Math // Multiplication & Division

Brackets in Expressions

Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols

Ages
10 to 11
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

Can the learner look at '3 × (4 + 5)' and work out the brackets first — getting '3 × 9 = 27' — rather than just multiplying left to right?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Evaluate 3 × (4 + 5) by computing inside the parentheses first
  • Evaluate {2 × [3 + (7 − 1)]} with nested grouping symbols
  • Insert parentheses into an expression to make it equal a target value

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Division with remaindersRequired

    Multiplication & Division // Ages 9 to 10

    Evaluating grouped expressions formalises multi-step calculation skills from Y5

  • Long multiplication (age 10+)Helpful

    Multiplication & Division // Ages 10 to 11

    Evaluating expressions requires fluent multiplication

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Brackets in Expressions

Ages 10 to 11 // Method

Leads to

2 topics
  • Order of operationsRequired

    Multiplication & Division // Ages 10 to 11

    The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations

  • Writing Number SentencesRequired

    Multiplication & Division // Ages 10 to 11

    Writing/interpreting expressions requires understanding grouping symbols

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For 10–11 year-olds: use and evaluate parentheses, brackets and braces in numerical expressions, including nested grouping. Learners discover that grouping symbols OVERRIDE the default order — whatever is inside is computed first, and nested groups are resolved inside-out — through evaluating grouped/nested expressions, inserting brackets to hit a target value, and explaining why placement changes the result. This sets up the full order-of-operations convention.

Common misconceptions

  • Ignoring brackets and applying only left-to-right or default order.
  • Evaluating nested brackets outside-in instead of inside-out.
  • Mismatching bracket pairs in nested expressions.
  • Believing brackets never change the answer (not seeing they override order).
  • Dropping a grouping level when rewriting mid-calculation.

Useful representations

  • Colour-matched bracket pairs and inside-out collapse steps
  • Expression tree / step ladder showing each group evaluated
  • Target-value insert-the-brackets puzzles
  • Contrasting expressions with/without brackets on the same numbers

Teaching practices

  • Establish that grouping symbols compute first and OVERRIDE default order, evaluating nested groups inside-out.
  • Use insert-the-brackets-to-hit-a-target tasks to prove brackets genuinely change the result (2+3×4 vs (2+3)×4).
  • Colour-code / match bracket pairs and rewrite the expression after collapsing each innermost group, to prevent nesting slips.
  • Introduce different grouping symbols (), [], {} as the same idea at different nesting levels.
  • Connect to real multi-step calculation and later to formulae and algebra.

Activities to try

  1. 1

    Bracket playground: move the brackets, watch the value change

    Why it works: Brackets are a genuine structural operation that overrides the default order — WHERE they go determines which operation happens first, so they change the result rather than being optional punctuation.

    1. Start with 2 + 3 × 4 and position bracket handles around different parts of the expression.
    2. Compare (2 + 3) × 4 = 20 against 2 + (3 × 4) = 14, reading the result each time.
    3. Given the numbers 2, 3, 4 with + and ×, slide the brackets until the expression equals a target of 20.
    4. State in your own words why where the brackets sit changes the answer.
  2. 2

    Collapse the innermost group: evaluating nested expressions inside-out

    Why it works: Nested grouping is resolved from the innermost pair outward; replacing each completed group with its value keeps the calculation tidy and prevents dropping or mismatching a level.

    1. Evaluate 3 × (4 + 5) by computing inside the parentheses first: 4 + 5 = 9, then 3 × 9 = 27.
    2. Evaluate the nested expression 2 × [3 + (7 − 1)] by resolving the innermost pair first: (7 − 1) = 6, then [3 + 6] = 9, then 2 × 9 = 18.
    3. After each step, rewrite the whole expression with the collapsed group replaced by its single value before continuing.
    4. Colour-code or circle matching bracket pairs so you never mismatch or skip a level.
  3. 3

    Insert brackets to hit a target and explain why

    Why it works: Inserting brackets to reach a required value shows that grouping genuinely reorders a calculation: under the convention that multiplication comes before addition, 2 + 3 × 4 is 14, and only grouping (2 + 3) makes it 20. Note that working strictly left to right also gives 20 here, so the learner must write the brackets and explain them; reaching 20 alone does not show the brackets were understood.

    1. Take 2 + 3 × 4 (which without brackets equals 14, using the convention that multiplication is done before addition) and insert parentheses to make it equal 20.
    2. Write out the bracketed version, then evaluate it step by step to confirm it reaches the target.
    3. Explain which operation your brackets forced to happen first, and why that changes the answer from 14 to 20.
    4. Try a second target on a fresh set of numbers and justify your placement.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
5.OA.1

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