Order of Operations Worksheets
PEMDAS and BODMAS practice from two-step warm ups to brackets inside brackets and squares. Every expression is built so that reading left to right gives the wrong answer, and every PDF carries its own answer key.
Ages 8-12
Updated July 2026
Order of operations chart
The rule as a four-step ladder for the wall, with PEMDAS and BODMAS lined up against it and a strip of four expressions to try.
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One example, solved line by line
A single expression carrying brackets, a square, a product and a difference, opened out one operation per line with a note beside each.
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The four mistakes to watch for
Four wrong answers next to their right ones: adding too soon, subtracting too soon, squaring the product, and reading divide before multiply.
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Warm up: plus and times to 5
The gentlest entry point: one plus sign, one times sign and no number above 5, so the only new idea on the page is which one goes first.
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Add and multiply to 9
Sixteen two-step lines, single digits only, every one shaped so the product has to be found before the sum.
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Add and multiply to 12
The same two-step shape stretched to the twelve times table, so the multiplying is real recall rather than counting on.
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Subtract and multiply
Minus in front of the product, which is where left to right hurts most: the answer is never the first two numbers subtracted.
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Add and divide
Division before addition, and every division comes out exact, so a wrong answer is always an order mistake and never a remainder.
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Subtract and divide
The hardest of the two-step pairs: a quotient taken away from the first number, with the divisor always dividing cleanly.
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Two steps, all four signs
All four signs shuffled across sixteen two-step lines, so the child has to decide the order line by line instead of settling into a pattern.
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Two steps, numbers to 20
Two operations again, but the operands run to 20, so products reach the hundreds and mental arithmetic stops being automatic.
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Two steps, numbers to 25
The top of the two-operation band: operands to 25 and answers into the high hundreds, printed for children who need the rule, not the drill.
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Three steps: plus and times
Four numbers and three operations, but only plus and times, so the new difficulty is the length of the line rather than the signs.
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Three steps: minus and times
Three operations with minus in the mix, so the subtractions have to wait their turn and never run before a product.
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Three steps: plus and divide
Divisions scattered through a four-number line, all of them exact, and every one of them due before the additions around it.
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Three steps: minus and divide
The two signs children hurry through, together: subtraction and division across four numbers, with the quotients always due first.
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Three steps, all four signs
Four numbers, three operations drawn from all four signs, numbers to 12: the standard third and fourth grade practice page.
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Three steps, numbers to 20
The same three-operation shape with operands to 20, which pushes most lines past the point where the answer can be guessed.
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Four steps, numbers to 12
Five numbers on a line and four operations to rank, which is where children start writing the intermediate steps whether you ask them to or not.
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Four steps, numbers to 20
The longest bracket-free lines in the set: five operands to 20, four operations, answers running into the hundreds.
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Brackets and multiplying
The first bracket page: a single number multiplied by a bracketed sum or difference, sixteen to a sheet.
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Brackets and dividing
Dividing by a bracket rather than by a number: the bracket has to be resolved before the divisor even exists.
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Brackets, mixed signs to 12
One bracket per line and any of the four signs outside it, so the bracket stops being a signal that the answer is a product.
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Brackets, numbers to 20
Bracketed three-term lines with operands to 20, where the value inside the bracket is itself worth writing down.
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Brackets in a four-term line
A bracketed pair buried inside a four-number line, so the brackets have to be spotted rather than simply obeyed at the start.
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Three numbers inside the bracket
Brackets that hold a whole calculation of their own, two or three numbers wide, so the rule has to be applied inside them too.
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Brackets in a five-term line
Five operands with one bracket somewhere among them: long enough that skipping a step shows up in the answer straight away.
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Five terms, wider brackets
The same five-term length with brackets that can swallow three numbers, so the inside of the bracket needs its own ordering decision.
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Two sets of brackets
Two separate brackets on the same line, each holding its own pair, both to be settled before the sign that joins them.
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Two brackets, all four signs
The same double-bracket shape with division allowed between and inside them, which is where the answers stop being guessable.
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Brackets inside brackets
Round brackets nested inside square ones, with no division anywhere, so the only new idea is working from the inside out.
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Nested brackets, five terms
Nested brackets stretched over five numbers with division in play, the hardest bracket page in the set.
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Squares with plus and times
One square per line, and it always has to come out before the sign next to it: 4 plus 3 squared is 13, never 49.
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Squares with divide
Squares sitting next to a division sign, so the power has to be worked out before the divisor or the dividend is even known.
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Squares in a three-step line
A square somewhere inside a four-number line, which puts the exponent step between the brackets step and the multiplying step.
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Squares and cubes
Cubes join the squares, with bases kept small so 4 cubed is a fact to recall rather than a multiplication to grind out.
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Two powers on one line
Two powers in the same expression, both due before any multiplying, which is the step children most often take out of turn.
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Powers and brackets
A bracket and a power on the same line, which is the first page where the full four-step ladder is actually needed.
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Powers, brackets and division
The same pairing with division allowed and wider brackets, so a power can sit inside the bracket as well as outside it.
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Five terms with a power
Five operands carrying one bracket and one power each, long enough that the working has to be written somewhere.
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Full PEMDAS practice
Every step of the ladder on every line: a bracket, a power and all four signs across five operands.
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Full PEMDAS practice, page two
A second page at the same full-ladder level, because one page of this is never enough to make the habit stick.
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Review: two-step lines
A quick recall page: sixteen two-operation lines with no brackets and no powers, for checking the basic rule is still there.
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Review: brackets
Twelve four-term lines, every one of them bracketed, as a check on the bracket habit before the exponent pages.
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Review: powers and brackets
Four-term review lines that always carry both a bracket and a power, so neither step can be skipped by luck.
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Review: the long lines
Five operands and a bracket on every line, numbers to 12: the stamina page rather than the new-idea page.
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Final review, everything at once
The last evaluation page: five terms, a bracket up to three numbers wide, a power, and all four signs on every line.
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Show your work: two steps
Two-operation expressions with a ruled line per step, teaching the habit of copying the untouched part of the line down.
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Show your work: three steps
Four-number expressions that take exactly three lines to unwind, one operation each, with no brackets to help.
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Show your work: brackets
Bracketed expressions unwound line by line, where the first line is always the bracket disappearing into a single number.
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Show your work: powers
Four working lines each, with the power getting a line of its own so it stops being folded into the multiplication.
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Show your work: the full ladder
A bracket and a power on the same line, unwound over four written steps: the page to mark when you want to see where the thinking broke.
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Put the brackets in
The rule run backwards: the answer is given and the brackets are missing, with plus and times only. Exactly one placement works on every line.
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Put the brackets in: with minus
The same puzzle with subtraction allowed, which is where a bracket can change the answer most sharply.
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Put the brackets in: all signs
Four-number puzzles with division allowed, so a misplaced bracket usually leaves a division that does not come out.
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Put the brackets in: five terms
Five numbers means far more places a bracket could go, and still only one of them gives the printed answer.
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True or false: two steps
Half of these answers were worked out left to right on purpose. Marking somebody else is easier than being marked.
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True or false: three steps
Longer lines with division in them, where the wrong answers are the ones a left to right reader would actually reach.
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Spot the mistake: brackets
Bracketed lines with half the answers wrong, so the check has to start by asking what the bracket was worth.
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Spot the mistake: powers
Every line carries a power, and the wrong answers come from taking the exponent step out of turn.
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Choose the right value
Three values per line, and one of the wrong ones is always the left to right answer, so a careless reader lands on it.
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Choose the right value: three steps
Four-number lines with all four signs, where two of the three options are the answers you get by breaking a different rule.
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Choose the right value: brackets
Bracketed lines where one distractor is what you get by ignoring the brackets entirely, which is the mistake worth naming.
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Choose the right value: powers
A power on every line and three values to pick from, so the exponent has to be placed correctly before anything is chosen.
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Compare two expressions
Two two-step expressions per line and a box between them: both sides have to be finished before the sign can be written.
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Compare expressions to 12
The same comparison with operands to 12, so the two sides land close together often enough that estimating stops working.
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Compare: with brackets
Both sides carry brackets, and the pairs are chosen so the wider looking expression is not always the bigger one.
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Compare: with powers
Powers on both sides of the box, which is where a small base can beat a much larger looking product.
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Write the missing sign
Two-step lines with one sign hidden and the answer given. Only one of the four signs fits, and the checker proves it.
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Missing sign: three steps
Four-number lines with the blank moved around, so the child cannot settle into filling the first gap every time.
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Missing sign: with brackets
The hidden sign can sit inside the bracket or beside it, which changes what the bracket is worth as well as the final answer.
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Number the operations
No arithmetic at all: a circle under each sign and a number to write in it. This separates knowing the order from being able to compute.
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Number the operations: brackets
Five-term bracketed lines to number rather than solve, so the bracket is seen as a jump to the front of the queue.
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Number the operations: powers
The power gets a circle of its own, so it is ranked explicitly against the bracket and the multiplication around it.
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Match: two-step expressions
Ten two-step expressions and ten lettered values, all different, so a wrong answer cannot hide behind a shared result.
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Match: bracketed expressions
Every expression carries a bracket, so the matching cannot be done by pattern spotting on the numbers alone.
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Match: three-step expressions
Four numbers per expression, ten of them, which turns the page into ten full calculations before a single line can be drawn.
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Word problems: two steps
Six stories that each become one two-step expression, worded so the number that comes first in the sentence is not the one you use first.
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Word problems: with brackets
Six stories that only come out right with a bracket, because something is counted per group before the groups are counted.
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Word problems: multi-step
Stories that need three or four operations, including one with a square and one where the division has to be bracketed.
Download PDFWhat is the order of operations?
The order of operations is the rule that decides which part of a calculation happens first: brackets, then exponents, then multiplying and dividing taken left to right, then adding and subtracting taken left to right. It exists so that one expression has exactly one answer. Without it, 6 + 4 x 5 could be 26 or 50, and both would be defensible.
That is the whole idea, and it is why every expression on these pages is built to punish reading straight across. If a line gives the same answer left to right as it does by the rule, it teaches nothing, so it never gets printed.
PEMDAS, BODMAS and the four steps
PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) and BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) are the same rule with different words. Brackets and parentheses are the same thing; orders and exponents are the same thing.
The trap is the letters themselves. MD is one step, not two: 24 divided by 4 times 2 is 12, because you take the divide and the multiply in the order they appear, left to right. AS is one step too. Four steps, not six, and the wall chart in this set is drawn that way on purpose.
What is on the 80 sheets
The set runs from two-operation warm ups (a plus sign and a times sign, numbers under ten) up to five-term expressions with brackets inside brackets and squares. Between those ends sit the formats that catch different mistakes: show your work with one operation per line, insert the missing brackets, spot the wrong answer, choose from three values, compare two expressions, fill in the missing sign, number the operations without calculating anything, match expressions to values, and word problems that have to be written as a single expression first.
Every PDF is two pages: the worksheet, then its answer key laid out in exactly the same order, so marking is a glance rather than a re-calculation. The reference charts carry a four-problem practice strip and their key solves it.
Which sheet should a child start on?
If they still read left to right, start with the two-step pages where multiplying and adding are the only signs, then the numbering page where nothing is calculated at all: deciding the order and doing the arithmetic are two different skills, and mixing them hides which one is broken. Brackets come next, exponents after that, and the mixed review pages last.
Print at 100% (choose "actual size" in the print dialog) on US Letter or A4 paper. These sheets assume the times tables are solid, so if they are not, work through the multiplication worksheets and the division worksheets first. The arithmetic underneath comes from the addition and subtraction sets, place value work lives in the place value worksheets, and the same bracket habits carry straight into the fraction worksheets.
