Understand the idea.
Choose a zero reference
An integer can be positive, negative or zero. Choose the reference before interpreting its sign: below sea level is negative height, while money owed can be a negative balance. A positive sign may be omitted, so .
The sign identifies a side of zero; the number's distance from zero tells its size in that direction. Zero itself is neither positive nor negative. Include units so that a signed number describes a particular 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
Separate the starting value from the change applied to it. A temperature can start negative and rise by a positive amount. A rise moves toward greater values, crossing zero only if the rise is large enough.
An account balance can become negative if an allowed payment exceeds the available money. The minus sign then communicates debt. After calculating, explain the final sign using the chosen reference instead of assuming a negative result is a mistake.
See the method in action.
Temperature crosses zero
The temperature is −4°C and rises by 7°C. Find the new temperature.
Worked solution
- 1
Use part of the rise to reach zero.
The starting temperature is four degrees below zero.
- 2
Find the rise still remaining.
Four of the seven degrees have been used to reach zero.
- 3
Apply the rest and state the temperature.
The remaining rise finishes three degrees above zero.
3°C
A payment creates a debt
An account contains 20 dollars. A payment of 27 dollars is allowed. Find the balance.
Worked solution
- 1
Compare the payment with the credit.
The payment requires seven dollars more than the account contains.
- 2
Subtract the full payment.
A payment decreases the balance, including the part that goes below zero.
- 3
Interpret the signed result.
The account has a debt of seven dollars after the allowed payment.
−7 dollars
Try it yourself.
Check your understanding
Write a signed height for a diver 12 m below sea level.
Show answer & reasoning
−12 m
Sea level is the zero reference. Twelve metres below it is on the negative side, so the signed height is .
Keep practising
6 worksheet questions · 13 marks
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 ↗