Chapter 6: Measurement, Area, Volume, and Rates
Measurement, Area, Volume and Rates
Use units, formulae and checking habits to solve measurement questions with clear working.
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Step-by-step teaching, practice and checkpoint.
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Workbook pages
Fun Maths Book 3 pages 62-76
Convert metric units, convert time, find area, perimeter, volume, speed, distance and time.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1What is being measured: length, area, volume, time or rate?
- 2Which units are used in the question?
- 3Which formula or relationship matches the situation?
- 4Does the answer have the right unit and a realistic size?
Visual teaching
See the method
A unit ladder converts metric values, square tiles fill area, cubes fill volume and a moving marker links distance, speed and time.
Worked examples
Convert 3.4 m into centimetres.
Step 1: First, what information is given?
The length is 3.4 metres, and we need centimetres.
Why: Before converting, identify the starting unit and target unit.
Step 2: What is the link between metres and centimetres?
1 metre = 100 centimetres.
Why: Centimetres are smaller units, so there are more of them.
Be careful: Do not divide by 100 when moving from metres to centimetres.
Step 3: Now convert.
3.4 x 100 = 340.
Why: Multiplying by 100 changes metres into centimetres.
Common mistake: Writing 34 cm because only one decimal place moved.
Find the area of a triangle with base 10 cm and height 8 cm.
Step 1: What information do we already know?
The base is 10 cm and the perpendicular height is 8 cm.
Why: Triangle area uses base and perpendicular height.
Step 2: Which formula should we use?
Area of a triangle = base x height ÷ 2.
Why: A triangle is half of a matching rectangle.
Be careful: Do not forget to divide by 2.
Step 3: Calculate the area.
10 x 8 = 80, and 80 ÷ 2 = 40.
Why: The rectangle would be 80 cm^2, so the triangle is half.
Common mistake: Using cm instead of cm^2, or forgetting the half.
A cuboid has volume 360 cm^3, length 12 cm and width 5 cm. Find the height.
Step 1: What are we trying to find?
We need the missing height of a cuboid.
Why: Volume questions may ask for a missing dimension, not only total volume.
Step 2: Which formula connects the values?
Volume = length x width x height.
Why: A cuboid is built from layers of rectangular bases.
Step 3: Find the base area first.
12 x 5 = 60 cm^2.
Why: Each layer has area 60 cm^2.
Step 4: Now find how many layers make 360 cm^3.
360 ÷ 60 = 6.
Why: Dividing volume by base area gives the height.
Common mistake: Multiplying all numbers given without noticing one dimension is missing.
Guided practice
A cyclist travels 150 km in 3 hours. What is the speed?
Independent practice
Your turn
Convert 3.4 m into cm.
Find the area of a triangle with base 10 cm and height 8 cm.
A car travels 180 km in 3 hours. What is its speed?
Mini checkpoint
Check your thinking
Convert 4.25 km into metres.
A rectangle has area 72 cm^2 and length 9 cm. Find its width.
Convert 1.75 hours into minutes.
Key idea
Measurement questions become clearer when you identify the quantity, choose the formula, and keep the unit attached. Convert units carefully, use formulae with meaning, and check that length, area, volume and rate answers use the correct units.
Parent signal
Check units carefully. Unit mistakes often hide correct arithmetic.