Number Patterns and Rules

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Number Patterns: The Hidden Rules Around Us

Have you ever noticed that your school's room numbers follow a pattern? Room 101, 103, 105, 107... What comes next? If you guessed 109, you've discovered an arithmetic pattern — numbers that follow a secret rule!

An arithmetic pattern is like a number train where each car is connected by the same rule. Once you find that rule, you can predict what comes next, just like following stepping stones across a creek.

Finding the Pattern Rule

Let's look at this sequence: 3, 7, 11, 15, 19, ___

To find the rule, we look at the difference between each number and the next one:

3 → 7

7 → 11

11 → 15

15 → 19

The rule is: Add 4 each time!

So the next number is 19 + 4 = 23

🔑 Key Insight

Not all patterns add! Some subtract the same amount each time. The sequence 20, 17, 14, 11, 8 follows the rule "subtract 3." The pattern still works — it just goes backwards instead of forwards!

Patterns in Real Life

Arithmetic patterns are everywhere! Think about:

🏠House numbers on a street: 12, 14, 16, 18...
🕐Clock hours: 3:00, 6:00, 9:00, 12:00...
💰Saving money: $5, letter: 'P', title: 'Number Patterns and Rules', concept: 0, letter: 'P', title: 'Number Patterns and Rules', concept: 5, $20...

Pattern Detective Steps

1. Look at the first two numbers
2. Find the difference between them
3. Check if the same difference works for the next pair
4. Use the rule to predict what comes next!

Key Takeaway:

Just like those school room numbers, every arithmetic pattern has a hidden rule waiting to be discovered. Once you find it, you become a number detective who can predict the future!

Sample questions

1. What are the next two numbers in the pattern: 4, 8, 12, 16, __, __?

○ 18, 20

✓ 20, 24

○ 24, 32

○ 20, 22

Answer: 20, 24 — The rule is +4. Adding 4 to 16 gives 20, and adding 4 to 20 gives 24.

2. Identify the rule for this sequence: 50, 45, 40, 35, 30.

○ Add 5

○ Multiply by 5

✓ Subtract 5

○ Subtract 10

Answer: Subtract 5 — Each number is 5 less than the one before it.

3. In the pattern 2, 4, 8, 16, 32, what is the rule?

○ Add 2

○ Add 4

○ Multiply by 4

✓ Multiply by 2

Answer: Multiply by 2 — This is a geometric pattern where each number doubles.

Skills in this topic

Identify arithmetic patterns in a number sequence
Extend repeating and growing shape patterns
Determine the rule for an addition/subtraction input-output table
Determine the rule for a multiplication/division input-output table
Find missing values in a function table

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