The idea, step by step
Choose the unit and method
Use a unit that fits the object: millimetres for the thickness of a small item, centimetres for a book, metres for a room and kilometres for a journey. Think about the required precision before selecting a measuring tool.
Start a ruler reading at zero. If an object starts at a different mark, subtract the starting reading from the finishing reading. For a curved or irregular boundary, explain a method such as using a flexible tape or a string that is then measured straight.
Use measurements to make a decision
A practical answer may need a second step. If a rectangular floor is to be covered with square tiles, find the floor area, find the area of one tile and compare them. State simple assumptions, such as no gaps, overlaps or cutting waste.
Keep an estimate alongside the exact calculation. A reported room width of 350 metres is unlikely; 350 centimetres, or 3.5 metres, is plausible. Measurement numbers are meaningful only when their units and context match.
A common trap
A ruler’s final reading always equals the object’s length.
Instead: That works only if the object starts at zero. Otherwise subtract the starting reading from the finishing reading.
See the thinking
Worked example 1
A ribbon begins at the 2.5 cm mark on a ruler and ends at 14.5 cm. Find its length.
- The ruler did not start at zero, so subtract the start reading.
- 14.5−2.5=12.
Worked example 2
A rectangular display board measures 120 cm by 80 cm. It is covered exactly by 20 cm by 20 cm square cards, without gaps or overlaps. How many cards are needed?
- Along the length, 120÷20=6 cards fit. Along the width, 80÷20=4 fit.
- There are 6 columns and 4 rows, so 6×4=24 cards are needed. The area check is 9,600÷400=24.
Check your understanding
An object begins at 3 cm and ends at 11 cm on a ruler. How long is it?
Show answer
8 cm.
11−3=8.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Choose the most suitable unit for a school oval’s length: millimetres, metres or kilometres.1 mark
- A pencil begins at 1.5 cm and ends at 16 cm. Find its length.1 mark
- A rectangular mat is 3 m by 2 m. Find its area.1 mark
- A 2-metre ribbon is cut into eight equal pieces. Find each length in centimetres.2 marks
- A board is 100 cm by 60 cm. Square stickers have sides of 10 cm and cover it without gaps. How many stickers fit?2 marks
- A room width is recorded as 420 m. Suggest a likely unit correction and explain why it is plausible.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Choose the most suitable unit for a school oval’s length: millimetres, metres or kilometres.1 mark
The length is large enough for metres but much less than a kilometre.
Metres. - A pencil begins at 1.5 cm and ends at 16 cm. Find its length.1 mark
16−1.5=14.5.
14.5 cm. - A rectangular mat is 3 m by 2 m. Find its area.1 mark
3×2=6.
6 square metres. - A 2-metre ribbon is cut into eight equal pieces. Find each length in centimetres.2 marks
2 m=200 cm; 200÷8=25.
25 cm. - A board is 100 cm by 60 cm. Square stickers have sides of 10 cm and cover it without gaps. How many stickers fit?2 marks
100÷10=10 across and 60÷10=6 down; 10×6=60.
60 stickers. - A room width is recorded as 420 m. Suggest a likely unit correction and explain why it is plausible.2 marks
A normal room is a few metres wide, not hundreds of metres. The actual unit must be checked rather than silently changed.
420 cm, or 4.2 m, is plausible.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Decimal metric conversions; deriving rectangle area; missing dimensions; practical measurement.
Official curriculum source ↗