Order of operations: what children learn
When a calculation uses more than one operation, parentheses and operation priority change the answer. Try 2 + 1 × 3 = 5, then compare it with (2 + 1) × 3 = 9.
Use PEMDAS as a reminder: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division have equal priority, as do addition and subtraction, so work from left to right within each pair. This game focuses on the four operations and parentheses; it does not include exponents.
Supports part of Common Core 6.EE.A.2.c. This focused game does not cover the entire standard.
Common Core connection: 6.EE.A.2.c. This is focused practice for part of the standard.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 150-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Parentheses first. Work out anything in parentheses before anything else. In (12 + 3) × 4, do 12 + 3 = 15 first.
- Then powers. Squares and cubes come next, for example 3² in 10 + 3². (The game itself doesn't include powers.)
- Then multiplication and division. These have equal priority. Work them out from left to right. In 20 + 18 ÷ 3, do 18 ÷ 3 = 6 first.
- Then addition and subtraction. These also have equal priority, worked from left to right. So 20 + 18 ÷ 3 = 20 + 6 = 26.
Worked examples
Example 1: 12 + 5 × 6 = ?
Working: Multiply first: 5 × 6 = 30. Then 12 + 30.
Answer: 42
Example 2: (20 + 9) × 6 = ?
Working: Parentheses first: 20 + 9 = 29. Then 29 × 6 = 174.
Answer: 174
Example 3: 8 × (11 − 4) = ?
Working: Parentheses first: 11 − 4 = 7. Then 8 × 7.
Answer: 56
Common mistakes and how to fix them
- Working left to right regardless of the operations: 12 + 5 × 6 = 17 × 6 = 102. Multiply first: 5 × 6 = 30. Then add 12 to get 42.
- Thinking multiplication always comes before division because M comes before D in PEMDAS. Multiplication and division have equal priority; work them from left to right. Addition and subtraction also have equal priority.
- Ignoring parentheses. Work inside parentheses first, then use that result in the rest of the calculation.
Activities to try at home
- Write a calculation without parentheses and challenge each other to add parentheses to make different answers: 2 + 3 × 4 can be 14 or 20.
- Use the four 4s puzzle: make each number from 1 to 10 using four 4s and any operations.
- Check calculator results: does your calculator follow the order of operations? (Most scientific ones do.)
Ideas for the classroom
- Use 'target number' games where students combine given numbers with operations and parentheses to reach a target.
- Ask students to find and explain the mistake in a worked example.
- Link to algebra: 3 + 2n means 3 + (2 × n), not (3 + 2) × n.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division share a priority, and addition and subtraction share a priority.
Does this game include exponents?
No. It practices the four operations and parentheses. Exponents are a separate skill in the full order of operations.
Should multiplication always come before division?
No. They have equal priority, so work from left to right. For example, 12 ÷ 3 × 2 = 4 × 2 = 8.