Pre-algebra and algebraGrades 5–6
Order of operations worksheets
Generates two-column sheets of whole-number expressions to simplify using the order of operations. The Basic level uses parentheses and four operations; the other level adds exponents and brackets. Answer key included.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
Why the order matters
Write 2 + 3 × 4 and two people can get two answers: 20 if they go left to right, 14 if multiplication comes first. Mathematicians agreed on one order so that everyone reads an expression the same way. Students in grades 5 and 6 need that agreement to be automatic, because every later topic, from equations to formulas, depends on it.
The order is: parentheses (and brackets) first, then exponents, then multiplication and division working left to right, then addition and subtraction working left to right. Many students remember it with an acronym, but the acronym hides the most common trap, that multiplication and division share a rank, as do addition and subtraction.
Settings that matter
- Skill. Choose "Order of operations."
- Level: Basic. Expressions have three numbers and two operations, or a pair of parentheses, such as 5 + 4 × 7, (6 + 3) × 8 or 40 ÷ (2 + 3). Numbers run up to 12.
- Level: With exponents and brackets. Everything in Basic, plus squares (like 6² + 4 × 3), a squared bracket, a division by a square, and nested forms with square brackets around round ones.
- Number of problems. Twenty is the default. Fewer problems with more time for each suit a first lesson.
Every expression is built so each step stays a whole number and the final answer is never negative. Division always comes out even, so a student who gets a fraction has made a mistake, which makes the page self-checking in a useful way. The Distributive form menu does not apply to this skill.
Worked example: 36 ÷ 3² + 5
This one comes from the exponent level.
- Exponents first. 3² = 3 × 3 = 9, so the line becomes 36 ÷ 9 + 5.
- Divide before adding. 36 ÷ 9 = 4, leaving 4 + 5.
- Add. 4 + 5 = 9.
The answer is 9. A common slip is to add first, turning 9 + 5 into 14 and dividing 36 by 14, which cannot come out even. Another slip is to read 36 ÷ 3 first, getting 12, and then square it, which silently changes the problem.
A second, shorter line for the Basic level: 12 × 4 − 8 + 3. Multiplication gives 48 − 8 + 3. Subtraction and addition share a rank, so go left to right: 48 − 8 = 40, then 40 + 3 = 43. Doing the addition first (8 + 3 = 11) would give 37.
What the answer key reveals
- Left to right only. The student ignores rank entirely. Their answers are often bigger than the key's on lines with a × after a +.
- Add before subtract. Right in the 12 × 4 − 8 + 3 example above. The key's answer is higher than the student's.
- Parentheses ignored. For (6 + 3) × 8 the correct 72 becomes 6 + 24 = 30.
- Squaring wrongly. Treating 4² as 4 × 2. Ask the student to write the multiplication out.
- Brackets in the wrong order. In nested forms, work from the innermost pair outward.
Making it stick
Ask students to rewrite the expression after every single step, one operation at a time, rather than doing several in their head. The page then shows their reasoning, and a wrong turn is easy to find. Pairing this sheet with evaluating algebraic expressions shows where the rules go next, and multiplying fractions is a good place to use them with new kinds of numbers.