Secondary 1 Math Arithmetic Free · no sign-up

Secondary 1 Whole Numbers and the Four Operations

By Marius — private math tutor in Montreal. Updated 30 August 2026

The widest sheet at this level, and the one everything else leans on. It runs through written addition, subtraction, division with a remainder, estimating a result before computing it, mental-math strategies you can explain, the vocabulary each operation is marked on — term, sum, difference, product, quotient — the properties that let a calculation be rearranged, and the order of operations. None of it is new to a student arriving from elementary school; all of it is about to be assumed by every other topic in the year. Nothing is locked behind a form, and the sheet prints at no cost.

Practice worksheet — free PDF

6 pages 11 questions Letter size, print-ready

Download the worksheet Read the questions here

No email, no account, no watermark. Teachers: photocopy it for your classes freely. Worked solutions and 9 harder problems come with the Secondary 1 Math bundle.

All 11 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one.

Q1Adding Whole Numbers

Calculate each sum, showing the columns you carried.
1. $4 812 + 3 271$
2. $12 405 + 8 796 + 250$
3. Over one weekend, a new skatepark in Rimouski welcomed $3 250$ visitors on Friday, $4 815$ on Saturday and $2 940$ on Sunday. How many visitors did it welcome in all?
Q2Addition

Answer using the correct vocabulary of addition.
1. In $486 + 157 = 643$ , name each of the three numbers.
2. Naïm claims that the sum of two whole numbers can be smaller than one of the numbers being added. Give an example, or explain why it is impossible.
3. Write an addition with three terms whose sum is $1 000$ and in which one of the terms is $0$ .
Q3Approximating the Answer of an Operation

Estimate each result. Do not calculate the exact answer.
1. $4 812 + 3 271$ , rounding each number to the nearest hundred.
2. $61 \times 397$ , rounding $61$ to the nearest ten and $397$ to the nearest hundred.
3. $3 964 \div 39$ , rounding $3 964$ to the nearest thousand and $39$ to the nearest ten.
Q4Arithmetic

Each line describes a calculation in words. Write it as a numerical expression, calculate it, then name both the operation used and the name given to its result.
1. the difference between $90$ and $34$
2. the product of $12$ and $25$
3. the quotient of $144$ by $6$
4. the sum of $48$ , $52$ and $100$
Q5Division

Divide.
1. $847 \div 6$ — give the quotient and the remainder.
2. $2 016 \div 24$
3. Check your answer to a) with one multiplication and one addition, and write that check as a single equation.
Q6Mental Math

Calculate mentally, then write down the strategy you used.
1. $998 + 457$
2. $5 000 - 1 999$
3. $25 \times 36$
4. $48 \times 5$
Q7Operations

For each situation, name the single operation you would use and say why. Do not calculate anything.
1. A snow-clearing route is shared equally between $4$ trucks; you know the total length of the route and want the length one truck covers.
2. You know how many goals each of two teams scored, and you want to know how many more goals the winner scored.
3. An arena has $18$ rows of $24$ seats and you want the number of seats.
4. Three deliveries of hockey pucks arrive and you want the total stock.
Finally, pair the four operations you named into two pairs of operations that undo each other.
Q8Properties of Operations

Each calculation below is done in an unusual order to make it easier. Name the property of the operations that makes each rearrangement legitimate.
1. $37 + 68 + 63 = 37 + 63 + 68 = 100 + 68 = 168$
2. $4 \times 97 = 4 \times (100 - 3) = 400 - 12 = 388$
3. $25 \times (8 \times 7) = (25 \times 8) \times 7 = 200 \times 7 = 1 400$
4. $156 \times 1 = 156$ and $156 + 0 = 156$
Q9Subtraction

Subtract.
1. $8 003 - 2 476$ , then check your answer with an addition.
2. $1 250 - 386 - 214$
3. A player starts a game with $1 500$ coins, then spends $675$ on a new board and $250$ on wheels. How many coins are left?
Q10The Order of Operations

Evaluate, showing the order in which you worked.
1. $24 - 3 \times 5 + 8 \div 2$
2. $(18 + 12) \div 6 \times 2$
3. $5 + 2 \times (7 - 3)^{2}$
4. $36 \div 6 \div 3$
Q11Synthesis — drawing on several sheets in this topic

A school canteen in Sherbrooke receives $6$ crates of apples, with $48$ apples in each crate. While unpacking, the staff find $17$ bruised apples and throw them out. The good apples are then shared equally among the school's $7$ homeroom classes.
1. Write the number of good apples as a single numerical expression.
2. Evaluate it, saying which operation you carried out first and why.
3. How many apples does each class get, and how many are left over? Check that division with one multiplication and one addition.

The 9 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

Which stream is this for? There is no stream to choose yet. Secondary 1 is the first year of the secondary program and everyone takes the same mathematics course; the split into options comes in Secondary 4. This set follows the Secondary 1 level of the Québec Education Program and its Progression of Learning: the four operations on whole numbers, their properties and the order of operations, with the reasoning written down rather than left in a calculator.

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

The sheet is a spread, and it is worth doing in order

These questions are not interchangeable drills. They move from computing, to estimating, to naming, to rearranging, to sequencing — and the later ones assume you can already do the earlier ones without thinking about it. Working them in order is what makes the last two questions feel like a review instead of a new topic.

What each part of the sheet is actually training

Five different skills, and only the first is arithmetic.

1
Written computation, with the working visible
Q1, Q5 and Q9 ask for sums, a division with a remainder and subtractions across zeros — and ask you to show the carries, the regrouping and the check. The answer alone is not the deliverable.
2
Estimating before computing
Q3 asks for the approximate result and explicitly forbids the exact one. Estimating is a separate skill from computing, and it is the one that tells you whether the exact answer you get later is plausible.
3
Naming what you did
Q2, Q4 and Q7 ask for the vocabulary — terms and sum, difference, product, quotient — and for which operation a described situation calls for. A calculation you cannot name is a calculation you cannot be asked about.
4
Justifying a rearrangement
Q8 shows four calculations done in an unusual order and asks which property makes each one legal. The property is the answer; the arithmetic is already given.
5
Sequencing several operations
Q10 and the two synthesis questions chain operations together, where the order is the whole difficulty and a reasonable-looking wrong order gives a reasonable-looking wrong answer.

Estimating is a decision, not a shortcut (Q3)

Rounding to make a calculation easy is not the same as rounding to find out whether something fits. Q3 is the first kind — round each number to the named place, compute, and stop. The second kind is the one that matters outside a classroom: when the estimate has to support a decision, the direction you round in is part of the method.

Round so the error falls on the safe side. Estimating a cost to see whether you can afford it means rounding every price up. Round down and each item is a little cheaper than it really is; multiply that by six items and the estimate quietly promises something the budget cannot pay for.

Roundings that pull in different directions cannot be resolved by intuition. If you round one quantity down and another up, the estimate could land on either side of the true value and you cannot tell which from the directions alone. That is a signal to compute the exact figure, not to trust the estimate harder.

Division: the remainder is part of the answer (Q5)

847 ÷ 6 does not come out evenly, and “141 remainder 1” is the complete answer rather than an apology for one. Q5 then asks for the check, written as a single equation, and that equation is the definition of what a division with a remainder means:

6 × 141 + 1 = 847

Every division question on this sheet can be verified that way — multiply the quotient by the divisor, add the remainder, and you must land back on the number you started with. It costs one line and it is the only check that catches an error in the middle digits of a long division.

A remainder is always smaller than the divisor. A remainder of 9 in a division by 7 is not a valid answer — it still contains a whole group of 7, which means the division was stopped one step early. If yours is too big, take another group out and add 1 to the quotient.

The properties are what make a rearrangement legal (Q8)

Q8 gives you four calculations that have already been reorganised to make them easy, and asks you to name the property that licenses each reorganisation. This is the question students find strangest, because there is no arithmetic left to do — and it is the one that transfers directly into algebra, where the same three properties are the only moves allowed.

The three properties, and what each one permits

Name the property; the rearrangement is the evidence, not the answer.

1
Commutativity — the order of the numbers
Swapping two terms of an addition, or two factors of a multiplication. It is what lets 37 + 68 + 63 be reordered so the 37 and the 63 meet and make 100.
2
Associativity — where the brackets go
Regrouping which pair is done first. It is what turns 25 × (8 × 7) into (25 × 8) × 7, and 200 × 7 is a calculation you can do in your head.
3
Distributivity — splitting one factor
4 × 97 becomes 4 × (100 − 3), then 400 − 12. The multiplication is spread over both parts of the split, and this is the property algebra uses most.
4
The neutral element — the number that changes nothing
Multiplying by 1 and adding 0. Trivial-looking, and the reason a term can be written in a more convenient form without changing its value.

Subtraction and division have none of the first three, and knowing that is as useful as knowing the properties themselves. 9 − 4 and 4 − 9 are different; 100 − (30 − 12) and (100 − 30) − 12 are different. Brackets in a chain of subtractions are not decoration.

The order of operations, and the pair everyone gets wrong (Q10)

Brackets, then exponents, then multiplication and division, then addition and subtraction. The clause that gets dropped is the one that matters: multiplication and division sit at the same level and are done left to right, and so do addition and subtraction. Division does not wait for every multiplication on the line to finish.

Two worked traps from Q10. (18 + 12) ÷ 6 × 2 is 30 ÷ 6 first, then × 2, giving 10 — not 30 ÷ 12. And 36 ÷ 6 ÷ 3 is 6 ÷ 3 = 2, not 36 ÷ 2 = 18. In both cases the “wrong” reading is the one that treats the operations as if a rule paired them up. Left to right is the rule.

Reading order is not priority order. The subtraction that appears first on the line still waits for the multiplication and the division that outrank it.

Q11: the operations in a situation that decides their order

The synthesis question unpacks crates of apples, throws some out, and shares the rest among classes. It asks first for a single numerical expression, then for its value with the order justified, then for a division whose remainder actually means something — the apples left over.

Writing the expression before computing is the habit being built. 6 × 48 − 17 needs no brackets, because the order of operations already does the multiplication first; noticing that brackets are unnecessary is a better answer than adding them defensively. And the remainder at the end is not a leftover from the arithmetic — it is five apples nobody got.

Getting the most out of it

Estimate first, compute second

Before any long calculation, round and get a rough figure. Then the exact answer has something to be compared against, and a slipped digit — a result ten times too big, or larger than the number you started from — announces itself immediately instead of being handed in.

Check a division with one multiplication and one addition

Quotient times divisor, plus remainder, equals the number you divided. One line, every time. It is the only check that catches an error buried in the middle of a long division, and this sheet asks for it explicitly because it is worth making automatic.

Write the strategy down, not just the answer

The mental-math and properties questions are marked on the explanation, not the number. “I took 998 up to 1000 and gave the 2 back at the end” is the answer. A bare 1455 is not, and a student who cannot say what they did cannot repeat it on a harder number.

Want the solutions, or something more challenging?

The worksheet, the questions above and every explanation on this page stay free permanently. Three more PDFs exist for this topic — the worked answer key, a harder problem set, and the answer key to that. They come with the Secondary 1 Math Solutions Bundle, which is what keeps the rest of the series free.

What else exists for Whole Numbers and the Four Operations

Three PDFs · 11 pages · all three are in the bundle below.

Answer key — 2 pages. All 11 questions worked step by step, including the restrictions and the justifications. Not a list of final answers.
Challenge problems — 7 pages, 9 problems. A separate sheet at exam-plus difficulty covering the same 10 concepts. Harder than anything on the free sheet.
Challenge answer key — 2 pages. Every challenge problem worked to the same standard, with the checks shown.
PDF, letter size, print-ready.

In the bundle See what's in it Not sold separately

The one thing that's for sale

Best value for the whole year

Every Secondary 1 Math topic — the complete Solutions Bundle

One download, one payment, the whole program. Every answer key and every challenge set for all 15 Secondary 1 Math worksheet sets — including this one.

15 sets · 45 PDFs · 182 pages$19.99

Worked solutions, not answer lists — every step written out
Covers the whole year's program at this level
Less than the price of one hour of tutoring — for the entire year's solutions

Everything paid, in one file $19.99CAD · one payment Secondary 1 Math bundle — coming soon Not on sale yet

Taking Secondary 2 Math as well? The Secondary 2 Math bundle covers all 14 of its sets — 42 PDFs, 181 pages — on the same terms.

Taking Secondary 3 Math as well? The Secondary 3 Math bundle covers all 11 of its sets — 33 PDFs, 154 pages — on the same terms.

Taking Secondary 4 Math as well? The Secondary 4 Math bundle covers all 17 of its sets — 51 PDFs, 154 pages — on the same terms.

Taking Secondary 5 Math as well? The Secondary 5 Math bundle covers all 21 of its sets — 63 PDFs, 228 pages — on the same terms.

Taking CEGEP Calculus I as well? The CEGEP Calculus I bundle covers all 8 of its sets — 24 PDFs, 82 pages — on the same terms.

Taking CEGEP Calculus II as well? The CEGEP Calculus II bundle covers all 8 of its sets — 24 PDFs, 90 pages — on the same terms.

Taking CEGEP Linear Algebra as well? The CEGEP Linear Algebra bundle covers all 7 of its sets — 21 PDFs, 82 pages — on the same terms.

Taking AP Calculus AB as well? The AP Calculus AB bundle covers all 8 of its sets — 24 PDFs, 126 pages — on the same terms.

Common questions

Is this worksheet really free?

Yes — the questions are on this page to read, and the PDF downloads directly, no email and no account. The one paid item is optional: the complete Secondary 1 Solutions Bundle, which covers every set at this level.

What is the order of operations, exactly?

Brackets, then exponents, then multiplication and division, then addition and subtraction — with the clause people forget: multiplication and division share a level and are done left to right, and so do addition and subtraction. So 36 ÷ 6 ÷ 3 is 2, not 18, and 30 ÷ 6 × 2 is 10, not 30 ÷ 12.

How do I check a division that has a remainder?

Multiply the quotient by the divisor and add the remainder; you must get back the number you divided. For 847 ÷ 6 that is 6 × 141 + 1 = 847. It also tells you when a remainder is invalid: a remainder must be smaller than the divisor, so a remainder of 9 in a division by 7 means the division was stopped one step too early.

Which way should I round when estimating a cost?

Up. An estimate can only settle a decision if its error falls on the safe side: rounding costs up can make you refuse something you could just afford, while rounding down can make you promise something you cannot pay for. And if some quantities were rounded up and others down, the estimate could land either side of the truth — that is the moment to compute exactly.

Why does my child have to name the property instead of just getting the answer?

Because naming it is what makes the move reusable. Commutativity, associativity and distributivity are the only rearrangements allowed, and they are the same three moves algebra runs on a year later. A student who can say why 4 × 97 becomes 4 × (100 − 3) will recognise the same step when the numbers turn into letters.

Is subtraction commutative or associative?

Neither, and this sheet asks students to demonstrate it. 9 − 4 and 4 − 9 are not the same thing, and 100 − (30 − 12) gives 82 while (100 − 30) − 12 gives 58. Brackets in a chain of subtractions genuinely change the answer, which is why they cannot be moved or dropped.

Can teachers use this in class?

Yes. Print and photocopy it for your own classes freely — I just ask that the tutorinmontreal.ca footer stays on the page.

I'm stuck on one question. Can you help?

Yes — through one-on-one tutoring, in Montreal or online. Get in touch to arrange a session, or see the current rates.

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