Grade 8 Integers Worksheets — Order of Operations & Multi-Step Practice
Grade 8 treats integer arithmetic as a tool, not a topic. Seven sub-skills are offered here and the page opens on Powers of Integers, where the difficulty control steps from Squares, to Cubes, to Two powers multiplied. Order of Operations with Integers and Mixed Operations are the multi-step sheets — exponents on negative bases, nested signs, and a correct sign carried through several steps — so students meet the sign rules the way algebra will actually use them. Each sub-skill keeps its own three levels, so a specific gap can be drilled without disturbing the rest.
Set the controls to suit the work: fewer, denser problems for a focused push, or a longer mixed set for consolidation. The answer key prints on its own page, the layout switches to give the Integer Word Problems sheet room to work beneath each question, and A4 or US Letter is your choice. Shuffle for fresh practice, and reopen the link any time for the exact same sheet.
Build your worksheet
Integers · Grade 8
The link is the save: it reopens this exact worksheet — same questions, same settings. Bookmark it or send it on. No account needed.
Printed on the worksheet only — never saved or sent anywhere
Live preview
Grade 8 · 2 pages · A4More Grade 8 integers skills
Each one generates a different kind of question, with its own three levels and answer key.
- Powers of IntegersSquare and cube positive and negative numbers, brackets included.
- Order of Operations with IntegersBrackets, powers and signed arithmetic in one expression.
- Mixed OperationsExpressions that combine two or three operations on signed numbers.
- Multiplying IntegersMultiply signed numbers and decide whether the answer is positive or negative.
- Dividing IntegersDivide signed numbers. Every answer is a whole number.
- Find the Missing IntegerFill the blank that makes each statement true, using inverse operations.
- Integer Word ProblemsTemperature, depth and balance stories where the sign carries the meaning.
What each level generates
Grade 8 powers of integers — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Squares
- Level 2Cubes
- Level 3Two powers multiplied
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 8 integers should cover
By Grade 8, the individual sign rules are assumed and the emphasis moves to using them accurately inside longer expressions: applying the order of operations when several terms are negative, handling exponents on negative bases, and carrying a correct sign through two or three steps into a final answer.
Order of Operations with Integers and Mixed Operations are built for exactly this. Expect problems where a single dropped sign midway changes the whole result — which is the point. This is the bridge to algebra, where −3(4 − 7) and 2 − 3 × (−5) must be evaluated without hesitation.
Where multi-step answers go wrong
Two mistakes dominate at this level. First, the exponent trap: −4² is −16 (the square applies to 4, then the result is negated), while (−4)² is 16. Grade 8 students must read the brackets carefully. Second, sign errors that hide in the middle of a chain — a student evaluates the bracket correctly, then mishandles the negative in front of it.
The fix is to slow down the middle, not the ends. Have your student rewrite every subtraction as adding the opposite before doing anything else, and to box the sign of each intermediate result. Then use the answer key not just to mark right or wrong, but to locate the exact step where a sign flipped — that single line is usually the whole lesson.
BODMAS, BIDMAS and PEMDAS with negative numbers
If you came here looking for a Grade 8 BODMAS sheet, this is the page. The acronym differs by region — BODMAS or BIDMAS in the UK, Asia and the Gulf, PEMDAS in North America — but all three name the same sequence: brackets, then powers, then multiplication and division left to right, then addition and subtraction left to right. Nothing about that order changes when the numbers turn negative. What changes at Grade 8 is that every step now carries a sign, which is why this practice is filed with Integers rather than under the Order of Operations topic — that topic teaches the rule on whole numbers across Grades 4 to 7, ending at /worksheets/grade-7/order-of-operations/.
Three sub-skills on this page carry it. Order of Operations with Integers is the closest match to a classic BODMAS sheet, running a power and a bracket inside one signed expression. Mixed Operations gives the same bracket-and-chain work without the exponents. Powers of Integers isolates the exponent step on its own, which is worth a session in its own right because it is the step the acronym hides. All three print with an optional answer key.
Frequently asked questions
▸What integer work is expected in Grade 8?
Applying all four operations within multi-step expressions: order of operations with negative numbers, exponents on negative bases, and carrying correct signs through several steps. Grade 8 uses integers as groundwork for algebra rather than teaching them in isolation.
▸Is −3² the same as (−3)²?
No. Without brackets, −3² means −(3 × 3) = −9, because the exponent binds tighter than the negative sign. With brackets, (−3)² = (−3) × (−3) = 9. Reading the brackets carefully is a key Grade 8 skill.
▸How do I stop sign errors in multi-step problems?
Rewrite each subtraction as adding the opposite, then note the sign of every intermediate result before continuing. Most multi-step mistakes are a single flipped sign in the middle, not a misunderstood rule.
▸How much room is there to work on the page?
The sheets print as a grid, and the grid narrows as the work gets longer: Mixed Operations drops to one problem per row at its third level, and Order of Operations with Integers prints two per row throughout, so a long signed expression is never squeezed against a neighbour. There is no pre-printed working box — students who need several lines should work them in an exercise book and write only the final answer on the sheet.
▸Can I make an easier review sheet from this page?
Yes — pick a narrower sub-skill rather than a lower level. Powers of Integers on its own, or Multiplying Integers, makes a clean warm-up; then move to Order of Operations with Integers or Mixed Operations for the main work. Within any sub-skill the difficulty control still steps through that skill's own three levels, so you can ease off twice over. Each sheet regenerates in seconds and is free, with an optional answer key.
▸Is this the Grade 8 BODMAS or PEMDAS worksheet?
Yes. BODMAS, BIDMAS and PEMDAS all name the same order — brackets, then powers, then × and ÷, then + and −, each pair worked left to right — and Grade 8 applies it to signed numbers, which is why it is filed here under Integers. Order of Operations with Integers is the sub-skill to start from. For the whole-number version, the Order of Operations topic runs Grades 4 to 7 and ends at /worksheets/grade-7/order-of-operations/.