Measures

• Mathematics
• Upper Secondary (Key Stage 4)
• GCSE

FS Maths

Measure conversions 

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Bill is a builder. On Monday he made mortar mix. He used 24 kg of sand and 5 kg of cement. On Tuesday Bill will make the same type of mortar mix. He will use 36 kg of sand.

How much cement does he need to make the same type of mortar mix?

Sand : Cement

24 : 5

1 : 0.208

36 : 7.5

Sand : Cement

24 : 5

12 : 2.5

36 : 7.5

Lesson Aim

Today you will learn how to convert between metric measures.

  

You will also learn how to convert between metric and imperial measures using conversion factors & graphs.

Lesson objectives

1. Convert between units of length, weight and capacity in metric systems.
2. Convert between metric measures & imperial measures using conversion factors.
3. Convert between measures using conversion graphs.

When do we see or use measurements?

What units do we use in the metric system for…

Capacity

Weight

Length

cm

mm

m

km

mg

g

kg

cl

L

ml

Length

Length

1 centimetre (cm) 

= 10 millimetres (mm)

1 metre (m) 

= 100 centimetres (cm)

1 kilometre (km) 

 = 1,000 metres (m)

Length

Weight

1 gram (g) 

= 1,000 milligrams (mg)

1 tonne (t) 

= 1,000 kilograms (kg)

1 kilogram (kg) 

= 1,000 grams (g)

Length

Capacity

1 centilitre (cl) 

= 10 millilitres (ml)

1 litre (L) 

= 1,000 millilitres (ml)

1 litre (L) 

= 100 centilitres (cl)

Convert 350 cm into m

1. 35 m
2. 3500 m
3. 3.5 m
4. 0.35 m

Convert 4.4 cm into mm

1. 440 mm
2. 0.44 mm
3. 0.044 mm
4. 44 mm

Convert 2000 g into kg

1. 20,000 kg
2. 2 kg
3. 200 kg
4. 20 kg

Convert 9.09 kg into g

1. 90,090 g
2. 90.9 g
3. 9,090 g
4. 909 g

Convert 2350 ml into litres

1. 235 l
2. 2.35 l
3. 23500 l
4. 23.5 l

Convert 75 cl into ml

1. 750 ml
2. 7500 ml
3. 7.5 ml
4. 7,500 ml

Write down any imperial measurement units for length, weight & capacity?

Imperial units of length

•  Inch
•  Foot/feet
•  Yard
•  Mile

Conversions:

• 1 inch = 2.54 cm
• 1 mile = 1.6 km
  

The distance between 2 drink stations along a marathon route is 5 miles.

1 kilometre (km) = 0.6214 mile

What is the distance in kilometres to two decimal places?

• 5 ÷ 0.6214
  
• = 8.0463469
  
• = 8.05 km

A swimmer has been using a pool with a 50-yard length.

 

How many lengths would the swimmer need to do in the 25 m length pool to equal 10 lengths in the 50-yard pool?

1 yard = 0.9144 metres

• 50 x 0.91444 = 45.722 m
• 45.722 x 10 = 457.22 m
• 457.22 ÷ 25 = 18.2888
• = 19 lengths

• 10 lengths x 50 = 500 yards
• 500 x 0.91444 = 457.22 m
• 457.22 ÷ 25 = 18.2888
• = 19 lengths

Imperial units of weight

•  Ounce (oz)
  
•  Pound (lb)
  
•  Stone

Conversions:

• 1 oz = 25 g
• 1 kg = 2.2 lbs

Isabella weighs 51 kg.

What is this weight to the nearest stone?

Use the conversion 1 kg = 2.2 pounds and 1 stone = 14 pounds.

• 51 x 2.2 = 112.2 pounds
  
• 112.2 ÷ 14 = 8.014
  
• = 8 stone
  

Children under 4 years old must be seated in a child seat or a trailer. Cycle hire centres need to know the ages and weights of children under 4 years old.

One of the children is 3 ½ years old and weighs 3 stone.

The other is 18 months and weighs 25 pounds.

1 stone = 14 pounds

1 kilogram = 2.2 pounds

What is the weight of each child in kilograms? Round your answers to 2 decimal places.

• Child 1 = 3 stones
• 3 stones x 14 pounds
•  = 42 pounds
• 42 ÷ 2.2 pounds
• = 19.09 kg

• Child 2 = 25 pounds
• 25 ÷ 2.2 pounds
• = 11.36 kg

Imperial units of Capacity

•  Pint
•  Gallon

Conversions:

• 1 gallon = 4.5 L
  
• 1 litre = 1      pints
  

​4​​3​​

A water tank holds 500 litres of water.

Use the conversion 10 litres = 2.2 gallons to find its capacity in gallons.

• Method 1:
  
• 500 ÷ 10
  
• = 50
  
• 50 x 2.2
  
• = 110 gallons

• Method 2:
  
• 2.2 ÷ 10
  
• = 0.22 (1 litre)
  
• 500 x 0.22
  
• = 110 gallons

When Amy is running, she needs to drink 70 fluid ounces of water.

How many litres is this?

Use the conversion 1 pint = 20 fluid ounces and 1 litre = 1     pints

​4​​3​​

• 70 ÷ 20 = 3.5 pints
  
• 3.5 ÷ 1.75 = 2
  
• = 2 litres

Converting currency

 £1 = €1.18

1) A couple changed £200 into Euros to go on holiday. How much in Euros did they receive?

2) They returned with 54 Euros and exchanged these into pounds. How much in pounds did they receive?

• £200 × 1.18
•  = 236 Euros

• 54 Euros ÷ 1.18
  
• = £45.76
  
• 
  

Conversion graphs 

Use the conversion graph to convert:

  

(a) 70 kg to pounds

(b) 120 pounds to kg

Activity

Complete the measures worksheet.

Review lesson objectives

1. Convert between units of length, weight and capacity in metric systems.
2. Convert between metric measures & imperial measures using conversion factors.
3. Convert between measures using conversion graphs.

Self-study

Complete the following on BKSB:

• Measures – Length, weight & capacity.
  
• Measures – Compound measures.
  

Learning module, skills check & progression check to be completed for each module.

Video links

Metric Units for Length Video – Corbettmaths

Metric Units for Mass Video – Corbettmaths

Metric Units for Capacity Video – Corbettmaths

Metric and Imperial Units Video – Corbettmaths

Imperial Units – Mass Video – Corbettmaths

Metric to Imperial Length Video – Corbettmaths

Metric to Imperial Mass Video – Corbettmaths

Metric to Imperial Capacity Video – Corbettmaths

Converting Imperial Length Video – Corbettmaths

Converting Imperial Capacity Video – Corbettmaths