KeyStage

Year 6 maths · Key Stage 2 · Measurement

Year 6 converting units, area of triangles and volume of cuboids

Year 6 measurement pulls together several skills. Children convert between metric units using decimals, change between miles and kilometres, calculate the area of triangles and parallelograms, and find the volume of cubes and cuboids. They also learn to recognise when a formula can be used, and that shapes with the same area can have different perimeters.

Units, area and volume, explained

Converting metric units means multiplying or dividing by 10, 100 or 1,000. Going from a larger unit to a smaller one (kilometres to metres) means more of them, so multiply: 2.35 km = 2.35 × 1,000 = 2,350 m. Going from a smaller unit to a larger one means fewer, so divide: 450 g = 450 ÷ 1,000 = 0.45 kg. Children convert length, mass, volume (capacity) and time, using decimals up to three decimal places. Time is the odd one out, because it isn’t decimal: 2.5 hours is 2 hours 30 minutes, and 0.25 of an hour is 15 minutes.

Children also convert between miles and kilometres. The usual approximation is that 5 miles is about 8 kilometres, so 30 miles is about 48 km (30 ÷ 5 = 6, and 6 × 8 = 48). This is a proportional relationship, which is why schools may link it to a graph that is a straight line through zero. Children learn to check that an answer is sensible: kilometres are shorter than miles, so there should be more of them. Some schools also introduce speed in miles per hour.

Area is the amount of surface a shape covers, and perimeter is the distance round its edge. Children recognise that shapes with the same area can have different perimeters, and the other way round: rectangles of 12 cm² can be 3 cm by 4 cm (perimeter 14 cm), 2 cm by 6 cm (16 cm) or 1 cm by 12 cm (26 cm). They also learn when a formula helps. For a rectangle, area = length × width. A parallelogram has area = base × perpendicular height, because a triangle cut from one end can be moved to the other to make a rectangle. Two identical triangles fit together to make a parallelogram, so a triangle’s area is half that: area = base × perpendicular height ÷ 2.

Volume is the space inside a three-dimensional shape. It is counted in cubes: one centimetre cube is 1 cm³. For a cuboid, volume = length × width × height, so a box 5 cm by 3 cm by 2 cm holds 30 cm³. Children compare and estimate volumes, and meet other units such as cubic metres (m³), and may hear about mm³ and km³ for very small and very large volumes. A useful link: 1 cm³ holds exactly 1 ml of liquid.

Words your child will hear

Perpendicular height
The height measured at a right angle to the base, not along a slanted side.
Parallelogram
A four-sided shape with two pairs of parallel sides, like a pushed-over rectangle.
Formula
A rule written in words or letters, such as volume = length × width × height.
Cubic centimetre (cm³)
The volume of a cube with sides of 1 cm; a standard unit of volume.
Convert
Change a measurement from one unit to another, such as metres to kilometres.
Metric units
Units based on 10, 100 and 1,000, such as millimetres, centimetres, metres and kilometres.
Imperial units
Older units still used in daily life in the UK, such as miles, pints and stones.

What the National Curriculum says

In Year 6, pupils should be taught to:

  • Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
  • Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places
  • Convert between miles and kilometres
  • Recognise that shapes with the same areas can have different perimeters and vice versa
  • Recognise when it is possible to use formulae for area and volume of shapes
  • Calculate the area of parallelograms and triangles
  • Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A parallelogram has a base of 9 cm, a slanted side of 6 cm and a perpendicular height of 5 cm. What is its area? What is the area of a triangle with the same base and the same perpendicular height?

  1. Choose the right measurements. The area of a parallelogram uses the base and the perpendicular height. The slanted side of 6 cm is a distractor: it isn’t needed.
  2. Use the formula for a parallelogram: area = base × perpendicular height. Estimate first: 9 is close to 10 and 10 × 5 = 50, so the answer should be a bit less than 50.
    9 × 5 = 45
  3. Write the units. The area is measured in squares, so the answer is 45 cm².
  4. A triangle with the same base and height is half of a parallelogram, so halve the answer: 45 ÷ 2 = 22.5 cm². Equivalently, 9 × 5 ÷ 2.
    45 ÷ 2 = 22.5
  5. Check: the triangle must be smaller than the parallelogram, and 22.5 cm² is half of 45 cm².

The parallelogram has an area of 45 cm² and the triangle has an area of 22.5 cm².

Common mistakes and how to help

Converting in the wrong direction

A child sees “change metres to kilometres” and multiplies by 1,000, getting 4,500 km for 4.5 m or a large number where a small one is expected.

What helps: Ask whether the new number should be bigger or smaller. There are fewer kilometres than metres, so divide. A rough picture of the size of each unit does most of the work.

Treating hours as if they were decimal: 2.5 hours = 2 hours 50 minutes

Everything else in metric is based on 10, so the .5 is read as 50 minutes.

What helps: Remind them that 1 hour is 60 minutes. A half is 30 minutes, a quarter is 15 minutes. So 2.5 hours is 2 hours 30 minutes. Use a clock face to see it.

Using the slanted side instead of the perpendicular height

The slanted side is drawn and labelled on the diagram, and it looks like a height. 9 × 6 = 54 gives a wrong answer for the parallelogram.

What helps: Draw the height as a dotted line at a right angle to the base. If a parallelogram were cut and moved into a rectangle, the rectangle’s width is that perpendicular height. Trace it on squared paper.

Believing that shapes with the same perimeter must have the same area

Perimeter and area both sound like “how big is it”, so the child assumes they go together.

What helps: Tie a 16 cm loop of string and stretch it into different rectangles on squared paper, then count the squares inside each. A 4 cm by 4 cm square and a 2 cm by 6 cm rectangle both have a perimeter of 16 cm, but areas of 16 cm² and 12 cm².

How to help at home

  • Convert what you see on labels. Food packaging shows grams, kilograms, millilitres and litres. Ask “How many 250 g packets make 1 kg?” or “What is 750 ml in litres?” Talk through whether to multiply or divide before calculating.
  • Miles and kilometres on journeys. Use road signs and maps. If a sign says 20 miles, roughly how many kilometres is that (about 32)? Use the rule that 5 miles is about 8 km, and keep it as an estimate, not an exact figure.
  • Cut and rearrange. Draw a parallelogram on paper, cut a triangle from one end and slide it to the other to make a rectangle. Your child sees why base × height works. Cut a rectangle along its diagonal to see two matching triangles.
  • Pack boxes. Fill a small box with sugar cubes or building bricks, counting the layers. Compare the count with length × width × height. Ask which of two boxes holds more.
  • Same area, different perimeter. Take 12 sticky notes or small squares and arrange them into different rectangles. Measure the distance around each. Your child will quickly see that the perimeter changes while the area stays the same.

Related topics

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Everything in Year 6 maths

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