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NSW SelectiveYear 7 entry

Number patterns for the Selective maths test

Independent. Not affiliated with the NSW Department of Education.

A number pattern follows a hidden rule, and the rule lets your child jump to any term without drawing them all. For Selective maths, find the difference, turn it into a rule, check it on every term, then use it.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Patterns & Rules (lesson preview)
A short preview from the SelectiveReady lesson “Patterns & Rules”, on number patterns for the NSW Selective test.
Published: 15 October 2026

Patterns & Rules is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan^{1SelectiveReady · 13 October 2026 · Published}. The preview plays here with English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns that a pattern is a code with a hidden rule, and that the rule lets them predict any later term. They'll be able to find the difference, write it as a rule, check the rule and use it on number and shape patterns.

The clip finds how many matchsticks are in shape ten without drawing a single one. The full lesson adds patterns inside patterns, three traps and a five-step checklist.

3

What are number patterns?

A number pattern is a list of numbers, called terms, that follow one rule. In 4, 7, 10, 13 the rule is add 3 each time. A shape pattern works the same way: count what each shape uses, and you have a number pattern.

The useful idea for Year 5 and 6 is the rule by position. Instead of adding 3 again and again, your child links each term to its place in the line. The lesson writes the place as n, so the rule for 4, 7, 10 is 3n + 1.

Position (n)	1	2	3	10
Term	4	7	10	?
3 × n	3	6	9	30
3 × n + 1	4	7	10	31

The difference gives the times number. The small adjustment makes the first term fit.

4

How do pattern questions show up in the Selective test?

Patterns can appear as numbers, shapes or real situations like rows of chairs. The Department publishes no topic list, so no one can say how many pattern questions a test will have. ^{2NSW Education · 13 October 2026 · Published}

The Department's rule	What it means for patterns
Questions use concepts your child already learns at school^{2NSW Education · 12 October 2026 · Published}	Patterns are school maths; the situation is new
Questions draw on concepts from the NSW curriculum up to Year 6^{2NSW Education · 12 October 2026 · Published}	No high school algebra is needed, only a rule in words or symbols
35^{2NSW Education · 12 October 2026 · Published} questions in 40^{2NSW Education · 12 October 2026 · Published} minutes	A rule beats drawing ten shapes
2^{3NSW Education · 12 October 2026 · Published} sheets of working paper, with more on request	Room for a quick table of positions and terms
5^{2NSW Education · 12 October 2026 · Published} options per question	Testing each option against the rule is a fair check

5

What is the method for pattern questions?

Find the difference first, then turn it into a rule. The lesson's most important habit comes next: check the rule against every term you already know.

From pattern to rule: a growing row of matchstick squares, then find the difference, write the rule, check the rule and use the rule.

Find the difference
Write the gap between each pair of terms. Is it the same each time, or growing?
Write the rule
The difference is the times number. Then adjust so the first term fits.
Check the rule
Test it on every term you know. The lesson says this takes five seconds and saves most mistakes.
Use the rule
Put in the position you need. Or work backwards from a total to the position.

6

What does a worked pattern question look like?

We wrote this question to show the four steps, including working backwards.

Question: A café pushes square tables into one long row. One table seats 4 people, two tables seat 6 and three tables seat 8. How many tables are needed to seat 30 people?

Step	What your child does
Find the difference	4, 6, 8: each new table adds 2 seats
Write the rule	2 × tables, then adjust: 2 × 1 + 2 = 4. The rule is 2n + 2
Check the rule	2 tables: 4 + 2 = 6. 3 tables: 6 + 2 = 8. It fits
Work backwards	2n + 2 = 30, so 2n = 28 and n = 14 tables
Check the answer	14 tables seat 28 + 2 = 30 people

The shared sides are the trap here. Dividing 30 by 4 treats every table as a separate table with four seats. Two seats are lost at each join.

7

Which mistakes catch children on pattern questions?

The most common mistake is trusting a rule too early. The lesson's example is 2, 4, 6: it looks like add 2, but the next term could be 9.

Trap	What it looks like	The fix
Rule too early	Sees 2, 4, 6 and writes 8 without checking	Check at least three steps
Forgetting the adjustment	Finds +3 and writes 3n, not 3n + 1	Test the rule on the first term
One step too many	Adds 3 nine times to reach row 9 from row 1	Row 1 to row 9 is eight steps
Counting shared sides twice	Every shape counted as if it stood alone	Count what each new shape adds

8

Can my child try one on their own?

Here is a question from our free maths set: rows of chairs in a hall. Your child writes the rule, then checks the explanation.

Practice question · SEL-MA-TST-31

Chairs are set out in rows in a school hall. The first row has 14 chairs. Each row after that has 3 more chairs than the row in front of it.

How many chairs are in row 9?

A
27
B
35
C
38
D
41
E
126

Show answer and explanation

Answer: C

Answer: C (38)

From row 1 to row 9 there are 8 steps, and each step adds 3 chairs.
Extra chairs: 8 × 3 = 24.
Row 9: 14 + 24 = 38 chairs.
Check by listing: 14, 17, 20, 23, 26, 29, 32, 35, 38.

Why the other options are wrong

A (27): This is 9 × 3, which leaves out the 14 chairs that the first row starts with.
B (35): This is the number of chairs in row 8; it adds 3 only seven times.
D (41): This adds 3 nine times, but there are only 8 steps from row 1 to row 9.
E (126): This multiplies 14 by 9, as if every row had 14 chairs.

Find the difference
Each row has 3 more chairs than the row in front of it.
Count the steps
Row 1 to row 9 is eight steps, not nine.
Use the rule
8 × 3 = 24 extra chairs, and 14 + 24 = 38. The answer is C.
Check the traps
D adds 3 nine times. A is 9 × 3 and leaves out the 14 chairs in the first row.

9

Questions parents ask about number patterns

What is the nth term?

It's the rule that turns a position into a term. For 4, 7, 10 it is 3n + 1, so the tenth term is 31.

Is this algebra?

It's the first step towards it. Your child can say the rule in words: three times the position, plus one.

Do patterns come up in Thinking Skills too?

Thinking Skills has its own question types, so see our Selective Thinking Skills page. This lesson covers maths patterns.

How can my child practise at home?

Build a pattern with toothpicks or blocks and ask for the tenth shape. Then ask how many shapes you could make from a box of a set size.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan^{1SelectiveReady · 13 October 2026 · Published}.

Next questions

Sources and checks

SelectiveReady
SelectiveReady · Checked 13 October 2026
Selective high school practice tests
NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.
Placement test
NSW Department of Education · Checked 12 October 2026 · CC BY 4.0 (NSW Department of Education copyright notice); quotes credited

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