time.

🔑 Key Takeaway

Just like our detective mystery at the beginning, every number pattern has a discoverable rule hiding inside it. Once you find that rule, you hold the key to generating an endless sequence of numbers. Math isn't just about memorizing — it's about being a pattern detective!

Sample questions

1. Start at 4 and follow the rule "Multiply by 2, then subtract 1." What are the first four terms?

○ 4, 8, 7, 14

✓ 4, 7, 13, 25

○ 4, 6, 8, 10

○ 4, 7, 10, 13

Answer: 4, 7, 13, 25 — (4×2)-1=7; (7×2)-1=13; (13×2)-1=25. This is a recursive pattern where each step builds on the last.

2. Rule: "Add 15." If the 1st term is 10, what is the 5th term?

○ 25

○ 85

✓ 70

○ 55

Answer: 70 — Term 1: 10, Term 2: 25, Term 3: 40, Term 4: 55, Term 5: 70.

3. Generate a pattern starting at 100 with the rule "Subtract 12." Which number will NOT be in the pattern?

✓ 60

○ 88

○ 76

○ 52

Answer: 60 — The pattern is 100, 88, 76, 64, 52, 40... 60 is skipped because it is not a multiple of 12 away from 100.

Skills in this topic

Generate a number pattern that follows a given rule
Identify the hidden rule in a number sequence
Find the next three terms in an alternating number pattern
Identify features of a pattern that were not explicit in the rule itself
Complete an input/output function table using a two-step rule

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