Order of operations explained for parents (Australia)

Homework shows 3 + 4 × 5 and Australian parents wonder why the answer is not 35 if you work left to right. In primary classrooms, order of operations is the shared rule for which calculation to do first when a number sentence mixes brackets, powers (lightly), multiplication, division, addition and subtraction. Many schools teach it with a mnemonic such as BODMAS or BIMDAS - useful as a memory hook, but not a substitute for why the order exists.

This guide owns the order-of-operations teach-through for Year 5–Year 6 (Year 4 lightly): concrete multi-step stories before abstract strings, the rule in plain language, BODMAS/BIMDAS (and a light PEMDAS note), left-to-right within equal steps, and calm home practice. Meaning of each operation: addition, subtraction, multiplication, division. Story problems: word problems. Written ÷: long division. Year maps: Year 4–Year 6 maths.

What order of operations means

Order of operations = the agreed sequence for evaluating a calculation that has more than one operation, so everyone gets the same answer.

In Australian primary language, the usual order is:

1. Brackets (parentheses) first - do the inside
2. Orders - powers and roots, lightly in upper primary (e.g. 2², √9 when the class meets them)
3. Division and multiplication, working left to right
4. Addition and subtraction, working left to right

So 3 + 4 × 5 is 3 + 20 = 23, not 35 - because multiplication sits above addition in the order, even though + appears first on the page.

Teachers may say order of operations, BODMAS, BIMDAS, "do brackets first", or "follow the rules". Echo the class phrase. The meaning is fairness and consistency - not a trick to trip children up.

Not the same as knowing + − × ÷ alone

Order of operations decides which calculation happens when several sit in one sentence. It does not replace understanding each operation:

• Addition explained - joining / total
• Subtraction explained - take away / difference
• Multiplication explained - equal groups / arrays
• Division explained - sharing / grouping
• Word problems explained - finding what the story asks before any order rule

At home: (1) be sure the child can do each single operation on friendly numbers; (2) act out a multi-step story before writing a mixed string; (3) apply the order rule when the sheet mixes operations. If × facts wobble mid-string, rebuild fluency separately - times tables explained - rather than blaming BODMAS alone.

Concrete multi-step stories before abstract strings

Abstract 2 + 3 × 4 lands better after a story children can see:

Bags of apples. "Four bags with 3 apples each, then add 2 more on the bench." Act it: 4 × 3 = 12, then + 2 = 14. Write 2 + 3 × 4 only after the story matches - and notice the × must happen before the + if the bags come first.

Shared lollies then leftovers. "Share 12 lollies between 3 friends, then each gets 1 more from Mum." Share first (12 ÷ 3 = 4), then + 1 → 5. Link sharing meaning to division and story shape to word problems.

Array then add a row. Sketch 2 rows of 5, then add 3 loose counters: (2 × 5) + 3 = 13. Arrays: arrays explained; equal piles: equal groups.

Keep materials short. The written string records the story; chanting a mnemonic without a story often produces left-to-right guesses.

The rule in plain language (not chant-only)

Say the steps out loud in everyday words before any acronym:

1. Anything in brackets first - brackets are a "do this bit now" box
2. Powers / roots next when they appear (Year 5–6 lightly) - "orders" in BODMAS/BIMDAS
3. Multiply and divide next, left to right - they sit at the same level; whichever comes first on the line wins
4. Add and subtract last, left to right - same idea: equal priority, scan left to right

Worked example: 8 − 2 × 3

• No brackets; no powers
• Multiplication before subtraction: 2 × 3 = 6
• Then 8 − 6 = 2

Worked example with brackets: (8 − 2) × 3

• Brackets first: 8 − 2 = 6
• Then 6 × 3 = 18

Same digits, different brackets, different answer - that is the whole point of the rule.

Worked example left-to-right among equals: 24 ÷ 4 × 2

• Division and multiplication are equal priority
• Left to right: 24 ÷ 4 = 6, then 6 × 2 = 12 (not 24 ÷ 8)

Honesty for parents: mnemonics alone fail when children treat every letter as a strict one after another ladder and forget that D and M (or B and I for "indices") share a level. Meaning first; letters second.

BODMAS, BIMDAS, and a light PEMDAS note

Australian schools vary:

• BODMAS - Brackets, Orders, Division, Multiplication, Addition, Subtraction
• BIMDAS - Brackets, Indices, Multiplication, Division, Addition, Subtraction (same idea; "indices" = powers)
• Some texts still show PEMDAS (Parentheses, Exponents, …) from overseas resources - parentheses = brackets; exponents = orders/indices

Match the teacher's letters. Do not fight over which acronym is "correct" - the underlying order is the same. Remind children that Division/Multiplication are a pair (left to right), and Addition/Subtraction are a pair (left to right). "Orders" / "indices" / "exponents" stay light in primary - square numbers and simple powers when the class introduces them; deep algebra is later.

Year by year: where order of operations shows up

Year 4 - multi-step thinking and mixed +/−/×/÷ in simpler forms; formal "order of operations" language may appear lightly (Year 4 maths; AC Year 4).

Year 5 - clearer classroom focus on brackets and the agreed order for mixed calculations (Year 5 maths; AC Year 5).

Year 6 - fluency with brackets, left-to-right among equals, and light powers/indices where the class goes (Year 6 maths; AC Year 6).

Australian Curriculum Mathematics (version 9) builds efficient, consistent calculation through these years. At home: one carefully spoken multi-step example beats a page of silent, left-to-right guesses.

Home games that do not feel like worksheets

Story then string. Invent a two-step kitchen or shopping story; act it; then write the number sentence and check the order matches the story (word problems).

Bracket vs no bracket. Same digits twice: once with brackets, once without. Compare answers and say why they differ.

Left-to-right card. Write a ÷ b × c with friendly numbers; cover the right half; finish the left operation first; uncover and continue.

Estimate whisper. Before calculating 5 + 6 × 4, whisper "about 30-ish if × first" - sense-check after (addition / multiplication fluency helps).

Keep games under ten minutes. If evenings fray - homework without tears.

A simple weekly home routine

1. Two minutes of meaning - one multi-step story with objects or a sketch.
2. Five minutes of one careful mixed string - say the rule in plain words, then apply BODMAS/BIMDAS letters if the class uses them.
3. Three minutes of a check - reverse a step, re-speak left-to-right among equals, or rebuild with brackets and without.

Stop while friendly. Operation skills sit on their own pages - this page owns the order only.

Common mix-ups (and kinder fixes)

Always left to right. Rebuild with a bags/apples story where × must come before +.

Treating BODMAS as six strict steps. Teach D/M as one band and A/S as one band; practise 24 ÷ 4 × 2.

Ignoring brackets. Point to the box: "this bit first - always."

Chant without meaning. Drop the acronym for a day; use only "brackets → ×÷ → +−" in speech.

Blaming order when ×/÷ facts are shaky. Warm the table, then return to one mixed string - times tables explained. Leftovers after ÷: remainders. Exact splits: factors and multiples. Written long ÷: long division.

Tears over a worksheet of strings. One carefully spoken example beats a page of crosses - homework without tears, maths anxiety.

Wider worry: Is my child behind in maths?; calm signals: when to worry about maths.

How this links to other guides

• Addition explained for parents - + meaning (not the order rule)
• Subtraction explained for parents - − meaning
• Multiplication explained for parents - × umbrella
• Division explained for parents - ÷ sharing / grouping
• Long division explained for parents - written bus-stop ÷
• Word problems explained for parents - story → which operation
• Times tables explained for parents - fluency inside mixed strings
• Equal groups explained for parents / Arrays explained for parents - concrete × meaning
• Factors and multiples explained for parents / Remainders explained for parents - light ÷ cousins
• Year 4–Year 6 maths (Year 5)
• Maths Help hub - more parent guides

Ask the teacher: "For mixed-operation homework, which mnemonic do you use - and should we echo brackets → ×÷ → +− in plain words at home?"

FAQ

What is order of operations?

The agreed sequence for calculating when a number sentence mixes brackets, powers (lightly), ×÷, and +− - so answers stay consistent.

What is BODMAS or BIMDAS?

Classroom mnemonics for that order. Letters vary by school; Division/Multiplication (and Addition/Subtraction) share a level and run left to right. Meaning beats chant alone.

Why isn't 3 + 4 × 5 equal to 35?

Multiplication comes before addition in the order, so it is 3 + 20 = 23.

When do Australian children meet this?

Often more formally in Year 5–Year 6, with Year 4 light multi-step work. Follow the class method.

Does this page teach addition and multiplication?

No - those skill pages own meaning. This page owns which calculation to do first when they mix.

A calm next step

When multi-step stories come before abstract strings, brackets are respected, and ×÷ then +− (left to right among equals) feels settled - and you want a wider number-skill snapshot at home - Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet calculation and related ideas at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.

Powers/orders include squares — meaning first in square numbers for parents.