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Brackets and Order of Operations

A 50-minute Grade 5 lesson on evaluating expressions with brackets, where the point is that the order is a convention agreed so everyone gets the same answer.

Brackets and Order of Operations is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.OA.A.1 — work out expressions with brackets, in the right order. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 5
Length:
50 minutes
Standard:
5.OA.A.1

Grade 5 · Operations & Algebraic Thinking

5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Objective

Students will be able to evaluate numerical expressions containing brackets and apply the order of operations correctly.

Students are successful when they can

  • Evaluates the innermost brackets first.
  • Multiplies and divides before adding and subtracting when no brackets say otherwise.
  • Writes an expression with brackets to match a described situation.

What you need

  • Expression cards with and without brackets
  • Whiteboards
  • Word situations to translate into expressions
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — two answers, one expression

6 min
  1. Write 3 + 4 × 5 and collect answers on whiteboards.
  2. Thirty-five and twenty-three will both appear. Do not settle it yet — the disagreement is the lesson's starting point.

Teach — the convention and the brackets

15 min
  1. Say plainly that both answers follow a sensible rule, and that is exactly the problem. Mathematicians agreed on one order so that an expression means one thing.
  2. State it: brackets first, then multiplication and division, then addition and subtraction.
  3. So 3 + 4 × 5 is 23. Write (3 + 4) × 5 = 35 beside it. The brackets are how you ask for the other one.
  4. Do a nested example: 2 × (8 + (6 ÷ 3)). Innermost first: 6 ÷ 3 is 2, then 8 + 2 is 10, then 2 × 10 is 20.
  5. Show that multiplication and division are done left to right where both appear: 24 ÷ 4 × 2 is 12, not 3.
  6. Translate a situation: three bags of four apples plus five loose apples. 3 × 4 + 5, and the brackets are not needed.
“The order is not a fact about numbers. It is an agreement, so that when you write an expression, everyone reading it gets the same answer you did.”

Guided practice — with and without

14 min
  1. Pairs evaluate matched pairs of expressions that differ only in bracket placement.
  2. They record both answers and say what the brackets changed.
  3. Then they write expressions for three described situations, deciding whether brackets are needed.

Independent practice

12 min
  1. Students complete an order of operations page.
  2. Left-to-right evaluation is the diagnostic error and shows on any expression where an addition precedes a multiplication.

Close

3 min
  1. Write 20 − 3 × 4 and take the answer.
  2. Eight. Anyone answering 68 is still reading left to right.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Evaluates 3 + 4 × 5 as 35 by working left to right.

Why: Reading order is left to right and every previous calculation has been done in the order written. There has never been a reason to do otherwise.

Fix: Show two people getting different answers to the same written expression. The need for a convention is felt before the convention is stated.

Does all multiplications before all divisions, so 24 ÷ 4 × 2 becomes 3.

Why: The rule has been memorised as a strict list with multiplication ahead of division, which the usual mnemonics encourage.

Fix: State that multiplication and division sit at the same level and are done left to right. Same for addition and subtraction.

Evaluates the outer bracket first in a nested expression.

Why: The outer bracket is read first, and reading order is being followed.

Fix: Underline the innermost bracket before starting. One physical mark decides the order and removes the choice.

If they are not there yet

  • Work with a single set of brackets before nesting any.
  • Rewrite each expression one line at a time, showing the result of each step, so the order is recorded rather than held.

If they finish early

  • Insert brackets into an expression to make it equal a given value.
  • Write an expression with three operations whose value changes three ways depending on bracket placement.
  • Evaluate an expression with brackets inside brackets inside brackets.

Exit ticket

Evaluate 5 + 2 × (9 − 3) and (5 + 2) × 9 − 3.

What to look for: 17 and 60. An answer of 42 to the first means the addition was done before the multiplication once the bracket was cleared.

Printable practice for 5.OA.A.1

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Brackets and Order of Operations

How long does the Brackets and Order of Operations lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Brackets and Order of Operations teach?

CCSS.MATH.CONTENT.5.OA.A.1 — 5.OA.A.1, Operations & Algebraic Thinking for Grade 5: “Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.” In plain terms, work out expressions with brackets, in the right order.

What do I need to teach this lesson?

Expression cards with and without brackets, whiteboards, word situations to translate into expressions and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: evaluates 3 + 4 × 5 as 35 by working left to right; does all multiplications before all divisions, so 24 ÷ 4 × 2 becomes 3 and evaluates the outer bracket first in a nested expression. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “Evaluate 5 + 2 × (9 − 3) and (5 + 2) × 9 − 3.” 17 and 60. An answer of 42 to the first means the addition was done before the multiplication once the bracket was cleared. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Brackets and Order of Operations?

Yes — 2 printable 5.OA.A.1 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Brackets and Order of Operations free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 5.OA.A.1 of the Common Core State Standards for mathematics.