Chapter 11 · ICSE Class 5 Math

Patterns

A pattern follows a rule — once you spot it, you can predict what comes next. Drag the sliders and watch a number sequence build itself.

The Pattern Machine
Rule: start at 3, add 4 each time
3
4

Try it: set Add each time to 1 — that's just counting!

A repeating shape pattern of circle, square, circle, square, with a question mark for what comes next A sequence showing circle, square, circle, square, circle, and a question mark box asking what shape comes next in the pattern What comes next? (square)
11.1

Number patterns

A number pattern is a sequence of numbers that follows a rule. Once you know the rule, you can find any term without listing every single number in between.

Growing pattern
2, 4, 6, 8...
Shrinking pattern
20, 17, 14, 11...
Skip counting
5, 10, 15, 20...
Everyday example — Counting by 5s to count coins, or counting by 2s to count shoes in pairs, are both number patterns you already use. Try setting the Pattern Machine above to Start 5, Add 5 to see skip counting live.
11.2

Shape and geometric patterns

1A repeating shape pattern

🔺🔵🔺🔵🔺🔵 ?

The pattern repeats every 2 shapes: triangle, circle. So the next shape is 🔺 (triangle)

2A growing shape pattern

A pattern of dots grows: 1 dot, then 3 dots, then 6 dots, then 10 dots — each new group adds one more dot than the last increase (2, then 3, then 4). Find the next number.

15 dots (adding 5 this time)

11.3

Finding the rule

1Spotting the difference

Look at: 6, 11, 16, 21. Find the difference between each pair of numbers.

11−6=5, 16−11=5, 21−16=5. Rule: add 5 each time

2Finding a missing term

7, 14, ___, 28, 35. What is the missing number?

The rule is add 7 each time, so 21

11.4

Worked examples

1Finding the next 2 terms

3, 8, 13, 18, ___, ___

Rule: add 5. Next terms: 23, 28

2A shrinking pattern

50, 44, 38, 32, ___

Rule: subtract 6 each time. Next term: 26

Watch out — Always check the difference between more than one pair of numbers before deciding on the rule — checking just one pair can trick you if the pattern isn't what it first looks like.
Practice

Exercises

Tap a question to reveal its answer once you've tried it yourself.

Assess

Sample tests

Two 20-mark, 30-minute tests. Reveal answers question by question.