This Year 5 metric and imperial units lesson is written for pupils aged 9-10 and follows the National Curriculum. In short, it shows you how to convert metric units, use approximate metric and imperial equivalents, find perimeter and area of rectilinear shapes and estimate volume. Before you start, it helps to revise decimals and thousandths and percentages, because this lesson builds on them.
Year 5 metric and imperial units lesson: what you will learn
Hello, I am Otto! We measure the world in units. We use centimetres and metres for length, grams and kilograms for mass, and millilitres and litres for capacity. Some people also use inches, feet, pints and pounds. In this chapter you change between units, find the perimeter and area of shapes and begin to measure volume by counting cubes.
Starter activity
Find a ruler. Measure the length of your pencil in centimetres and then in millimetres. Now measure the width of your desk using a metre stick. Which unit was easiest to use for each? Notice how 10 mm make 1 cm and 100 cm make 1 m. Keep these facts in mind as you read the rules below.
Metric units
Definition: metric units
Metric units are based on 10, 100 and 1,000. For length we use millimetres (mm), centimetres (cm), metres (m) and kilometres (km). For mass we use grams (g) and kilograms (kg). For capacity we use millilitres (ml) and litres (l).
| Length | Mass | Capacity |
|---|---|---|
| 10 mm = 1 cm | 1,000 g = 1 kg | 1,000 ml = 1 l |
| 100 cm = 1 m | 1 l = 100 cl | |
| 1,000 m = 1 km |
Rule: changing between units
To change from a bigger unit to a smaller unit, multiply by 10, 100 or 1,000, because you need more small units. To change from a smaller unit to a bigger unit, divide.
Example 1
Change 3.5 km to metres, and 4,500 g to kilograms.
Kilometres to metres: bigger to smaller, so multiply by 1,000. 3.5 × 1,000 = 3,500 m. Grams to kilograms: smaller to bigger, so divide by 1,000. 4,500 ÷ 1,000 = 4.5 kg.
Example 2
A jug holds 2.4 litres of juice. How many 200 ml glasses can be filled?
2.4 l = 2.4 × 1,000 = 2,400 ml. 2,400 ÷ 200 = 12 glasses.
Imperial units
Key fact: approximate equivalents
Some people in Britain still use imperial units. You should know these rough equivalents: 1 inch is about 2.5 cm; 1 foot is about 30 cm; 8 km is about 5 miles; 1 kg is about 2.2 pounds (lb); 1 pint is about 570 ml; 1 gallon is about 4.5 litres.
Example 3
A table is 3 feet long. About how long is it in centimetres? A recipe needs 2 pints of milk. About how many millilitres is that?
3 feet ≈ 3 × 30 = 90 cm. 2 pints ≈ 2 × 570 = 1,140 ml.
Watch out
The imperial equivalents are only approximate, so use the sign ≈ and say "about". Also, never mix units in a calculation. Change everything into the same unit first, for example change metres to centimetres before you add them to centimetres.
Perimeter
Definition: perimeter
The perimeter of a shape is the total distance around its edge. It is measured in units of length such as cm or m.
Rule: perimeter of a rectangle
A rectangle has two long sides and two short sides. Perimeter = 2 × (length + width). For the rectangle above: 2 × (8 + 5) = 2 × 13 = 26 cm.
Example 4
A rectangular field is 120 m long and 80 m wide. How far is it round the field? How many times must Ravi run round to cover 1 km?
Perimeter = 2 × (120 + 80) = 2 × 200 = 400 m. 1 km = 1,000 m, and 1,000 ÷ 400 = 2.5. Ravi must run round 2 and a half times.
Example 5
Find the perimeter of the L-shape above.
The shape is a 10 cm by 8 cm rectangle with a 4 cm by 3 cm corner removed. Cutting a corner out of a rectangle does not change the perimeter, so the perimeter is the same as the rectangle: 2 × (10 + 8) = 36 cm. You can check by adding all six sides: 10 + 3 + 4 + 5 + 6 + 8 = 36.
Area
Definition: area
The area of a shape is the amount of flat space inside it. We measure it in square units, such as square centimetres (cm²) or square metres (m²). One square centimetre is a square with sides of 1 cm.
Rule: area of a rectangle
Area of a rectangle = length × width. The rectangle above is 9 cm by 6 cm, so its area is 9 × 6 = 54 cm². It is the same as counting the 54 small squares.
Method: area of a composite shape
- Split the shape into rectangles, or imagine a bigger rectangle with a corner taken away.
- Find the area of each part (or of the big rectangle and the corner).
- Add the parts together, or subtract the missing corner.
- Write the answer in square units.
Example 6
Find the area of the L-shape that is a 10 cm by 8 cm rectangle with a 4 cm by 3 cm corner removed.
Area of the big rectangle: 10 × 8 = 80 cm². Area of the corner removed: 4 × 3 = 12 cm². Area of the L-shape: 80 − 12 = 68 cm².
Volume
Definition: volume
Volume is the amount of space inside a solid shape. We estimate it by counting how many 1 cm cubes fit inside. A cube with edges of 1 cm has a volume of 1 cubic centimetre, written 1 cm³.
Example 7
A cuboid is made of 1 cm cubes. It is 3 cubes long, 2 cubes wide and 2 cubes high. What is its volume?
The bottom layer has 3 × 2 = 6 cubes. There are 2 layers, so 6 × 2 = 12 cm³.
Did you know?
The metric system was invented in France in the 1790s to give the world a single, simple set of measures based on 10. The metre was first defined as one ten-millionth of the distance from the North Pole to the equator. Britain used imperial measures for much longer and still uses miles on road signs today.
Otto's tip
Before you calculate, check the units. Write the unit with every answer: cm for perimeter, cm² for area and cm³ for volume. If your answer for an area has no little 2 on the unit, you may have found a perimeter instead!
How to use this Year 5 metric and imperial units lesson
First, read the key points so that you know where the Year 5 metric and imperial units lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the metric and imperial units, perimeter, area and volume worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the metric and imperial units, perimeter, area and volume test and mark it with the test answers.
Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 5 metric and imperial units lesson gives you everything you need for the chapter.
To sum up, regular practice works better than one long session. For instance, ten minutes a day is often enough. Besides, mistakes are useful, because they show what to revise next. Then, once a method feels easy, try a harder question. As a result, you build confidence step by step.
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