5th grade order of operations

5th grade order of operations (class 5): a quiz for kids, then every skill in order with lessons, a checklist and a plan.

What 5th grader learn about the order of operations

In grade 5 (class 5), children learn to use parentheses, brackets and braces, and to work out expressions in the right order. They write simple expressions from words and read expressions without calculating them. The rule that × and ÷ come before + and −, with partners from left to right, sits underneath everything.

• 5.OA.A.1: use parentheses, brackets or braces in numerical expressions, and evaluate expressions with these symbols.
• 5.OA.A.2: write simple expressions that record calculations with numbers, and interpret expressions without evaluating them.
• 4.OA.A.3 (review): solve multi-step word problems with the four operations.
• 5.NBT.B.5–7: the multiplication, division and decimal skills used inside the expressions.

Other grades: 5th grade · 6th grade

The big idea in grade 5

Grade 5 is the year brackets arrive. Children use parentheses, brackets and braces in expressions and work them out from the inside (5.OA.A.1).

They also write simple expressions from words, like “add 8 and 7, then multiply by 2”, and describe expressions without calculating them (5.OA.A.2).

Underneath it all is the order of operations: × and ÷ before + and −, and partners from left to right. Exponents come next year.

When your child gets stuck

Most grade 5 trouble comes from working left to right every time. Ask your child to underline every × and ÷ before starting, and work those out first.

If brackets are the problem, use the calculator to show each step, then cover it and try a similar question on paper.

5th grade order of operations skills, in order

Work down the list. Each lesson explains the idea for parents with pictures and has a quiz for your child.

By the end of grade 5, your child should be able to…

• Work out 3 + 4 × 2 and explain why the answer is 11.
• Work out 12 ÷ 3 × 2 from left to right.
• Work out 2 × [3 + (8 − 2)] from the inside out.
• Add brackets to 5 + 3 × 4 to make 32.
• Write “add 8 and 7, then multiply by 2” as an expression.
• Write one expression for a two-step shopping story and work it out.

Unsure where your child is? The order of operations levels page has a short test for every step from two operations to decimals and negatives.

A 4-week plan for 5th grade order of operations

Add 5 minutes a day with the order of operations practice tool, and check any expression with the step-by-step calculator.

More for grade 5

All 5th grade math · CBSE class 7: Arithmetic Expressions · BODMAS (the Indian and UK name) · Order of operations quiz for grades 5 to 7 · Order of operations for kids

What to say to your child

More worked examples

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

1. 6 + 3 × 5
2. (6 + 3) × 5
3. 24 ÷ 4 × 2
4. 15 − 6 + 4
5. 3 × [2 + (7 − 3)]
6. Brackets in 4 + 6 × 2 to make 20
7. “Subtract 4 from 10, then multiply by 3”
8. 3 packs of 8 pens and 5 more
9. Is 18 − 6 ÷ 3 = 4 true?
10. Stretch: {40 − [3 × (2 + 4)]} ÷ 2

Common mistakes

How to teach it at home

Five minutes a day

Short daily practice beats long weekend sessions.

Make a target

Use three numbers and any signs and brackets. Who can make 20? Who can make 30?

Shopping sums

Turn a shopping list into one expression and work it out in the right order.

By grade

• Before: multiplication and division facts, and two-step word problems
• After: 6th grade order of operations

Worksheets and practice

Order of operations worksheet: printable PDF with an answer key.

All worksheets