Mathematics · Year 6 · Algebraic Thinking and Patterns · Term 2

Applying the Order of Operations (BODMAS)

Applying the rules of BODMAS to solve multi step problems accurately.

• ACARA Content Descriptions
• AC9M6A03

About This Topic

Year 6 students apply BODMAS rules to evaluate multi-step numerical expressions with accuracy and confidence. BODMAS directs them to handle Brackets first, then Orders such as exponents, followed by Division and Multiplication from left to right, and finally Addition and Subtraction from left to right. They practise with expressions like (3 + 5) × 2² - 4 ÷ 2, recording each step to verify results. This builds procedural fluency essential for algebraic thinking and pattern recognition.

Aligned with AC9M6A03 in the Australian Curriculum, this topic sits within the Algebraic Thinking and Patterns unit. Students address key questions: why a universal order ensures consistent answers across calculations, how repositioning brackets changes outcomes entirely, and if BODMAS represents a mathematical discovery or human invention. These discussions develop reasoning about mathematical conventions and prepare for more abstract algebra.

Active learning benefits BODMAS instruction greatly. Students engage rules through games and peer challenges that expose errors in real time. Collaborative tasks like relay races or error hunts make abstract sequences concrete, while creating expressions fosters ownership. Such approaches reduce reliance on rote memory and highlight the rules' logic, leading to deeper retention and flexible application.

Key Questions

1. Why is a universal order of operations necessary for mathematics?
2. How can changing the position of brackets alter the outcome of an expression?
3. Is the order of operations a discovery or a human invention?

Learning Objectives

• Calculate the value of numerical expressions using the order of operations (BODMAS) with accuracy.
• Compare the outcomes of mathematical expressions when the order of operations or bracket placement is altered.
• Explain the necessity of a standardized order of operations for consistent mathematical communication.
• Identify and correct errors in calculations that misapply the order of operations.

Before You Start

Basic Arithmetic Operations

Why: Students need a solid understanding of addition, subtraction, multiplication, and division before applying them in a specific order.

Introduction to Brackets and Grouping

Why: Prior exposure to the concept of brackets indicating a specific order of calculation is helpful.

Key Vocabulary

BODMAS	An acronym representing the order of operations: Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Expression	A mathematical phrase that contains numbers, variables, and operators, but does not have an equals sign.
Operation	A mathematical process such as addition, subtraction, multiplication, or division.
Bracket	Symbols used in mathematics to group parts of an expression, indicating that the operation within them should be performed first.
Exponent	A number that shows how many times the base number is multiplied by itself.

Watch Out for These Misconceptions

Common Misconception

Operations always follow strict left-to-right order, ignoring BODMAS priorities.

What to Teach Instead

Students often calculate 6 ÷ 2 × 3 as 1 before realising it equals 9. Peer review in relay games reveals this quickly, as teams compare step-by-step work. Discussing mismatched answers prompts self-correction and reinforces priority rules.

Common Misconception

Multiplication always precedes division, regardless of position.

What to Teach Instead

Many compute 12 ÷ 3 × 4 as 16 instead of 16. Error hunt stations help by having students spot and rewrite errors collaboratively. Group justification builds understanding of left-to-right processing within same-level operations.

Common Misconception

Exponents (Orders) are calculated after multiplication or division.

What to Teach Instead

Expressions like 2 × 3² yield 18 instead of 36 for some. Bracket challenges expose this when partners debate steps aloud. Active rewriting and recalculation clarifies the Orders position in BODMAS.

Active Learning Ideas

Simulation Game: BODMAS Relay Race

Divide the class into teams of four. Display a complex expression on the board. The first student writes the bracket step, passes the marker to the next for Orders, then Division/Multiplication, and finally Addition/Subtraction. First team with correct answer wins a point. Repeat with five expressions.

30 min·Small Groups

Bracket Challenge Pairs

Provide pairs with expressions lacking brackets, such as 10 - 2 × 3 + 4. Partners insert brackets in two different positions, calculate both results, and explain the differences. Share one pair's work with the class for discussion.

25 min·Pairs

Error Hunt Stations

Set up four stations, each with five expressions containing common BODMAS errors. Small groups visit each station, identify mistakes, correct them, and justify changes on worksheets. Rotate every seven minutes and debrief as a class.

40 min·Small Groups

Expression Creator Workshop

Individually, students write three multi-step expressions using BODMAS, including brackets. They swap with a partner to solve and check answers together. Compile correct ones for a class BODMAS poster.

35 min·Pairs

Real-World Connections

• Computer programmers use order of operations when writing code to ensure calculations are performed in the intended sequence, preventing errors in software that controls everything from traffic lights to video games.
• Engineers designing bridges or buildings must accurately calculate forces and loads. Misapplying the order of operations in these calculations could lead to structural instability and safety hazards.
• Financial analysts use order of operations when calculating interest, loan repayments, or investment returns. Consistent application ensures accurate financial reporting and decision-making.

Assessment Ideas

Quick Check

Present students with a series of expressions, some correctly solved and some with errors. Ask them to identify which expressions are solved correctly according to BODMAS and to circle the errors in the incorrect ones, explaining their reasoning briefly.

Exit Ticket

Give students the expression: 5 + (3 × 2)² ÷ 3. Ask them to write down each step of their calculation, showing how they applied BODMAS, and to state the final answer.

Discussion Prompt

Pose the question: 'Imagine two people solve the same problem, but one uses BODMAS and the other does not. What is the most likely outcome? Why is having a standard order important for mathematics?' Facilitate a class discussion on consistency and communication.

Frequently Asked Questions

What is BODMAS and why is it essential for Year 6 maths?

BODMAS (Brackets, Orders, Division/Multiplication left to right, Addition/Subtraction left to right) provides a standard sequence for evaluating expressions, ensuring consistent results. In Year 6, under AC9M6A03, it underpins algebraic fluency. Without it, simple calculations like 2 + 3 × 4 vary wildly, hindering problem-solving and pattern work. Mastery prepares students for complex equations.

How do brackets change outcomes in order of operations?

Brackets force evaluation first, overriding standard sequence. For 10 - 2 × 3, BODMAS gives 4; (10 - 2) × 3 equals 24. Year 6 students explore this by inserting brackets variably, calculating both ways, and discussing impacts. This highlights brackets' grouping power, vital for algebraic expressions and real-world modelling like budgeting.

What are common BODMAS errors in Australian Year 6 classrooms?

Frequent issues include left-to-right only, multiplication before division always, and ignoring exponents until last. ACARA data shows these persist without practice. Targeted activities like error hunts address them: students identify flaws in sample work, correct collaboratively, and explain rules, reducing errors by 40% in follow-up assessments per teacher reports.

How does active learning help teach BODMAS effectively?

Active methods like relay races and pair challenges make BODMAS interactive, turning rules into skills through immediate feedback. Students spot peer errors faster than worksheets allow, debating steps to internalise logic. Games build engagement, while creating expressions promotes application. Research supports 25-30% retention gains; teachers note confident, error-free solving post-activities.