Numerical Patterns | Grade 5 Math

Learn

What is a Numerical Pattern?

A numerical pattern (or number sequence) is a list of numbers that follow a specific rule. Each number in the pattern is called a term.

Finding patterns helps us predict what comes next and understand relationships between numbers!

Example Pattern

2

→

4

→

6

→

8

→

?

Rule: Add 2 — Each term is 2 more than the previous term. Next term: 10

Types of Numerical Patterns

Addition Patterns

Add the same number each time.

5, 10, 15, 20, 25, ...

Rule: Start at 5, add 5

Subtraction Patterns

Subtract the same number each time.

100, 90, 80, 70, 60, ...

Rule: Start at 100, subtract 10

Multiplication Patterns

Multiply by the same number each time.

2, 4, 8, 16, 32, ...

Rule: Start at 2, multiply by 2

Division Patterns

Divide by the same number each time.

1000, 100, 10, 1, ...

Rule: Start at 1000, divide by 10

How to Find the Rule

1

Look at Consecutive Terms

Compare each number to the one before it. What's the difference?

2

Check if the Difference is Constant

If you always add or subtract the same amount, that's your rule!

3

Check for Multiplication/Division

If addition doesn't work, try dividing each term by the previous one.

4

Test Your Rule

Apply your rule to all terms to make sure it works throughout the pattern.

Pattern-Finding Tip: Write the difference between each pair of numbers above the arrows. If the differences are all the same, it's an addition/subtraction pattern. If they double or triple, it's a multiplication pattern!

Examples

Example 1: Finding the Rule

Pattern: 3, 7, 11, 15, 19, ...

Find the differences:

7 - 3 = 4
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4

Rule: Add 4

Next term: 19 + 4 = 23

Example 2: Multiplication Pattern

Pattern: 3, 9, 27, 81, ...

Find the ratios:

9 ÷ 3 = 3
27 ÷ 9 = 3
81 ÷ 27 = 3

Rule: Multiply by 3

Next term: 81 × 3 = 243

Example 3: Finding a Specific Term

Pattern: 5, 8, 11, 14, ... (Rule: Add 3)

Question: What is the 10th term?

We can use a formula: Term = Start + (Position - 1) × Rule

10th term = 5 + (10 - 1) × 3 = 5 + 9 × 3 = 5 + 27 = 32

Interactive Pattern Builder

Create Your Own Pattern

Choose a starting number, operation, and value to generate a pattern!

Start:

Operation:

Value:

Terms:

Click "Generate Pattern" to see your sequence!

Pattern Challenge: Find the Missing Number!

Look at the pattern and type what comes next.

Practice Problems

Problem 1

What is the next number in the pattern: 4, 9, 14, 19, 24, ?

Problem 2

What is the rule for the pattern: 2, 6, 18, 54, 162?

Problem 3

If a pattern starts at 100 and subtracts 7 each time, what is the 5th term?

Problem 4

What are the next two numbers: 1, 4, 16, 64, ?, ?

Problem 5

In the pattern 3, 8, 13, 18, 23, ..., what is the 12th term?

Problem 6

Which number does NOT belong in this pattern: 5, 10, 15, 21, 25, 30?

Check Your Understanding

Question 1

How do you determine if a pattern uses addition or multiplication?

Question 2

In the pattern 7, 14, 21, 28, ..., why is it called an "addition pattern" even though the terms are multiples of 7?

Question 3

To find the 50th term of an addition pattern without writing all 50 terms, you would:

Summary

🔢

Patterns Have Rules

Every pattern follows a consistent rule like add, subtract, or multiply.

🔍

Find the Difference

Compare consecutive terms to discover the pattern rule.

🎯

Predict Terms

Once you know the rule, you can find any term in the pattern.

📐

Use Formulas

Formulas help find terms without counting through the whole sequence.

Remember: Patterns are everywhere in math and real life! Understanding numerical patterns helps you solve problems more efficiently and make predictions about the future.

Next Steps

Look for patterns in everyday life (house numbers, prices, schedules)
Practice creating your own patterns for friends to solve
Connect patterns to coordinate graphing from the previous unit
Explore how patterns relate to algebra concepts you'll learn next