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.

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

Students should be comfortable with addition and subtraction facts to 20, simple equal groups and number sentences, and using symbols to represent an unknown or repeated relationship. Revisit a concrete or pictorial model first if the symbols are not yet meaningful.

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

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.

• 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. Which fact is related to 37 + 25 = 62?

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

2. Complete the unknown.

   Prompt: 47 + □ = 83

3. What is the unknown in □ − 28 = 45?

   • 73
   • 17
   • 63
   • 83

4. Write four related facts for 54, 36 and 90.

5. Match the unknown sentence to its answer.

   Match: 29 + □ = 84 • □ − 18 = 42 • 96 − □ = 39 ↔ 57 • 60 • 55

6. Complete the inverse check.

   Prompt: 96 − 57 = 39, and 39 + □ = 96.

1. Create a fact-family puzzle with one hidden number and enough clues to find it.

2. Solve 348 + □ = 725 using partitioning and an inverse operation. Explain each step.

Explain the reasoning, not only the final answer.

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.

• I can identify whole and parts.
• I can write fact families.
• I can solve unknowns.
• I can use inverse checks.
• I can explain connections.

Quick check: Write a fact family for 28, 35 and 63. • Solve 47 + ? = 83. • Solve ? − 28 = 45.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

Use reliable, community-approved sources and identify the specific Nation, People or community where the source does. Do not present diverse First Nations knowledges as one generic tradition. Follow local cultural and intellectual property protocols before reproducing cultural material or inviting community participation.

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

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

• AC9M3A02 — Efficient Mental Addition and Subtraction
• All Year 3 Mathematics topics

Curriculum equivalents for And explain the connection between addition and subtraction as inverse...

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

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.