AC9M3A01 • Year 3 Maths

And explain the connection between addition and subtraction as inverse...: Year 3 Maths topic guide

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

What students learn in AC9M3A01

This unit helps students build a clear, usable understanding of And explain the connection between addition and subtraction as inverse.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.

  • Start with the main idea: recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences.
  • Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
  • 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 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
  • Finish with mixed questions so students must choose the correct strategy rather than copy the last example.

Curriculum coverage and elaborations

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.

  • 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)

How to use this unit

Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.

Teacher resource

AC9M3A01 teacher slide

Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.

Open teacher slide (PDF)

Common mistakes to watch for

  • Rushing to a rule before checking the concrete model, drawing or number sentence.
  • Using the correct answer once but not being able to explain why it works.
  • Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.

International curriculum mapping

This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.

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 And explain the connection between addition and subtraction as inverse... and related outcomes.
United StatesCommon Core / NGSSGrade 3 Common Core Mathematics/ELA closest topic match for And explain the connection between addition and subtraction as inverse....
England / UKNational CurriculumKey Stage 2 / Year 3: closest programme-of-study match for And explain the connection between addition and subtraction as inverse....
CanadaProvincial and territory curriculaGrade 3 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference.
New ZealandNew Zealand CurriculumLevel 2 Maths: closest achievement-objective topic for And explain the connection between addition and subtraction as inverse....
IndiaNCERT / CBSEClass 3 closest NCERT/CBSE topic match for And explain the connection between addition and subtraction as inverse....

Related Year 3 Maths topics

Official curriculum references