Order of operations practice in four levels, from two operations with no parentheses up to exponents. The first sheet explains the order and the three mistakes students make most. The answer keys show every step, not just the final number. Two more sheets have students write expressions from words and say what an expression means without solving it.
The four steps in order, one problem solved a line at a time, and three common mistakes.
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Twenty problems with two operations. Multiply or divide before adding or subtracting. Step-by-step key.
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Twenty problems where the parentheses change the answer. Step-by-step key.
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Fourteen longer problems with parentheses and room to show each step. Step-by-step key.
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Fourteen problems with squares, some inside parentheses. Step-by-step key.
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Ten equations that are wrong until one pair of parentheses is added. Includes answer key.
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Turn words such as "add 6 and 9, then multiply by 4" and four short stories into expressions. Includes answer key.
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Match expressions to words, write them in words, and compare two expressions without solving them. Includes answer key.
Download PDFThe order of operations is the agreement that lets everyone get the same answer from the same problem: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Most errors come from reading PEMDAS as six separate steps. Multiplication does not come before division, and addition does not come before subtraction: each pair is done together, left to right. The lesson sheet shows this with 24 ÷ 4 × 2 and 12 − 4 + 3.
The sets build one idea at a time. Set A has no parentheses, so the only decision is which operation goes first. Set B adds parentheses, and every problem is one where they change the answer. Set C has three operations. The exponents sheet adds squares.
Every answer key prints the working line by line, so a student can find the exact step where their answer went wrong. Add the Parentheses turns the skill around: the answer is given and the student decides where the parentheses must go.
Writing and Reading Numerical Expressions cover the other half of the 5th grade standard: turning "add 6 and 9, then multiply by 4" into (6 + 9) × 4, and seeing that 3 × (4,618 + 925) is three times as large as 4,618 + 925 without working either one out.
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