Year 6: Measures, area, volume and time
Part of the Year 6 sats maths revision chapter. Chapter overview · whole chapter on one page
Measures, area, volume and time
In the SATs you must change between units. Think about the size of each unit: there are 1,000 metres in a kilometre, 1,000 grams in a kilogram and 1,000 millilitres in a litre. A bigger unit needs a smaller number.
The area of a rectangle is length times width. A parallelogram has the same area as a rectangle with the same base and perpendicular height. A triangle is half of a rectangle with the same base and height. The volume of a cuboid is length × width × height.
Times are on a 24-hour clock. There are 60 minutes in an hour, so carry the minutes when they reach 60.
Key ideas
- Convert with the number of smaller units in one bigger unit: 1 km = 1,000 m, 1 kg = 1,000 g, 1 litre = 1,000 ml.
- Area is in square units (cm²). Volume is in cubic units (cm³).
- Half of a rectangle is a triangle. Area of a triangle = base × height ÷ 2.
- Add the minutes, and carry 60 minutes into an hour.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the length, width and height together.
- Write the formula. The volume of a cuboid is length times width times height.volume = length × width × height
- Multiply the first two numbers. Find the area of the base first.8 × 3 = 24
- Multiply by the height. Each layer has this many cubes, and there are this many layers.24 × 2 = 48
Check. Count the layers: there are 2 layers of 24 cubes, which is 48. ✓
Watch out. The answer is in cubic units, such as cm³, not in square units.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the base by the height, then halve the answer.
- Write the formula. A triangle is half of a rectangle with the same base and height.area = (base × height) ÷ 2
- Multiply the base by the height. This gives the area of the rectangle.10 × 7 = 70
- Halve it. The triangle is half the rectangle.70 ÷ 2 = 35
Check. Two of these triangles make a rectangle 10 by 7, with area 70. ✓
Watch out. Halve at the end. Do not forget the division by 2.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Add the hours and the minutes separately, and carry any 60 minutes into an hour.
- Write the start time and the length of time. Use the start time, then add the time that passes.19:25 + 1 h 50 min
- Add the hours. Add the whole hours first.19 + 1 = 20 hours
- Add the minutes. If the minutes are 60 or more, take 60 away and add 1 more hour.25 + 50 = 75 minutes, which is 1 hour and 15 minutes
- Write the finishing time. Give the time on the 24-hour clock with two digits for the hours and minutes.21:15
Check. Count on: 1 hours and 50 minutes after 19:25 reaches 21:15. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not add the hours and minutes as one number.
Watch out
Common mistake: writing the area in cm instead of cm², or the volume in cm² instead of cm³. Also, a triangle is half of the rectangle, so do not forget the divide by 2.
Exercise 13E Timed set: measures, area, volume and time (about 12 minutes)
Non-calculatorKey words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Use the number of m in one km, and multiply by it.
- Write the fact about the units. There are 1000 m in 1 km.1 km = 1000 m
- Multiply by 1000. To change km into m, multiply by 1000.3.4 × 1000 = 3400
Check. 3400 ÷ 1000 = 3.4, so the conversion is right. ✓
Watch out. Check the size: changing to a smaller unit gives a bigger number, and changing to a bigger unit gives a smaller number.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Use the number of g in one kg, and divide by it.
- Write the fact about the units. There are 1000 g in 1 kg.1 kg = 1000 g
- Divide by 1000. To change g into kg, divide by 1000.2500 ÷ 1000 = 2.5
Check. 2.5 × 1000 = 2500, so the conversion is right. ✓
Watch out. Check the size: changing to a smaller unit gives a bigger number, and changing to a bigger unit gives a smaller number.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Use the number of ml in one l, and multiply by it.
- Write the fact about the units. There are 1000 ml in 1 l.1 l = 1000 ml
- Multiply by 1000. To change l into ml, multiply by 1000.1.8 × 1000 = 1800
Check. 1800 ÷ 1000 = 1.8, so the conversion is right. ✓
Watch out. Check the size: changing to a smaller unit gives a bigger number, and changing to a bigger unit gives a smaller number.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Add up every side length, going round the shape once.
- Write down every side. Go round the shape once, and write each side length.5 , 3 , 2 , 4 , 6 , 4
- Add the sides. The perimeter is the total of every side.5 + 3 + 2 + 4 + 6 + 4 = 24
Check. Add the sides in a different order: the total is still 24. ✓
Watch out. Count every side, including the short ones.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the base by the perpendicular height.
- Write the formula. The area of a parallelogram is the base times the perpendicular height.area = base × height
- Multiply the base by the height. Use the height that is at right angles to the base, not the slanted side.12 × 7 = 84
Check. A parallelogram with the same base and height has the same area as a rectangle 12 by 7. ✓
Watch out. Do not use the slanted side. Use the perpendicular height.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the base by the height, then halve the answer.
- Write the formula. A triangle is half of a rectangle with the same base and height.area = (base × height) ÷ 2
- Multiply the base by the height. This gives the area of the rectangle.9 × 6 = 54
- Halve it. The triangle is half the rectangle.54 ÷ 2 = 27
Check. Two of these triangles make a rectangle 9 by 6, with area 54. ✓
Watch out. Halve at the end. Do not forget the division by 2.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the length, width and height together.
- Write the formula. The volume of a cuboid is length times width times height.volume = length × width × height
- Multiply the first two numbers. Find the area of the base first.6 × 4 = 24
- Multiply by the height. Each layer has this many cubes, and there are this many layers.24 × 5 = 120
Check. Count the layers: there are 5 layers of 24 cubes, which is 120. ✓
Watch out. The answer is in cubic units, such as cm³, not in square units.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the length, width and height together.
- Write the formula. The volume of a cuboid is length times width times height.volume = length × width × height
- Multiply the first two numbers. Find the area of the base first.5 × 3 = 15
- Multiply by the height. Each layer has this many cubes, and there are this many layers.15 × 2 = 30
Check. Count the layers: there are 2 layers of 15 cubes, which is 30. ✓
Watch out. The answer is in cubic units, such as cm³, not in square units.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Add the hours and the minutes separately, and carry any 60 minutes into an hour.
- Write the start time and the length of time. Use the start time, then add the time that passes.08:45 + 3 h 30 min
- Add the hours. Add the whole hours first.8 + 3 = 11 hours
- Add the minutes. If the minutes are 60 or more, take 60 away and add 1 more hour.45 + 30 = 75 minutes, which is 1 hour and 15 minutes
- Write the finishing time. Give the time on the 24-hour clock with two digits for the hours and minutes.12:15
Check. Count on: 3 hours and 30 minutes after 08:45 reaches 12:15. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not add the hours and minutes as one number.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the hours by 60, then add the extra minutes.
- Change the hours to minutes. There are 60 minutes in 1 hour.2 × 60 = 120 minutes
- Add the extra minutes. Add the minutes that are left over.120 + 35 = 155
Check. 155 ÷ 60 = 2 remainder 35, which is 2 hours and 35 minutes. ✓
Watch out. Multiply the hours by 60 first, then add the minutes.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Multiply the number of miles by 1.6, because 1 mile is 1.6 kilometres.
- Write the rule. The question says 1 mile is 1.6 kilometres, so multiply the miles by 1.6.15 × 1.6
- Multiply. Multiply the miles by 1.6 to get kilometres.15 × 1.6 = 24
Check. 24 ÷ 1.6 = 15, so the conversion is right. ✓
Watch out. Multiply to change miles into kilometres. A kilometre is a shorter unit, so the number gets bigger.
Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.
Method. Work out the area and the perimeter of each shape, then compare them.
- Work out the area of each shape. Multiply the length by the width.rectangle: 4 × 9 = 36 cm²; square: 6 × 6 = 36 cm²
- Work out the perimeter of each shape. Add all four sides.rectangle: 4 + 9 + 4 + 9 = 26 cm; square: 6 + 6 + 6 + 6 = 24 cm
- Compare. The areas are the same, but the perimeters are different.26 cm is not 24 cm
Check. Both shapes have an area of 36 cm², but the perimeters are 26 cm and 24 cm. ✓
Watch out. Two shapes with the same area can have different perimeters. Always work out both.