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SATs practice · Year 6Chapter 8 · Measures and conversions
Year 6 · Chapter 8

Measures and conversions

By the end of this chapter you will be able to

  • Convert between metric units of length, mass and capacity
  • Convert between units of time, including hours with decimals
  • Use an approximate conversion between miles and kilometres, or inches and centimetres
  • Find the perimeter of a shape made of rectangles
  • Find and compare areas of rectangles and squares, and estimate capacity

You should already know

  • Multiplying and dividing by 10, 100 and 1000 (Chapter 2 of this book)
  • Area and perimeter of rectangles (Year 4 and 5 maths)

Where this leads

  • Ratio and proportion, including scale factors (Chapter 5 of this book)

KS2 SATs practice for arithmetic (Year 6). Original questions in the style of the national tests. Content: Convert between metric units of length, mass, capacity and time, including decimals up to three decimal places (Year 5-6), Convert between miles and kilometres, and use approximate equivalences between metric and common imperial units (Year 5-6), Solve problems involving the calculation and conversion of units of measure (Year 6), Calculate and compare the perimeter of composite rectilinear shapes (Year 5), Calculate and compare the area of rectangles and squares using standard units (Year 5), Solve problems involving converting between units of time (Year 5-6), Estimate volume and capacity (Year 5).

Exercise P  Do you remember?

Non-calculator
1
FHow many centimetres are in 1 metre?
2
FHow many grams are in 1 kilogram?
3
FHow many minutes are in 2 hours?
4
FWork out the area of a rectangle 4 cm long and 5 cm wide.
5
FHow many millilitres are in 1 litre?
8.1

Metric length and mass conversions

Year 6
Convert between metric units of length and mass, including decimals up to three decimal places (Year 5-6)
Video lesson: Metric length and mass conversionsComing soon
Practice material. Non-calculator practice. This book is practice in the style of the Year 6 arithmetic test. It is not the official test, and no official test item is used. Do every question without a calculator. Marks and timings are a practice guide only.
Story. A builder measures a wall as 3.245 m long. The plan asks for the length in millimetres, and the supplier asks for the mass of the sand in kilograms.

Rule

Length: 1 km = 1000 m, 1 m = 100 cm, 1 m = 1000 mm, 1 cm = 10 mm.

Mass: 1 kg = 1000 g.

To change to a smaller unit, multiply. To change to a bigger unit, divide. Move the decimal point the same number of places as the zeros.

Key ideas

  • Smaller unit: multiply. Bigger unit: divide.
  • 3.245 m = 3,245 mm, because there are 1000 mm in 1 m.
  • Check the direction: a bigger unit gives a smaller number.
Worked example 8.1.1
Convert 3.245 m to millimetres.

Method. Multiply by 1000, because a millimetre is smaller than a metre.

  1. Write the conversion fact. 1 m is 1000 mm.
    1 m = 1000 mm
  2. Multiply to change to the smaller unit. Each m has 1000 mm, so multiply.
    3.245 × 1000 = 3245
  3. Write the answer.
    3245 mm

Check. 3,245 ÷ 1000 = 3.245 m. ✓

Watch out. Moving the point three places to the right gives 3,245, not 3.245.

Worked example 8.1.2
Convert 4,500 g to kilograms.

Method. Divide by 1000, because a kilogram is bigger than a gram.

  1. Write the conversion fact. 1000 g is 1 kg.
    1000 g = 1 kg
  2. Divide to change to the bigger unit. Each kg is 1000 g, so divide.
    4500 ÷ 1000 = 4.5
  3. Write the answer.
    4.5 kg

Check. 4.5 × 1000 = 4,500. ✓

Worked example 8.1.3
Convert 2.5 km to metres.

Method. Multiply by 1000, because a metre is smaller than a kilometre.

  1. Write the conversion fact. 1 km is 1000 m.
    1 km = 1000 m
  2. Multiply to change to the smaller unit. Each km has 1000 m, so multiply.
    2.5 × 1000 = 2500
  3. Write the answer.
    2500 m

Check. 2,500 ÷ 1000 = 2.5 km. ✓

Exercise 8A  Practice: metric length and mass

Non-calculator
1
FConvert 3.4 m to cm.
2
FConvert 2.75 m to mm.
3
FConvert 5600 m to km.
4
FConvert 780 mm to cm.
5
FConvert 0.046 kg to g.
6
FConvert 3250 g to kg.
7
FConvert 1.205 kg to g.
8
FConvert 6040 mm to m.
9
FConvert 0.5 km to m.
10
FConvert 12300 cm to m.
11
PSA rope 3.5 m long is cut into 7 equal pieces. How long is each piece, in centimetres?
12
PSSam buys 2.5 kg of flour and 750 g of sugar. What is the total mass in grams?
13
RAli says 2.5 km = 250 m. Is he right? Explain.
8.2

Capacity and time conversions

Year 6
Convert between metric units of capacity and time, including decimals up to three decimal places (Year 5-6), Solve problems involving converting between units of time (Year 5-6)
Video lesson: Capacity and time conversionsComing soon
Story. A recipe needs 1.5 litres of milk, and the bottle holds 2 litres. The class plans a film that starts at 14:20 and lasts 1 hour 50 minutes.

Rule

Capacity: 1 litre = 1000 ml. Time: 1 hour = 60 minutes, and 1 minute = 60 seconds.

A decimal hour is worked out as minutes: 2.5 hours = 2 hours and 0.5 × 60 = 30 minutes, so 2 h 30 min = 150 minutes.

Key ideas

  • 1 litre = 1000 ml; 2.75 litres = 2750 ml.
  • 1 hour = 60 minutes; 0.5 hours = 30 minutes.
  • Add times in hours and minutes, carrying 60 minutes into an hour.
Worked example 8.2.1
Convert 2.75 litres to millilitres.

Method. Multiply by 1000.

  1. Write the conversion fact. 1 litres is 1000 ml.
    1 litres = 1000 ml
  2. Multiply to change to the smaller unit. Each litres has 1000 ml, so multiply.
    2.75 × 1000 = 2750
  3. Write the answer.
    2750 ml

Check. 2,750 ÷ 1000 = 2.75 litres. ✓

Worked example 8.2.2
Convert 3.5 hours to minutes.

Method. Multiply by 60, because each hour has 60 minutes.

  1. Find the minutes in 3 hours. 3 × 60 = 180.
    180 minutes
  2. Find the minutes in 0.5 hours. 0.5 × 60 = 30.
    30 minutes
  3. Add. 180 + 30 = 210.
    210 minutes
  4. Write the answer.
    210 minutes

Check. 210 ÷ 60 = 3.5 hours. ✓

Worked example 8.2.3
A film starts at 14:20 and lasts 1 hour 50 minutes. What time does it finish?

Method. Add the hour, then the minutes, carrying past 60.

  1. Add the hour. 14:20 + 1 hour = 15:20.
    15:20
  2. Add the minutes. 15:20 + 50 minutes = 16:10, since 20 + 50 = 70 and 70 - 60 = 10.
    16:10
  3. Write the answer.
    16:10

Check. 1 h 50 min is 110 minutes. ✓

Exercise 8B  Practice: capacity and time

Non-calculator
1
FConvert 0.6 litres to millilitres.
2
FConvert 2.05 litres to millilitres.
3
FConvert 4,250 ml to litres.
4
FConvert 750 ml to litres.
5
FConvert 2.5 hours to minutes.
6
FConvert 3 hours 45 minutes to minutes.
7
FConvert 300 seconds to minutes.
8
FConvert 4 minutes 30 seconds to seconds.
9
PSA bus leaves at 09:45 and the journey takes 2 hours 35 minutes. What time does it arrive?
10
PSA bottle holds 1.25 litres. Five bottles are filled. How many litres are there in total?
11
PSA school day starts at 08:50 and finishes at 15:20. How long is the day in hours and minutes?
12
PSA jug holds 2 litres. A glass holds 250 ml. How many glasses can be filled from the jug?
13
RSam says 2 hours 30 minutes is 2.3 hours. Is he right? Explain.
8.3

Miles, kilometres and imperial approximations

Year 6
Convert between miles and kilometres, and use approximate equivalences between metric and common imperial units (Year 5-6)
Video lesson: Miles, kilometres and imperial approximationsComing soon
Story. A road sign says 40 km. Ruby has a map with distances in miles, so she converts the sign using a rough equivalence.

Rule

These are approximate equivalences, so use the word "about" when you give an answer:

8 km is about 5 miles. 1 inch is about 2.5 cm. 2 pounds is about 1 kilogram. 2 pints is about 1 litre.

To change km to miles, divide by 8 and multiply by 5. To change miles to km, divide by 5 and multiply by 8.

Key ideas

  • 8 km is about 5 miles.
  • Divide by 8 then multiply by 5 to change km to miles.
  • Give imperial conversions as "about", because they are rough.
Worked example 8.3.1
40 km is about how many miles?

Method. Divide by 8, then multiply by 5.

  1. Divide by 8. 40 ÷ 8 = 5 lots of 8 km.
    5
  2. Multiply by 5. Each 8 km is about 5 miles, so 5 × 5 = 25.
    25 miles
  3. Write the answer.
    about 25 miles

Check. 40 km is about 25 miles, because 8 km is about 5 miles. ✓

Worked example 8.3.2
10 inches is about how many centimetres?

Method. Multiply by 2.5, because 1 inch is about 2.5 cm.

  1. Use the fact. 1 inch is about 2.5 cm.
    2.5 cm
  2. Multiply. 10 × 2.5 = 25.
    25 cm
  3. Write the answer.
    about 25 cm

Check. 25 cm ÷ 2.5 = 10 inches. ✓

Worked example 8.3.3
6 kilograms is about how many pounds?

Method. Use 2 pounds is about 1 kilogram, so multiply by 2.

  1. Use the fact. 1 kg is about 2 pounds.
    2 pounds
  2. Multiply. 6 × 2 = 12.
    12 pounds
  3. Write the answer.
    about 12 pounds

Check. 12 pounds ÷ 2 = 6 kg. ✓

Exercise 8C  Practice: miles, kilometres and approximate equivalences

Non-calculator
1
FAbout how many miles is 24 km?
2
FAbout how many miles is 64 km?
3
FAbout how many miles is 80 km?
4
FAbout how many miles is 16 km?
5
FAbout how many miles is 56 km?
6
FAbout how many km is 15 miles?
7
FAbout how many km is 25 miles?
8
FAbout how many km is 50 miles?
9
FAbout how many centimetres is 4 inches?
10
FAbout how many pounds is 5 kg?
11
FAbout how many pints is 3 litres?
12
FAbout how many litres is 10 pints?
13
PSRuby runs 15 miles in a week. About how many kilometres is that?
14
PSA cupboard is 20 cm high. About how many inches is that?
15
RExplain why 5 miles is about 8 km, but 5 km is not about 8 miles.
8.4

Perimeter of composite rectilinear shapes

Year 6
Calculate and compare the perimeter of composite rectilinear shapes (Year 5)
Video lesson: Perimeter of composite rectilinear shapesComing soon
Story. A classroom floor is shaped like the letter L. The teacher wants to put a skirting board along every wall, so she needs the total length of the walls, which is the perimeter.

Rule

A composite shape is made of rectangles. Its perimeter is the total length of all its outside edges.

For an L-shape, the missing sides are found by subtracting. Check the total: an L-shape cut from a rectangle has the same perimeter as the rectangle around it.

Key ideas

  • The perimeter is the distance all the way around the outside.
  • Find any missing lengths by subtracting from a known length.
  • An L-shape has the same perimeter as the rectangle around it.
Worked example 8.4.1
An L-shape is made from a 10 cm by 8 cm rectangle with a 4 cm by 3 cm corner removed. What is its perimeter?

Method. Find each missing side, then add all six sides.

  1. Find the missing lengths. The notch is 4 cm by 3 cm, so the sides are 5 cm, 6 cm and so on.
    8 - 3 = 5, 10 - 4 = 6
  2. List the six sides. An L-shape has six straight sides.
    10 cm, 5 cm, 4 cm, 3 cm, 6 cm, 8 cm
  3. Add the sides. Add every side to get the perimeter.
    10 + 5 + 4 + 3 + 6 + 8 = 36
  4. Write the answer.
    36 cm

Check. 2 × (10 + 8) = 36 cm. ✓

Watch out. Do not forget the missing sides; there are six sides, not four.

Worked example 8.4.2
An L-shape is made from a 12 m by 9 m rectangle with a 5 m by 4 m corner removed. What is its perimeter?

Method. Use the same method: find the missing sides, then add.

  1. Find the missing lengths. The notch is 5 cm by 4 cm, so the sides are 5 cm, 7 cm and so on.
    9 - 4 = 5, 12 - 5 = 7
  2. List the six sides. An L-shape has six straight sides.
    12 cm, 5 cm, 5 cm, 4 cm, 7 cm, 9 cm
  3. Add the sides. Add every side to get the perimeter.
    12 + 5 + 5 + 4 + 7 + 9 = 42
  4. Write the answer.
    42 m

Check. 2 × (12 + 9) = 42 m. ✓

Worked example 8.4.3
A 9 m by 5 m rectangle has a 2 m square cut from one corner. What is the perimeter of the shape left?

Method. Find the missing sides, then add all six.

  1. Find the missing lengths. The notch is 2 cm by 2 cm, so the sides are 3 cm, 7 cm and so on.
    5 - 2 = 3, 9 - 2 = 7
  2. List the six sides. An L-shape has six straight sides.
    9 cm, 3 cm, 2 cm, 2 cm, 7 cm, 5 cm
  3. Add the sides. Add every side to get the perimeter.
    9 + 3 + 2 + 2 + 7 + 5 = 28
  4. Write the answer.
    28 m

Check. 2 × (9 + 5) = 28 m. ✓

Exercise 8D  Practice: perimeter of composite shapes

Non-calculator
1
FAn L-shape is made from a 12 cm by 9 cm rectangle with a 5 cm by 4 cm corner removed. Find its perimeter.
2
FAn L-shape is made from a 14 cm by 10 cm rectangle with a 6 cm by 5 cm corner removed. Find its perimeter.
3
FAn L-shape is made from a 9 cm by 7 cm rectangle with a 3 cm by 2 cm corner removed. Find its perimeter.
4
FAn L-shape is made from a 15 cm by 11 cm rectangle with a 7 cm by 6 cm corner removed. Find its perimeter.
5
FAn L-shape is made from a 8 cm by 6 cm rectangle with a 3 cm by 2 cm corner removed. Find its perimeter.
6
FAn L-shape is made from a 16 cm by 12 cm rectangle with a 10 cm by 8 cm corner removed. Find its perimeter.
7
PSA garden is an L-shape made from a 10 m by 6 m rectangle with a 4 m by 2 m corner missing. How much fence is needed round the outside?
8
RAli says the L-shape from a 7 cm by 5 cm rectangle with a 3 cm by 2 cm corner removed has perimeter 22 cm. Is he right? Write the correct perimeter.
9
RA 6 cm by 4 cm rectangle is compared with an L-shape made by cutting a 2 cm by 2 cm corner from it. Do they have the same perimeter? Write Yes or No.
10
RExplain why cutting a corner out of a rectangle does not change the perimeter.
8.5

Area of rectangles and squares, and estimating capacity

Year 6
Calculate and compare the area of rectangles and squares using standard units (Year 5), Estimate volume and capacity (Year 5)
Video lesson: Area of rectangles and squares, and estimating capacityComing soon
Story. A room is 7 m long and 4 m wide. The carpet is sold by the square metre, so the room needs an area calculation. The class also estimates how many glasses a jug holds.

Rule

The area of a rectangle is length × width, and it is measured in square units, such as cm² or m².

A square has all four sides equal, so its area is side × side.

Key ideas

  • Area of a rectangle = length × width.
  • Area of a square = side × side.
  • Compare areas by working them out, not by comparing the sides.
Worked example 8.5.1
Find the area of a rectangle 7 m long and 4 m wide.

Method. Multiply length by width.

  1. Write the formula. Area of a rectangle is length × width.
    A = l × w
  2. Multiply. Multiply 7 m by 4 m.
    7 × 4 = 28
  3. Write the answer.
    28 m²

Check. 28 ÷ 4 = 7. ✓

Watch out. Area is in square metres, m², not metres.

Worked example 8.5.2
Find the area of a square with sides of 9 cm.

Method. Multiply the side by itself.

  1. Write the formula. Area of a square = side × side.
    A = 9 × 9
  2. Multiply. 9 × 9 = 81.
    81
  3. Write the units. Area is in square centimetres.
    81 cm²
  4. Write the answer.
    81 cm²

Check. 81 = 9 × 9. ✓

Worked example 8.5.3
Which has the bigger area: a rectangle 6 m by 5 m, or a square with sides of 6 m?

Method. Work out both areas, then compare.

  1. Rectangle. 6 × 5 = 30 m².
    30 m²
  2. Square. 6 × 6 = 36 m².
    36 m²
  3. Compare. 36 is bigger than 30.
    the square
  4. Write the answer.
    the square

Check. 36 > 30, so the square is bigger. ✓

Exercise 8E  Practice: area and capacity

Non-calculator
1
FFind the area of a rectangle 12 cm by 5 cm.
2
FFind the area of a rectangle 8 cm by 9 cm.
3
FFind the area of a rectangle 14 cm by 3 cm.
4
FFind the area of a rectangle 11 cm by 4 cm.
5
FFind the area of a rectangle 20 cm by 6 cm.
6
FFind the area of a square with sides of 7 cm.
7
PSA room is 5 m long and 4 m wide. What is its area?
8
PSA rectangle is 2 m long and 50 cm wide. What is its area, in m²?
9
PSA bottle holds 1.5 litres. How many 250 ml glasses can be filled from it?
10
PSA jug holds about 1 litre. Estimate how many 250 ml glasses it takes to fill it.
11
RA rectangle is 9 cm by 4 cm, and a square has sides of 6 cm. Are the two areas equal? Write the area of the rectangle.
12
RAli says a 4 cm by 8 cm rectangle has the same area as a 4 cm by 4 cm square because both have a side of 4. Is he right? Explain.
13
REstimate the capacity of a bucket that holds about 10 litres, in ml, and say how many 500 ml bottles fill it.

Chapter summary

SkillMethod
Metric length1 m = 100 cm = 1000 mm; 1 km = 1000 m. Smaller unit: multiply.
Mass and capacity1 kg = 1000 g; 1 litre = 1000 ml.
Time1 hour = 60 minutes; 1 minute = 60 seconds; 2.5 hours = 150 minutes.
Miles and kilometresAbout 8 km = 5 miles: divide by 8, multiply by 5.
Imperial rough guideAbout 1 inch = 2.5 cm, 2 pounds = 1 kg, 2 pints = 1 litre (approximate).
Perimeter of L-shapeFind the missing sides, then add all six sides.
AreaRectangle: length × width. Square: side × side. Give square units.

Can you…?

  • I can convert between metric units of length, mass and capacity, including decimals
  • I can convert hours and minutes, and find an end time
  • I can use an approximate conversion between miles and kilometres
  • I can find the perimeter of an L-shaped composite shape
  • I can work out and compare areas of rectangles and squares
  • I can estimate a capacity and say so with the word about

Key terms

composite shape
a shape made from two or more rectangles
perimeter
the total length of the outside edges of a shape
area
the amount of flat surface inside a shape, in square units
capacity
the amount a container can hold, usually in litres or millilitres
approximate
close to the real value, but not exact

Exercise 8Z  Check-up

Non-calculator
1
Convert 6.25 m to centimetres.
2
Convert 8,300 g to kilograms.
3
Convert 4.5 litres to millilitres.
4
Convert 2.25 hours to minutes.
5
A train leaves at 16:40 and the journey takes 2 hours 35 minutes. What time does it arrive?
6
About how many miles is 56 km?
7
About how many centimetres is 12 inches?
8
An L-shape is made from an 11 cm by 7 cm rectangle with a 4 cm by 3 cm corner removed. Find its perimeter.
9
Find the area of a rectangle 13 m by 4 m.
10
Explain why a 50 cm long rope is half a metre, and how you would change 0.5 m to centimetres.

Total 20 marks. Allow about 20 minutes.

Exercise 8X  Practice test questions

Non-calculator
1
FConvert 7.5 km to metres.[1 mark]
2
FConvert 3,600 seconds to minutes.[2 marks]
3
FConvert 1.75 kg to grams.[1 mark]
4
PSA bottle holds 750 ml. How many bottles are needed to fill a 3-litre container?[2 marks]
5
FAbout how many kilometres is 30 miles?[2 marks]
6
PSAn L-shape is made from an 8 cm by 5 cm rectangle with a 2 cm by 2 cm corner removed. Find its perimeter.[3 marks]
7
FFind the area of a square with sides of 12 cm.[1 mark]
8
FA rectangle is 6 m long and 3 m wide. What is its area?[2 marks]
9
RA school hall holds about 2 litres of water for each child. Estimate how many litres 25 children need, and say how many 500 ml bottles that is.[3 marks]
10
RAli says the perimeter of a 5 cm by 4 cm rectangle is 20 cm, and the perimeter of a square with sides 5 cm is 20 cm. Is he right? Explain.[3 marks]
← Chapter 7: Mental arithmeticChapter 9: Practice papers: arithmetic →

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