What this chapter is about
Patterns are arrangements that repeat or follow a rule. You see patterns everywhere — in floor tiles, in the petals of a flower, in the way days of the week repeat. Mathematics is full of patterns too. When you spot a pattern, you can often predict what comes next.
This chapter helps you notice patterns in numbers, shapes and everyday life. You will learn to describe a pattern, continue it and even create your own. Finding patterns is one of the most important skills in mathematics because it helps you solve problems faster and understand how numbers behave.
After studying this chapter, you should be able to spot a pattern in a list of numbers or shapes, describe the rule behind it, and write the next few terms.
Key ideas
- A pattern is a set of numbers, shapes or objects arranged according to a rule that repeats or grows in a fixed way.
- To find a pattern, look at how each term changes to the next — is it adding, subtracting, multiplying, or changing shape?
- Number patterns can go up (like 2, 4, 6, 8) or down (like 20, 15, 10, 5).
- Shape patterns can repeat (circle, square, circle, square) or grow (one dot, two dots, three dots).
- Even numbers (2, 4, 6, 8, …) and odd numbers (1, 3, 5, 7, …) are simple patterns you already know.
- Recognising a pattern helps you predict what comes next without counting everything from the start.
- The same rule can create different patterns depending on the starting number.
Formulas and facts to remember
- Counting numbers: 1, 2, 3, 4, 5, … (each number is one more than the one before).
- Even numbers: 2, 4, 6, 8, … (add 2 each time; all are divisible by 2).
- Odd numbers: 1, 3, 5, 7, … (add 2 each time; leave remainder 1 when divided by 2).
- Multiples of 5: 5, 10, 15, 20, … (add 5 each time).
- Rule for any pattern: Difference between terms = Next term − Current term.
Worked examples
Example 1: Find the next two numbers
Pattern: 3, 6, 9, 12, ?, ?
Step 1: Look at how the numbers change. 6 − 3 = 3, 9 − 6 = 3, 12 − 9 = 3.
Step 2: The rule is "add 3 each time".
Step 3: Next number = 12 + 3 = 15. After that = 15 + 3 = 18.
Answer: 15, 18.
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Example 2: Continue the shape pattern
Pattern: △ ○ △ ○ △ ?
Step 1: Notice what repeats. Triangle, circle, triangle, circle, triangle.
Step 2: The rule is "triangle then circle" over and over.
Step 3: After triangle comes circle.
Answer: ○
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Example 3: Find the missing number
Pattern: 50, 45, 40, ?, 30
Step 1: Find the difference. 45 − 50 = −5, 40 − 45 = −5.
Step 2: The rule is "subtract 5 each time".
Step 3: Missing number = 40 − 5 = 35.
Check: 35 − 5 = 30 ✓
Answer: 35.
Common mistakes
- Thinking every pattern adds the same number → some patterns subtract, multiply or follow other rules.
- Looking only at the first two terms and guessing → always check at least three gaps before deciding the rule.
- Mixing up even and odd numbers → even numbers end in 0, 2, 4, 6, 8; odd numbers end in 1, 3, 5, 7, 9.
- Forgetting to verify the rule for all given terms → after guessing a rule, test it on every term.
- Writing the next term by counting on fingers without finding the rule → always state the rule first.
Quick revision
- A pattern follows a rule that tells you how to get from one term to the next.
- Find the rule by checking the difference or change between terms.
- Even numbers: 2, 4, 6, … (add 2). Odd numbers: 1, 3, 5, … (add 2).
- Shape patterns often repeat a fixed group of shapes.
- Once you know the rule, you can predict any term without listing all the terms before it.