The idea, step by step
Zero is a reference
An integer is a whole number that can be positive, negative or zero. Negative numbers describe positions on the other side of a chosen zero: below zero degrees, below sea level or floors below the ground floor.
State the reference. A height of −3 metres means 3 metres below the chosen zero height; it does not mean a measured length is negative.
Read both sign and amount
A plus sign may be omitted: +5 and 5 name the same positive number. In −5, the minus sign belongs to the number and locates it on the negative side of zero.
In a simple account model, a balance of −12 dollars means 12 dollars owed, not 12 dollars available to spend. The sign describes the direction from zero; the digits give the amount.
A common trap
Negative numbers mean a calculation has gone wrong.
Instead: They describe real quantities relative to zero, such as below-zero temperatures or debts.
See the thinking
Worked example 1
A freezer shows −7°C. Describe this relative to 0°C.
- The negative sign means below the reference 0°C.
- The number 7 counts how many degrees below zero.
Worked example 2
Ground level is 0 metres. A tunnel is 4 metres below ground and a balcony is 6 metres above. Write their heights.
- Below ground gives a negative height; above gives a positive height.
- Use the amounts 4 and 6 with their correct signs.
Check your understanding
Ground floor is 0. What does floor −2 mean?
Show answer
Two floors below ground.
The minus sign locates the floor below the zero reference.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Write 5 degrees below zero as a signed temperature.1 mark
- A diver is 9 metres below sea level, which is 0. Write the position.1 mark
- Describe a balance of −18 dollars.2 marks
- Write 12 metres above sea level as a signed height.1 mark
- Is zero positive or negative?1 mark
- A game starts at 0 points. Amira has −3 and Ben has +4. Explain each score.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write 5 degrees below zero as a signed temperature.1 mark
Below zero is negative.
−5°C. - A diver is 9 metres below sea level, which is 0. Write the position.1 mark
Use a negative position below sea level.
−9 m. - Describe a balance of −18 dollars.2 marks
The sign describes debt relative to zero.
The account is 18 dollars below zero, or 18 dollars is owed. - Write 12 metres above sea level as a signed height.1 mark
Above the reference is positive.
+12 m or 12 m. - Is zero positive or negative?1 mark
Zero separates the positive and negative sides.
Neither. - A game starts at 0 points. Amira has −3 and Ben has +4. Explain each score.2 marks
Use the same zero reference for both.
Amira is 3 below the starting score; Ben is 4 above it.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Positive/negative contexts; ordering; number lines; connection to coordinates.
Official curriculum source ↗