Year 6 Mathematics · AC9M6A02

Unknown Values with Brackets and Mixed Operations

Use equality, operation properties and inverse reasoning

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students interpret equality as balance, follow grouping, identify the role of the unknown and use inverse operations or number properties before substituting to check.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
Key conceptTeach from the board

Solve 4(□ + 7) = 100

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

1Interpret4 equal groups total 100
2Undo ×4□ + 7 = 25
3Undo +7□ = 18
4Substitute4(18 + 7) = 100
5Confirmboth sides equal

Undo operations in reverse order while respecting brackets. The method follows the structure of the expression rather than moving symbols without meaning.

Use properties to simplify before solving

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

6(□ + 4) = 180divide by 6, then subtract 4
3□ + 5□ = 96combine like multiplicative groups: 8□ = 96
5(20 − □) = 35divide, then solve 20 − □ = 7
(□ + 8) ÷ 4 = 9multiply by 4, then subtract 8

The unknown may appear in a subtracted position, so operation order and meaning matter. Always check in the original equation.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6A02 - Unknown Values with Brackets and Mixed Operations
Example 1

1 Interpret 4 equal groups total 100

Example 2

6(□ + 4) = 180 divide by 6, then subtract 4

Example 3

: using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 \times (4 + 6) = \square, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication

Example 4

: constructing equivalent number sentences involving brackets and combinations of the 4 operations; explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions

Curriculum examplesCopied content

AC9M6A02: find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

  • E1: using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 \times (4 + 6) = \square, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication
  • E2: constructing equivalent number sentences involving brackets and combinations of the 4 operations; explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
  • E3: finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6+4\times8\;=\;6\times\bigtriangleup+\square
  • E4: applying knowledge of inverse operations and number properties to create equivalent number sentences; removing one of the numbers and replacing it with a symbol, then swapping with a classmate to find the unknown values

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Solve 4(x+7)=100.
  • Solve 5(20−x)=35.
  • Combine 3x+5x.
  • Explain reverse order.
  • Substitute and check.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Operations undone in written orderUndo the outer operation first.
Bracket ignoredTreat the grouped expression as one quantity.
Subtraction assumed commutative20 − x is not x − 20.
Check performed on a simplified but altered equationSubstitute into the original.
Curriculum alignmentStart here

Learning goal

Students interpret equality as balance, follow grouping, identify the role of the unknown and use inverse operations or number properties before substituting to check.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.