Understand the idea.
Zero is a reference
An integer can be a positive whole number, a negative whole number or zero. A negative sign places a value below or on the opposite side of a chosen zero, such as a temperature below .
Always identify the reference. A height of can mean three metres below ground when ground is zero. The tunnel has a positive depth of three metres; its signed height describes where it is.
Read both sign and amount
The sign describes the side of zero and the digits describe how far away the value is. Thus is five units on the negative side. The positive sign is optional: and name the same value.
Interpret the sign using the situation. In a simple account model, a balance of dollars means twelve dollars owed. It does not describe twelve dollars available to spend, even though the digits are the same.
See the method in action.
Worked example 1
A freezer shows −7°C. Describe this relative to 0°C.
Worked solution
- 1
Identify the reference temperature.
The question asks for the temperature relative to zero degrees Celsius.
- 2
Read the sign and the distance.
The minus sign means below zero and the 7 gives the number of degrees, so it is 7 degrees Celsius below zero.
7°C 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.
Worked solution
- 1
Set ground level as the reference.
Both heights must use the same zero.
- 2
Write the height below ground.
Four metres below the reference uses a negative sign.
- 3
Write the height above ground.
Six metres above the reference uses a positive sign.
Tunnel −4 m; balcony +6 m.
Try it yourself.
Check your understanding
Ground floor is 0. What does floor −2 mean?
Show answer & reasoning
Two floors below ground.
Ground floor is the zero reference. Floor is two floor levels below it.
Keep practising
6 worksheet questions · 8 marks
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 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 and Ben has . 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.
. - A diver is 9 metres below sea level, which is 0. Write the position.1 mark
Use a negative position below sea level.
m. - Describe a balance of 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.
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 and Ben has . 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 ↗