order of operations through simple multiplication problems

Across Australian classrooms from Brisbane to Perth, teachers introduce the order of operations once students have grown comfortable with their times tables. The challenge is that acronyms like BODMAS or PEMDAS can sound like a foreign language to a Year 4 student who only recently mastered the sixes. By framing the rule as a story about following fair steps, educators can keep the maths accessible without watering down the maths.

This guide walks through practical ways to teach the order of operations using simple multiplication problems. It covers why the rule matters in the early years, how to scaffold it gradually, the slip-ups children commonly make, and printable activities that reinforce the idea at home and in the classroom.

Why order of operations matters in the early years

In the Australian Curriculum, working with order of operations sits within the Number and Algebra strand, typically introduced across Years 5 to 6. By then, students in a typical Sydney primary classroom are juggling multi-digit calculations, fractions, and the beginnings of algebraic thinking. Without a reliable method for deciding which part of a problem to solve first, even confident mathematicians begin to guess.

Order of operations is not simply a school rule. It is the shared language that lets a Year 6 student in Melbourne and a tutor in Adelaide read the same expression and reach the same answer. Once children understand that multiplication happens before addition, they can evaluate more advanced calculations such as prime factorisation with confidence.

Introducing the rule without overwhelming students

Australian teachers often borrow the "Please Excuse My Dear Aunt Sally" mnemonic, but younger learners respond better to a visual story. Imagine three friends queuing at a canteen: the friend who holds the multiplication ticket is always served first, followed by anyone holding an addition ticket. Walking through problems on the board with coloured markers lets students see the order rather than memorise a string of letters.

A simple starting problem such as 3 + 4 × 2 lets the class compare two possible answers. Most children guess 14, the result of reading left to right, and are surprised when the correct answer of 11 appears. The disagreement is a perfect teaching moment. Once students feel the confusion, they are ready to accept the rule because it resolves a real puzzle rather than an arbitrary instruction.

Building problems step by step

Scaffolding is essential in the early weeks. Start with expressions that contain only one operation, such as 5 × 3 + 2, then progress to mixed problems like 6 + 2 × 4. Children in a Brisbane Year 5 classroom might then move on to expressions with brackets, also called parentheses, such as (3 + 2) × 4, which shows how grouping changes the outcome. Each step adds a single new layer of complexity, so the rule feels earned rather than imposed.

Colour-coding can support the scaffolding. Ask students to circle every multiplication sign in one colour and every addition sign in another. They then rewrite the problem showing only the multiplications first, followed by the additions. This physical act of separating the steps reinforces the priority of multiplication without turning the lesson into a chant about acronyms.

Common mistakes and how to address them

The most frequent error is reading from left to right, treating the problem as a string of equal steps. Another common slip is forgetting that brackets change everything inside them, which leads to answers that are close but incorrect. When students miss these points, they often develop shaky foundations that reappear later when tackling fractions or algebra.

Targeted practice pages help correct these habits. A short daily drill of five problems, where every expression includes both addition and multiplication, gives children repeated exposure to the correct order. Parents tutoring at home in regional Western Australia have found that a five-minute warm-up each morning works better than a long weekly session, because the rule settles into muscle memory through small, frequent touches.

Printable practice ideas for the classroom and home

Worksheets remain a reliable tool across Australian schools, and printable libraries make lesson planning easier for busy teachers. Puzzles that hide expressions inside a maze, or colour-by-number pages where the answer determines the shade, transform drill into play. Pairing these with factor tree printables extends the practice into prime factorisation once students are ready for the next step.

For homeschoolers following the Australian Curriculum from kitchen tables in Hobart or Darwin, printable resources remove the need to invent every problem from scratch. Many families build a small binder of mixed practice pages that they reuse each term, swapping in fresh problems as the year progresses. The approach keeps maths visible at home, which is especially helpful during the long summer holidays when skills can quietly fade.

Browse the full worksheet resource library to find order-of-operations pages, times-table drills, and puzzle packs ready to print for the new term.