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NSW SelectiveYear 7 entry

Order of operations for the Selective maths test

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Order of operations is the rule for which part of a calculation comes first: brackets, then multiplication and division, then addition and subtraction. In Selective maths, where no calculator1NSW Education · 12 October 2026 · Published is allowed, BODMAS keeps each step right.

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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

Number Operations Mastery (lesson preview)

A short preview from the SelectiveReady lesson “Number Operations Mastery”, on order of operations for the NSW Selective test.

Published:

Read the video transcript

Okay, so the problem is 3 + 4 times 2 - 1. First step, we use BODMAS. We scan the line and bam we see multiplication, so we do that first. 4 times 2 is 8. Now let's just rewrite the problem. 3 + 8 - 1. Since addition and subtraction are on the same level, we just work left to right. 3 + 8 is 11 and 11 - 1 is 10. And there it is, the correct answer is 10. Now what's really cool about this slide is seeing those two paths right next to each other. On the left, if you just go straight from left to right with no BODMAS, you get 13. But on the right, by following the rule and doing the multiplication first, you get the correct answer, 10. This right here, this is the difference between getting the question right and falling right into the trap.

Number Operations Mastery 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 plan2SelectiveReady · 13 October 2026 · Published. The preview plays on this page with English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns that every calculation hides a code: the order you do things in. They'll be able to use BODMAS, work a long line one level at a time, and use three mental shortcuts that save time without a calculator.

The clip solves 3 + 4 × 2 − 1 two ways, side by side, and shows why only one answer is right. The full lesson adds the shortcuts, a decoder for word problems, the zero trap and a five-point checklist.

3

What is the order of operations?

The order of operations is the agreed rule for which part of a calculation to do first. Without it, two people could work out the same line and get two answers. The lesson calls it BODMAS, and some classrooms say BIDMAS: the rule is the same.

The lesson compares it to a queue at a theme park. Brackets go first, and multiplication and division hold a fast pass, so they jump ahead of addition and subtraction wherever they stand in the line.

LevelLettersWhat it meansOur example
FirstBBrackets(2 + 3) × 4 = 5 × 4 = 20
SecondOOrders: powers and square rootsRare in primary problems
ThirdD and MDivide and multiply, left to right12 ÷ 3 × 2 = 4 × 2 = 8
LastA and SAdd and subtract, left to right10 − 4 + 3 = 6 + 3 = 9

Division doesn't always come before multiplication, and addition doesn't always come before subtraction. Each pair shares a level, so your child reads them from left to right, like a book.

4

How do calculations show up in the Selective maths test?

They sit inside almost every question: in our practice sets, most problems take two or three steps. The Department publishes no topic list, so no one can say how many questions turn on the order of operations. 1NSW Education · 13 October 2026 · Published

The Department's ruleWhat it means for calculating
351NSW Education · 12 October 2026 · Published questions in 401NSW Education · 12 October 2026 · Published minutesQuick, accurate steps leave time for thinking
No calculator1NSW Education · 12 October 2026 · Published in any sectionEvery step is done by hand, so the order matters
23NSW Education · 12 October 2026 · Published sheets of working paper, with more on requestRoom to write one step per line
Questions use concepts your child already learns at school1NSW Education · 12 October 2026 · PublishedBODMAS is school maths; the problem around it is new
51NSW Education · 12 October 2026 · Published options per questionIn our practice sets, wrong options are usually the result of one slip

Mathematical Reasoning is 25%1NSW Education · 12 October 2026 · Published of the whole test.

5

What is the method for a multi-step calculation?

Scan the whole line before working anything out, then work down the levels one at a time. Rewriting the shorter line after each step is what stops a slip.

Which part comes first: brackets, then orders, then divide and multiply left to right, then add and subtract left to right.

  1. Scan the whole line

    Look for brackets, then for × and ÷, before calculating anything. The lesson says the multiplication should jump out at you.

  2. Do the top level first

    Brackets first. Then multiplication and division, from left to right.

  3. Rewrite the shorter line

    After each step, write what's left on a new line. Your child can see what's still to do.

  4. Finish left to right, then check

    Addition and subtraction last, in reading order. Then compare the answer with a rough estimate.

6

Which mental maths shortcuts does the lesson teach?

The lesson's toolkit has three shortcuts. They matter because no calculator1NSW Education · 12 October 2026 · Published is allowed, so speed comes from knowing numbers well.

Split a number

47 × 6 is hard. Split the 6 into 5 and 1: 235 + 47 = 282.

Double and halve

25 × 12 looks tricky. Double 25 and halve 12: 50 × 6 = 300.

Use place value

60 × 70 is 6 × 7 tens of tens: 42 hundreds, or 4,200.

7

What does a worked word problem look like?

We wrote this problem to show the method. The words decide the operations, and the order decides the answer.

Problem: Ana takes 3 friends to the pool. Tickets cost $9 each, and Ana pays for everyone with a $50 note. How much change does she get?

StepWhat your child writes
Read what is askedChange, so the cost comes off the $50
EstimateAbout 4 tickets at $10 is $40, so about $10 change
Write one line50 − (1 + 3) × 9
Brackets first1 + 3 = 4 people, so 50 − 4 × 9
Multiply next4 × 9 = 36, so 50 − 36
Subtract last50 − 36 = 14
Check$14 is close to the estimate, and it is change

Two slips give wrong answers that look possible. Forgetting Ana herself gives 50 − 3 × 9 = 23. Working left to right without the brackets gives a number far bigger than $50.

8

What is the most common order-of-operations mistake?

The most common mistake is working straight from left to right. In the clip, 3 + 4 × 2 − 1 gives 13 that way, but the right answer is 10.

TrapWhat it looks likeThe fix
Left to right only3 + 4 × 2 becomes 7 × 2 = 14Multiply first: 3 + 8 = 11
Multiply always before divide12 ÷ 3 × 2 becomes 12 ÷ 6 = 2Same level, so left to right: 8
Missing the word clue"How many more" read as addingHow many more means subtract; shared equally means divide
The zero trap5 × 0 written as 5Any number times zero is zero
9

Can my child try one on their own?

Here is a question from our free maths set. Your child writes one line for it, works it out on paper, then checks the explanation.

Practice question · SEL-MA-TST-01

Tuan's school sold 214 raffle tickets at $3 each. The prizes cost $186 altogether.

How much money did the raffle raise after paying for the prizes?

  1. A

    $456

  2. B

    $544

  3. C

    $556

  4. D

    $642

  5. E

    $828

Show answer and explanation

Answer: A

Answer: A ($456)

  1. Money from the tickets: 214 × $3 = $642.
  2. Take away the cost of the prizes: $642 − $186 = $456.

Why the other options are wrong

  • B ($544): In 642 − 186, this takes the smaller digit from the larger one in each column instead of regrouping.
  • C ($556): This regroups in the ones and tens but forgets that the hundreds digit drops from 6 to 5.
  • D ($642): This is the money from the tickets before the prizes are paid for.
  • E ($828): This adds the cost of the prizes instead of taking it away.

  1. Read what is asked

    Money raised after paying for the prizes, so the prizes come off the ticket money.

  2. Write one line

    214 × 3 − 186. Multiplication comes first.

  3. Work down the levels

    214 × 3 = 642, then 642 − 186 = 456. The answer is A.

  4. Check the traps

    D is the ticket money before the prizes. E adds the prizes instead of taking them away.

10

Questions parents ask about order of operations

What does BODMAS stand for?

Brackets, orders, division, multiplication, addition and subtraction.

Is BODMAS the same as PEMDAS?

Yes. Parentheses are brackets and exponents are orders, so the rule is the same.

How can my child practise at home?

Write a short line, such as a shopping total with change, and solve it two ways. Talk about which way is right and why.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan2SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Mathematical Reasoning →Lesson: Algebraic Thinking →Lesson: Fractions, Decimals & Percentages →Free Selective practice test →The NSW Selective test explained →

Sources and checks

  1. 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.

  2. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  3. 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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