Grade 5 Order of Operations Worksheets — Brackets First, Free PDF
Fifth grade is where the order of operations stops being a habit and becomes a formal rule — and it is the year grouping symbols arrive with it, because a Grade 5 student is expected to put parentheses or brackets into a numerical expression and then evaluate one. So this page opens on brackets. The difficulty control walks that skill in three steps: One bracket, then Bracket and a third step once the grouping is taken automatically, then Brackets with division, where the division is built to land exactly. Set the difficulty and question count below and the worksheet redraws instantly.
Brackets are not the only sheet here. The sub-skill cards also cover plain chains where × and ÷ have to be spotted before + and −, naming the step you would work out first without finishing the sum, putting one missing pair of brackets in so a printed answer comes true, brackets inside brackets, and finding the first wrong step in a worked solution somebody else has already written out. Exponents are the one piece Grade 5 leaves out, and they arrive in the Grade 6 sheets. Tick the answer key box and the answers print on their own page, so you can hand out the questions and keep the key aside; the link in your address bar stores the exact worksheet for a reprint or a class, and Shuffle makes a fresh set at the same settings.
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Order of Operations · Grade 5
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Grade 5 · 2 pages · A4More Grade 5 order of operations skills
Each one generates a different kind of question, with its own three levels and answer key.
- Brackets FirstWork out what is inside the brackets before you do anything else.
- Two OperationsNo brackets: decide whether to multiply, divide, add or subtract first.
- Which Step Comes FirstName the part you would work out first — no need to finish the sum.
- Insert the BracketsPut one pair of brackets into each expression so the answer shown is correct.
- Brackets Inside BracketsMore than one set of brackets — start with the innermost pair and work out.
- Find the first wrong step (HOTQ)A worked answer with one wrong step in it. Find the first step that breaks the rule and write the step that belongs there.
What each level generates
Grade 5 brackets first — the exact skill behind each difficulty setting, straight from the generator.
- Level 1One bracket
- Level 2Bracket and a third step
- Level 3Brackets with division
Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →
What Grade 5 order of operations should cover
Most curricula introduce the convention in Grade 5, and they introduce it together with grouping symbols: work out what is inside the brackets first, then multiplication and division, then addition and subtraction. That is why this page opens on brackets rather than on the plain two-operation chains it shares with Grade 4 — the grouping symbol is the part of the rule that is genuinely new this year, and a bracket is the one thing that can overrule the priority of × and ÷.
The progression built into the difficulty control mirrors a sensible teaching order. Begin at One bracket until the grouping is taken without prompting; move to Bracket and a third step so the bracket has to be finished before anything around it can happen; and use Brackets with division as a stretch. If a student is still choosing × or ÷ over + or − by luck rather than by rule, go to the Two Operations card first: the priority has to be steady before a bracket is layered on top of it. Exponents are not part of Grade 5 here; they arrive in the Grade 6 sheets alongside substituting a value for a letter.
The two acronyms — and the mistake they hide
You will meet this rule as PEMDAS in some places and BODMAS or BIDMAS in others. They describe the same order; the letters just differ by region (P or B for the parentheses or brackets this page opens on, E, O, or I for the exponents Grade 5 leaves out). Teach whichever your school uses, but say the words in full — "brackets, then multiply and divide, then add and subtract" — so the meaning survives when the acronym is forgotten.
The classic Grade 5 error is reading strictly left to right: writing 3 + 4 × 2 = 14 instead of 11. A reliable habit is to scan the whole expression first and lightly underline the bracket, then the multiplication or division, before touching anything else. If mistakes persist, drop the question count to 8–10 and ask for the first step to be circled on every problem before any answer is written.
Frequently asked questions
▸What is the order of operations in Grade 5?
Brackets first, then all multiplication and division, then addition and subtraction; operations of equal rank are worked left to right. Grade 5 is the year the brackets join the rule, which is why these sheets open on them. Exponents are the piece that waits for Grade 6.
▸Do these Grade 5 worksheets include brackets?
Yes — brackets are the sheet this page opens on, and four more cards use them: Insert the Brackets asks you to put one missing pair in so the printed answer comes true, Brackets Inside Brackets nests one pair in another, Which Step Comes First asks you to name the bracket without evaluating it, and the middle level of Find the first wrong step puts one in the working somebody else wrote. Choose the Two Operations card for plain chains instead.
▸Is it PEMDAS or BODMAS?
Both name the same order — PEMDAS is common in North America, BODMAS or BIDMAS in the UK and elsewhere. The P or B means parentheses or brackets, and the E, O, or I means exponents, which these Grade 5 sheets leave for Grade 6. Teach whichever version your school uses.
▸What do the three difficulty levels do?
On the Brackets First sheet this page opens with, One bracket gives a single pair with one operation around it, Bracket and a third step adds a third operation outside the bracket, and Brackets with division adds a division that always lands exactly. Every other sub-skill card has its own three levels, and the difficulty control moves within whichever card you are on.
▸How many problems should a Grade 5 sheet have?
Ten to fifteen works well. Each problem needs a couple of deliberate steps, so a short accurate set beats a long rushed one. Use the question-count stepper to size the sheet to your session.
▸Can I print an answer key?
Yes — tick the answer key box and the final answers print on their own page at the end, numbered to match the questions, so you can hand out the worksheet and keep the key aside.