Year 3 Mathematics · AC9M3A01

Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

Addition and subtraction undo each other. A whole and two parts create related number sentences that can solve unknown values

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Learning goalsSay it simply

Addition and subtraction undo each other. A whole and two parts create related number sentences that can solve unknown values.

Learning routine: Identify whole and parts → Write related facts → Find unknown → Check with inverse

Success looks like

  • Identify whole and parts
  • Write fact families
  • Solve unknowns
  • Use inverse checks
  • Explain connections

Success criteria:

  • Identify whole and parts
  • Write fact families
  • Solve unknowns
  • Use inverse checks
  • Explain connections
Key conceptTeach from the board

Key idea: Addition and subtraction undo each other. A whole and two parts create related number sentences that can solve unknown values.

Learning routine: Identify whole and parts → Write related facts → Find unknown → Check with inverse

inverse operations
operations that undo each other
unknown
a value that has not yet been found
number sentence
a mathematical statement using numbers and symbols
Clean visual examplesOne-page board

Clean one-page examples

AC9M3A01 - Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Example 1

37 + 25 = 62 25 + 37 = 62 62 − 37 = 25 62 − 25 = 37

Example 2

47 + □ = 83 □ − 28 = 45 96 − □ = 39

Example 3

Use a fact family for 37, 25 and 62 62 37 25 37 + 25 = 62 25 + 37 = 62 62 − 37 = 25 62 − 25 = 37 The same whole and parts create two addition and two subtraction facts. Read every label and identify what each quantity or feature represents. Describe the relationship shown by the model. Check that the conclusion answers the original question.

Example 4

Find an unknown part 84 29 ?= 29 + ? = 84 Use 84 − 29 to find the missing part, then add to check. Apply the same relationship to the new context, then justify the answer using the labels and evidence shown.

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
  • E1: partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models; for example, 16 + 8 = 24, 24\space - \space8 = 16, 8 = 24 \space-\space 16
  • E2: using the inverse relationship between addition and subtraction to find unknown values with a calculator; for example, representing the problem, “Peter had some money and then spent \$375, now he has \$158 left. How much did Peter have to start with?” as \square - \$375 = \$158 and solving the problem using \$375 + \$158 = \$533; solving 27 + \square = 63 using subtraction, \square = 63\space - \space27 or by counting on; 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so \square = 36
  • E3: exploring First Nations Australians’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place (teaching context)

Australian, Victorian and NSW alignment retained from the previous page

RegionCurriculumClosest mapping
AustraliaAustralian Curriculum v9.0AC9M3A01 — recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
VictoriaVictorian Curriculum F-10Year 3 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference.
NSWNSW CurriculumStage 2 Maths: closest content focus for Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences and related outcomes.
Questions and answersWith answers
What is the big idea in this topic?
Addition and subtraction undo each other. A whole and two parts create related number sentences that can solve unknown values.
What routine should I use?
Identify whole and parts → Write related facts → Find unknown → Check with inverse
How do I know I am ready to move on?
You can identify whole and parts, write fact families, solve unknowns, use inverse checks, explain connections and explain how your model or calculation supports the answer.
Practice and reviewReady for practice
  • Reversing subtraction freely — Addition is commutative; subtraction usually is not.
  • Using the wrong whole — The largest amount is usually the whole in a fact family.
  • No inverse check — Substitute the unknown into the original sentence.

  1. Explain why 84 − 29 can solve 29 + □ = 84.

  2. A student writes 62 − 25 = 37 and 25 − 62 = 37. Explain which fact is incorrect and why.

Review hint: Follow the routine “Identify whole and parts → Write related facts → Find unknown → Check with inverse” and use the worked model to check whether your answer is reasonable.

Curriculum alignmentStart here

Addition and subtraction undo each other. A whole and two parts create related number sentences that can solve unknown values.

Learning routine: Identify whole and parts → Write related facts → Find unknown → Check with inverse

Success looks like

  • Identify whole and parts
  • Write fact families
  • Solve unknowns
  • Use inverse checks
  • Explain connections

Success criteria:

  • Identify whole and parts
  • Write fact families
  • Solve unknowns
  • Use inverse checks
  • Explain connections
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