Primary 5 · Number & Algebra

P5 number and shape patterns

Patterns are not a P5 chapter of their own, but P5 papers often set them. Your child finds how much a pattern changes each time, writes the rule, and uses it to reach a far term, such as Figure 24, without drawing every figure.

Taught in: Term 4
Syllabus: Exam skill
Usual slip: One jump too many

Updated 10 October 2026

The pattern 5, 9, 13, 17 on a number line, jumping 4 each time

What your child learns in P5 number and shape patterns

Three skills, each with what it looks like on a worksheet.

Not a chapter of its own in the MOE syllabus. Schools test it as problem sums.

Find the common difference

Find how much the pattern grows each time. 5, 9, 13, 17 grows by 4, the common difference. The 10th term is 9 jumps of 4 after the first: 5 + 9 × 4 = 41.

Point	Value
5	5
9	9
13	13
17	17

Each jump is 4

Shape patterns in a table

Count each figure and write the counts in a table under the figure numbers. The table shows the common difference, and the rule follows from it: 3, 5, 7, 9 grows by 2 each time.

Figure	1	2	3	4
Matchsticks	3	5	7	9

The counts grow by 2

Repeating patterns

Some patterns repeat a group, such as red, blue, blue. Find how many items are in the group, then divide. 20 ÷ 3 = 6 R 2, so the 20th item is the 2nd in its group: blue.

Position	1	2	3	4	5	6
Colour	red	blue	blue	red	blue	blue

The group red, blue, blue repeats

Key facts and formulas

Term 4

Number pattern: any termTo reach the 20th term, add 19 jumps to the first term.20th term → $4 + 19 \times 7 =$ $137$
Shape patternFigure 1 is 4 sticks. Each new square adds 3 sticks.Figure 10 → $4 + 9 \times 3 =$ $31$
Repeating patternDivide by the length of the repeat. The remainder is the place: R 2 is the 2nd shape, a triangle.50th, repeat of 4 → $50 \div 4 =$ $12\text{ R }2$

Words to know

Term: Each number in a pattern. In 5, 9, 13, the 2nd term is 9.
Common difference: The amount a pattern goes up or down by each time.
Rule: A way to work out any term from its term number, without listing them all.
Repeating group: The part of a pattern that repeats, such as red, blue, blue.

The sentence that costs the mark

Look at the pattern 5, 8, 11, 14, … What is the 10th term?

What the working usually does

5 +10 × 3=35

Multiplies by the term number, 10, so it counts ten jumps of 3. But the first term is already there before any jump is taken.

What the question asked

5 +(10 − 1) × 3=32

Takes 9 jumps, because the 10th term sits nine steps after the first. The first term costs no jump.

Both start at 5 and add a run of 3s, and both land on a number that looks like a term. The only difference is 10 jumps or 9, and the 10th term is nine jumps along.

The same P5 number and shape patterns question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

The figures below are made from equal-sized squares, following a pattern. Find the number of squares in Figure 24.

Figure 1

Figure 2

Figure 3

Step 1 of 5▌

Count the squares: Figure 1 has 4, Figure 2 has 7 and Figure 3 has 10. Each figure grows by 3 squares, so the common difference is 3.
Figure 3 is 2 jumps of 3 after Figure 1, one fewer than its figure number. 4 + 2 × 3 = 10, which matches the count.
So Figure 24 is 24 − 1 = 23 jumps after Figure 1. Taking 24 jumps here is the slip: it counts one jump too many.
Use the rule: start at 4 and add 23 jumps of 3. 4 + 23 × 3 = 4 + 69 = 73.
So Figure 24 has 73 squares.

Every question in StudyLah comes with a walkthrough like this one.

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Three quick P5 number and shape patterns questions

Try them together, then tap to check.

Question 1

The table shows the arrows in Figures 1 to 4 of a pattern. What is the total number of shaded and white arrows in Figure 10?

Figure Number	1	2	3	4
Number of shaded arrows	2	4	6	8
Number of white arrows	2	3	4	5

Show answer

Answer31. Shaded arrows are 2 × 10 = 20 and white arrows are 10 + 1 = 11, so 20 + 11 = 31.

Question 2

A pattern repeats 1, 4, 1, 1, 4, 1, … The sum of all its numbers is 53. How many numbers are in the pattern?

Show answer

Answer26. Each group of 1, 4, 1 adds to 6. 8 groups are 24 numbers and 48. Then 1 + 4 = 5 is 2 more numbers.

Question 3

There are 6 friends in a room. Each friend shakes hands with every other friend once. How many handshakes are there in total?

Show answer

Answer15. The 1st friend shakes 5 hands, the 2nd 4 new ones, and so on, so 5 + 4 + 3 + 2 + 1 = 15.

Helping at home

How to tell it has clicked

You do not need to know the rule to check this. Ask your child how many jumps it takes to reach the 10th term from the first. The answer is 9. A child who says 10 has found the exact slip.

A child who understands counts the gaps between terms, not the terms. A child who multiplies by the term number lands one step too far, every time.

Try this tonight

Stand on the first step of a staircase and climb to the 10th. That is 9 more steps, because you started on the first one. Reaching the 10th of anything is 9 moves from the 1st.

Try it on a pattern in the homework: how many jumps from the first term to the one they want? Always one fewer than the term number.

Before and after P5 number and shape patterns

Builds on
Primary 4 Numbers to 100 000
Reads each digit by its place value
You are here
Primary 5 Number and Shape Patterns
Finds a rule to reach far terms

The methods your child will use here

Systematic list

In the PSLE's hardest questions

2026 Paper 2 Question 15: the stick pattern

More in Primary 5

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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