KS3 Order of Operations Worksheets
Brackets (A)
Brackets (B)
Calculator Predictions
Order of Operations - Calculating with Indices
Order of Operations - Addition and Subtraction
Order of Operations - Introducing Brackets and Indices
Order of Operations - Multiplication, Division, Addition and Subtraction
Order of Operations - Understanding Fractions as Division
Order of Operations – Expression Trails
What are order of operations worksheets used for?
Order of operations worksheets train students to apply BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) or BODMAS consistently when evaluating numerical expressions. This foundational skill underpins everything from simplifying algebraic expressions to solving equations at GCSE, where incorrect operation ordering accounts for significant mark loss even when students understand the underlying concept.
These ordering operations worksheets systematically build fluency through varied question types, from straightforward calculations to expressions mixing fractions, indices, and nested brackets. Many teachers find that students who struggle haven't internalised that multiplication and division hold equal priority (working left to right), nor do addition and subtraction, causing them to always multiply before dividing or add before subtracting regardless of position in the expression.
Which year groups study order of operations?
Order of operations appears across Year 7, Year 8, and Year 9 within the KS3 National Curriculum, introduced as students transition from primary arithmetic to more complex numerical and algebraic work. Year 7 typically focuses on mastering BIDMAS with whole numbers and simple brackets, establishing the hierarchy before indices feature prominently.
By Year 8, students encounter expressions involving negative numbers, fractions, and squared terms, whilst Year 9 work incorporates indices beyond squares, mixed operations with fractions, and increasingly complex nested brackets that mirror the algebraic expressions they'll manipulate at GCSE. This progression ensures students automate the correct sequence before the cognitive load increases with algebraic terms and equation solving.
How do brackets change order of operations calculations?
Brackets override the standard BIDMAS hierarchy by forcing operations inside them to be completed first, regardless of whether they're addition, subtraction, or any other operation. Introducing brackets fundamentally alters calculation outcomes: 3 + 4 × 2 equals 11, but (3 + 4) × 2 equals 14 because the brackets elevate addition above multiplication in priority, demonstrating why correct interpretation matters.
This concept connects directly to programming and spreadsheet functions, where parentheses control calculation order in formulae. Engineers and data analysts rely on brackets to ensure complex formulae execute correctly—miscalculating stress loads or financial projections due to bracket errors can have serious real-world consequences, making this seemingly abstract skill vital in STEM careers and everyday technical work.
How can teachers use these order of operations worksheets effectively?
The worksheets scaffold learning by gradually increasing complexity, starting with expressions requiring two or three operations before introducing fractions, indices, and nested brackets. This structure allows teachers to assign worksheets matching current class capability, whilst complete answer sheets enable students to self-check working and identify exactly where their method diverges from correct application of BIDMAS.
Teachers commonly use these resources for intervention with students who've developed systematic errors, for homework reinforcement after introducing each new element (like indices or negative numbers), or as starter activities to maintain fluency. The operations sheet format also works well for paired work where students complete alternate questions then check each other's methods, encouraging mathematical discussion about why particular operations take precedence and identifying where misconceptions arise.