Example 1
Model integer subtraction
- Start with 5−(−4).
- Subtracting −4 means adding its opposite, +4.
- Move four units right from 5.
- Arrive at 9.
Final answer: 5−(−4)=9.
Check: Check that 9+(−4)=5.
What students learn in AC9M7N07
We are learning to compare, order and solve problems involving addition and subtraction of integers.
Integers are whole numbers, their negatives and zero. Their order is represented on a number line, with greater values to the right and opposites equally distant from zero.
Addition represents a signed change. Subtraction can be rewritten as addition of the opposite, so 5 − (−4) = 5 + 4 rather than a leftward move.
Contexts such as temperature, elevation and account balance need a reference zero and stated direction. A negative result can be valid, while distance between two integers is always non-negative.
Success criteria
- I can compare and order integers on a number line.
- I can add and subtract integers using opposites and directed movement.
- I can interpret an integer result and distinguish change from distance.
Key vocabulary
- integer
- whole number, its negative, or zero.
- opposite
- number the same distance from zero on the other side.
- directed quantity
- quantity with magnitude and positive/negative direction.
Visual models and representations
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
4 worked numerical & application examples
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 2
Compare a temperature change
- Morning temperature is −6°C.
- Afternoon temperature is 5°C.
- Calculate change: 5−(−6)=11.
- Interpret this as an 11°C rise.
Final answer: The temperature rises by 11°C.
Check: Starting at −6 and moving 11 right reaches 5.
Example 3
Application problem 1
Problem: At 6 am the temperature is −4°C. It rises 9°C, falls 6°C, then rises 3°C. Find the final temperature and represent the changes as one integer calculation.
- Plan: Represent the information first, then calculate, interpret and independently check the result.
- Work: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.
- Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Final answer: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Application problem 2
Problem: Create and solve an integer expression for the change from −15°C to 8°C and back to −4°C.
- Plan: Check that −15+11=−4.
- Work: The changes are +23 then −12; net change is +11°C, ending at −4°C.
- Interpret: Net change equals final minus initial.
Final answer: The changes are +23 then −12; net change is +11°C, ending at −4°C.
Check: Net change equals final minus initial.
Common misconceptions
Common mistake: Negative sign treated only as subtraction.
Correction: It can indicate a number or direction.
Common mistake: -3-5 made positive.
Correction: Moving 5 left from -3 gives -8.
Common mistake: Subtracting negative rule memorised without meaning.
Correction: Connect it to removing a negative change or adding the opposite.
10 important problems to solve
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Order −7, 2, −3 and 0 from least to greatest.
Check answer
Answer: −7, −3, 0, 2.
Hint: Place them on a number line.
Why: Numbers farther left are smaller.
2. Calculate −8+13.
Check answer
Answer: 5.
Hint: Count through zero.
Why: A rightward move of 13 from −8 reaches 5.
3. Calculate 6−(−9).
Check answer
Answer: 15.
Hint: Rewrite as 6+9.
Why: Subtracting a negative adds the opposite.
4. Find the distance between −4 and 7.
Check answer
Answer: 11 units.
Hint: Subtract the lower coordinate from the higher.
Why: Distance is the positive difference 7−(−4).
5. A lift moves from level 3 to level −5. What is its change?
Check answer
Answer: −8 levels.
Hint: Use final−initial.
Why: Final minus initial gives −5−3=−8.
6. The temperature changes from −2°C to −9°C. Find the change.
Check answer
Answer: −7°C.
Hint: Calculate −9−(−2).
Why: The negative change represents a fall of 7°C.
7. An account balance is −$18 and a $25 deposit arrives. Find the balance.
Check answer
Answer: $7.
Hint: Calculate −18+25.
Why: The deposit adds 25 to the signed balance.
8. A diver is at −12 m, rises 7 m, descends 9 m and rises 5 m. Find the final position.
Check answer
Answer: Starting at −12 m gives −12+7−9+5=−9 m, so the diver finishes 9 m below sea level.
Hint: Record rises positive and descents negative.
Why: Signed movements combine in sequence.
9. Create and solve an integer expression for the change from −15°C to 8°C and back to −4°C.
Check answer
Answer: The changes are +23 then −12; net change is +11°C, ending at −4°C.
Hint: Check that −15+11=−4.
Why: Net change equals final minus initial.
10. At 6 am the temperature is −4°C. It rises 9°C, falls 6°C, then rises 3°C. Find the final temperature and represent the changes as one integer calculation.
Check answer
Answer: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Curriculum coverage and elaborations
Content description: compare, order and solve problems involving addition and subtraction of integers.
International curriculum mapping
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Adding and Subtracting Integers
Math Antics — Add and subtract positive and negative integers.
As you watch: How can subtracting a negative number change a value?
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Try it: Show -3 + 7 and 4 - (-2) on a number line and explain each movement.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Compare, order and solve problems involving addition and subtraction of...
Mapped skill: compare, order and solve problems involving addition and subtraction of integers
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.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7N07 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N07 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-INT-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
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.
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Topic reference: AC9M7N07 — Comparing, Adding and Subtracting Integers
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