The idea, step by step
Choose a zero reference
Integers are whole numbers, zero and their negative opposites. A negative value describes a position below or less than a chosen zero. Its meaning depends on the reference: zero degrees, sea level or a zero balance. A positive sign may be omitted, so 8 and +8 mean the same number.
The sign tells the side of zero; the size tells the distance from zero. Zero is neither positive nor negative. Always include units or a description when an integer represents a real quantity.
| Situation | Reference | Signed value |
|---|---|---|
| Diver 6 m below sea level | Sea level | −6 m |
| Credit of 15 dollars | Zero balance | +15 dollars |
| Ground floor | Ground level | 0 |
Interpret a change
A rise of 7 degrees is a positive change, even if the starting temperature is negative. From −4°C, four degrees of the rise reach zero and three more reach +3°C.
A negative balance can describe debt when borrowing is allowed. Adding money reduces the debt, but a small deposit may still leave a negative balance. A negative answer is not automatically an error: interpret it.
A common trap
Zero is a positive integer.
Instead: Zero is the reference between positive and negative integers and belongs to neither side.
See the thinking
Temperature crosses zero
The temperature is −4°C and rises by 7°C. Find the new temperature.
- Move 4 degrees upward to zero.
- There are 3 degrees of the rise still to apply.
- The final temperature is 3 degrees above zero.
A payment creates a debt
An account contains 20 dollars. A payment of 27 dollars is allowed. Find the balance.
- The payment is 7 dollars greater than the available credit.
- .
- The negative result means a debt of 7 dollars.
Check your understanding
Write a signed height for a diver 12 m below sea level.
Show answer
−12 m
Below sea level is on the negative side of the chosen reference.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- A submarine is 60 m below sea level. Write its height as a signed number.2 marks
- A platform is 8 m above ground level. Write its signed height.2 marks
- The morning temperature is −3°C and the afternoon temperature is +5°C. How much warmer is the afternoon?2 marks
- An account has a debt of 25 dollars. A deposit of 10 dollars is made. Find the signed balance.2 marks
- Ground floor is labelled 0. Basement B2 is two floors below it. Which integer labels B2?2 marks
- A lift travels from floor −1 to floor 4. Write the signed change.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A submarine is 60 m below sea level. Write its height as a signed number.2 marks
Sea level is zero.
A position below it is negative.
−60 m - A platform is 8 m above ground level. Write its signed height.2 marks
Ground level is zero.
Above ground is positive.
+8 m - The morning temperature is −3°C and the afternoon temperature is +5°C. How much warmer is the afternoon?2 marks
From −3 to zero is 3 degrees.
From zero to +5 is 5 degrees.
The increase is 8 degrees.
8°C warmer - An account has a debt of 25 dollars. A deposit of 10 dollars is made. Find the signed balance.2 marks
Represent the debt by −25.
.
−15 dollars - Ground floor is labelled 0. Basement B2 is two floors below it. Which integer labels B2?2 marks
Two floors below the zero reference is −2.
−2 - A lift travels from floor −1 to floor 4. Write the signed change.3 marks
One floor upward reaches zero.
Four more upward floors reach 4.
The total change is +5.
+5 floors
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum
Positive and negative numbers in context; comparing and ordering integers; number lines and directed change; adding integers; subtracting integers; mixed addition/subtraction problems. Multiplication/division of negative integers is a labelled preview, not the Year 7 core endpoint.
Official curriculum source ↗