Mathematics · Year 7 · The Power of Number · Autumn Term

Order of Operations (BIDMAS/BODMAS)

Establishing a universal hierarchy for mathematical operations to ensure consistency in calculation.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

About This Topic

Order of Operations, known as BIDMAS or BODMAS, sets a clear hierarchy for calculations: Brackets first, then Indices or Orders, followed by Division and Multiplication from left to right, and finally Addition and Subtraction from left to right. Year 7 students master this to evaluate complex expressions consistently, avoiding ambiguity in multi-step problems. They justify its necessity by comparing results from different orders, see how brackets change priorities, and spot errors in peer calculations.

This topic anchors the Number strand of the KS3 curriculum, preparing students for algebraic expressions and real-world applications like budgeting or coding. It fosters precision and logical reasoning, key mathematical habits. Practice with varied expressions builds confidence and reveals patterns in operation precedence.

Active learning shines here because students uncover the order through trial and error in collaborative tasks. Games and puzzles make abstract rules concrete, while group critiques of mistaken calculations encourage peer teaching and immediate feedback. These methods turn potential frustration into discovery, ensuring retention and deeper understanding.

Key Questions

1. Justify the need for a specific order of operations in complex calculations.
2. Analyze how brackets alter the priority of operations within an expression.
3. Critique a calculation that has been performed incorrectly due to misapplication of BIDMAS.

Learning Objectives

• Calculate the value of complex numerical expressions by correctly applying the order of operations (BIDMAS/BODMAS).
• Analyze how the placement of brackets alters the sequence and outcome of operations within an expression.
• Critique a given calculation, identifying and explaining errors resulting from the misapplication of BIDMAS/BODMAS rules.
• Compare the results of calculations performed with and without adherence to the standard order of operations to justify its necessity.

Before You Start

Addition and Subtraction

Why: Students must be proficient in performing basic addition and subtraction before they can apply them as the final steps in the order of operations.

Multiplication and Division

Why: A solid understanding of multiplication and division is necessary, as these operations have a higher precedence than addition and subtraction.

Basic Arithmetic

Why: Familiarity with performing calculations involving single operations is foundational for tackling multi-step problems.

Key Vocabulary

BIDMAS/BODMAS	An acronym representing the order of mathematical operations: Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction.
Brackets	Symbols used to group parts of a mathematical expression, indicating that operations within them must be performed first.
Indices/Orders	Operations involving exponents, such as squares or cubes, which are performed after brackets but before multiplication, division, addition, and subtraction.
Operation Precedence	The established hierarchy that dictates the sequence in which mathematical operations should be performed to ensure a consistent result.

Watch Out for These Misconceptions

Common Misconception

Always work strictly left to right, ignoring priorities.

What to Teach Instead

BIDMAS requires handling division and multiplication left to right after brackets and indices, not pure left-to-right order. Pair discussions of example calculations help students trace steps aloud and compare results, revealing why priority matters. Active error-sharing builds collective correction skills.

Common Misconception

Multiplication always before division, regardless of position.

What to Teach Instead

Division and multiplication share equal priority, performed left to right. Group sorting activities with operation cards clarify this sequence visually. Students defend their orders in debates, strengthening rule application through peer challenge.

Common Misconception

Brackets only group additions and subtractions.

What to Teach Instead

Brackets override all other operations first. Relay games expose this when teams falter on bracketed divisions, prompting instant group fixes and reinforcing hierarchy through repeated practice.

Active Learning Ideas

Error Hunt: Spot the BIDMAS Mistakes

Provide worksheets with 10 expressions solved incorrectly. In pairs, students identify the error, explain the correct BIDMAS application, and rewrite the solution. Pairs then swap sheets with another pair for verification.

30 min·Pairs

Card Sort: Build and Solve Expressions

Distribute cards with numbers, operations, and brackets. Small groups assemble expressions following BIDMAS rules, solve them, and justify their order to the class. Extend by creating challenging ones for others.

45 min·Small Groups

Relay Critique: Team Calculation Race

Divide class into teams. Each student solves one step of a long expression on a board, passing a baton. If a BIDMAS error occurs, the team discusses and corrects before continuing.

35 min·Small Groups

Bracket Builder: Individual Challenges

Students receive expressions without brackets and add them to achieve target answers. They test solutions using BIDMAS and share strategies in a whole-class debrief.

25 min·Individual

Real-World Connections

• Computer programmers use order of operations to ensure calculations in software, such as financial modeling applications or physics simulations, are executed correctly and produce accurate results.
• Engineers designing bridges or aircraft rely on precise calculations following a strict order of operations to ensure structural integrity and safety, preventing catastrophic failures.
• Scientists performing data analysis in fields like genetics or climate science use order of operations to correctly interpret complex datasets and draw valid conclusions.

Assessment Ideas

Quick Check

Present students with three expressions: one simple, one with brackets, and one that requires careful application of BIDMAS/BODMAS. Ask them to calculate the value of each and show their working steps clearly, highlighting where they applied the order of operations.

Discussion Prompt

Write a calculation on the board that has been solved incorrectly due to a BIDMAS/BODMAS error, e.g., 5 + 3 x 2 = 16. Ask students to identify the mistake, explain why it is wrong using the BIDMAS/BODMAS rule, and then demonstrate the correct calculation and answer.

Exit Ticket

Give each student a card with a numerical expression. Ask them to write down the first operation they would perform according to BIDMAS/BODMAS and why. They should also write the final answer to the expression.

Frequently Asked Questions

Why teach BIDMAS in Year 7 maths?

BIDMAS ensures consistent results in multi-operation calculations, vital for Number objectives in KS3. It prevents confusion in expressions like 2 + 3 x 4, teaching students to prioritise correctly. Mastery here supports later algebra and problem-solving, building reliable computational fluency from the start.

How do brackets change BIDMAS calculations?

Brackets force evaluation first, altering operation order. For example, 2 + 3(4 + 1) becomes 2 + 3 x 5 = 17, not 15. Students analyse paired examples to see shifts, then create their own to test peers, deepening insight into priority.

How can active learning help students master BIDMAS?

Active tasks like card sorts and error hunts engage students kinesthetically, making rules memorable. Collaborative critiques reveal misconceptions quickly, with peers explaining steps. These approaches boost retention over rote drills, as students own the discovery process and apply rules in fun, low-stakes contexts.

Common BIDMAS errors and fixes for Year 7?

Errors include ignoring left-to-right for DM or misplaced brackets. Use station rotations where groups solve, swap, and critique. Visual aids like flowcharts during discussions clarify steps. Regular low-stakes quizzes with peer review track progress and embed corrections effectively.