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Primary Maths · Year 3Chapter 5 · Length, mass, capacity and perimeter
Year 3 · Chapter 5

Length, mass, capacity and perimeter

By the end of this chapter you will be able to

  • Measure a length with a ruler in mm, cm and m
  • Change between mm and cm, cm and m, g and kg, and ml and l, using whole numbers
  • Compare lengths, masses and capacities written in different units
  • Add and subtract lengths, masses and capacities after changing them to the same unit
  • Solve word problems that use measures
  • Measure the perimeter of a simple 2-D shape by adding its sides or counting squares
  • Find a missing side when the perimeter is known

You should already know

  • Choosing and using cm, m, g, kg, litres and ml (Year 2, Chapter 5)
  • Adding and subtracting numbers with up to 3 digits (Year 3, Chapter 2)
  • Place value and fractions (Year 3, Chapters 1 and 4)

Where this leads

  • Converting between units with decimals, such as 2.5 m and 1.5 kg (Year 4 and Year 5)
  • Perimeter of rectilinear shapes, and area (Year 4 and Year 5)

National Curriculum for England, Key Stage 2 mathematics, Year 3. Content: Measure, compare, add and subtract lengths (m, cm, mm), Measure, compare, add and subtract mass (kg, g), Measure, compare, add and subtract volume and capacity (l, ml), Measure the perimeter of simple 2-D shapes.

Exercise P  Do you remember?

Non-calculator
1
FWhich unit would you use to measure the length of a pencil: metres or centimetres?
2
FWhich unit is best to weigh a small apple: grams or kilograms?
3
FWhich unit is best for the water in a bath: millilitres or litres?
4
FWork out 47 + 35.
5
FWrite the number that is 100 more than 260.
5.1

Measuring length: mm, cm and m

Year 3
Measure, compare, add and subtract lengths (m, cm, mm)
Video lesson: Measuring length: mm, cm and mComing soon
Mei has a pencil, a ruler and a long piece of string. She wants to know how long each one is. She measures in three units: millimetres, centimetres and metres.

We measure length with a ruler. A ruler is marked in centimetres (cm). Each centimetre is split into ten small marks. Each small mark is one millimetre (mm).

To measure, put the zero mark at one end of the object. Then read the mark at the other end.

012345678910
The pencil starts at 0 and ends at 6, so it is 6 cm long.
UnitShort nameHow many make 1 metre?
millimetremm1000
centimetrecm100
metrem1

Use millimetres for very small lengths, like the width of a fingernail. Use centimetres for things like a pencil. Use metres for very long things, like a door or a room.

To change to a smaller unit, multiply. To change to a bigger unit, divide.

Key ideas

  • 1 cm = 10 mm.
  • 1 m = 100 cm.
  • 1 m = 1000 mm.
  • Use mm for very small lengths, cm for small things and m for long things.
  • Measure from the zero mark, or subtract the start mark from the end mark.
Worked example 5.1.1
How long is the crayon? Give your answer in cm.012345678910

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Subtract the start mark from the end mark. Read both marks in the same unit.

  1. Find the mark where the object starts. Read the number on the ruler where the object begins.
    start: 1 cm
  2. Find the mark where the object ends. Read the number on the ruler where the object stops.
    end: 8 cm
  3. Subtract the start from the end. The length is the distance between the two marks.
    8 − 1 = 7
  4. Write the answer. The question asks for the length in cm.
    7

Check. 1 + 7 = 8. ✓

Watch out. Do not read the end of the ruler. Read the mark where the object stops.

Worked example 5.1.2
Write 4 cm in mm.

Key words. To convert means to write the same amount in a different unit. The amount stays the same.

Method. A bigger unit is worth more small units, so we multiply by 10 to change cm into mm.

  1. Find how many small units make one big unit. 1 cm is the same as 10 mm.
    1 cm = 10 mm
  2. Multiply by the number of big units. We have 4 cm, so we have 4 groups of 10 mm.
    4 × 10 = 40
  3. Write the answer. The answer is in mm.
    40

Check. 40 ÷ 10 = 4, so the change is right. ✓

Watch out. Ask first: is the new unit bigger or smaller? A smaller unit needs more of them.

Worked example 5.1.3
Write 500 cm in m.

Key words. To convert means to write the same amount in a different unit. The amount stays the same.

Method. A smaller unit is worth less, so we divide by 100 to change cm into m.

  1. Find how many small units make one big unit. 1 m is the same as 100 cm.
    1 m = 100 cm
  2. Share the small units into groups. Each group of 100 cm makes one m.
    500 ÷ 100 = 5
  3. Write the answer. The answer is in m.
    5

Check. 5 × 100 = 500, so the change is right. ✓

Watch out. Ask first: is the new unit bigger or smaller? A smaller unit needs more of them.

Watch out

Watch out: 1 m is 100 cm, not 10 cm. Ten is the number of millimetres in one centimetre, not the number of centimetres in one metre.

Exam tip

Before you change units, ask: is the new unit bigger or smaller? A smaller unit needs more of them, so we multiply.

Exercise 5A  Measuring and changing units of length

Non-calculator
1
FHow long is the stick? Give your answer in cm.
012345678910
2
FHow long is the crayon? Give your answer in cm.
012345678910
3
FHow long is the leaf? Give your answer in mm.
012345678910
4
FWrite each length in mm.
(a)2 cm = how many mm?
(b)8 cm = how many mm?
(c)5 cm = how many mm?
5
FWrite 300 cm in m.
6
FWrite 6 m in cm.
7
FWrite 7 cm in mm.
8
FChoose the best unit for the height of a door: mm, cm or m? Write the unit.
9
FChoose the best unit for the width of a fingernail: mm, cm or m? Write the unit.
10
PSPriya's garden fence is 4 m long. How many centimetres long is the fence?
11
PSA bench is 200 cm long. Write its length in metres.
12
RSam says 1 metre is the same as 10 centimetres. Is he right? Explain.
5.2

Comparing lengths

Year 3
Measure, compare, add and subtract lengths (m, cm, mm)
Video lesson: Comparing lengthsComing soon
At sports day, Noah jumps 2 m, Leo jumps 180 cm and Zainab jumps 165 cm. Who jumps the furthest? To answer, we must first write every jump in the same unit.

To compare two lengths, change them to the same unit. Then the bigger number is the longer length.

Look at the units first. 2 m is 200 cm, which is more than 180 cm, even though 2 is a smaller number than 180.

We use the signs > (greater than) and < (less than). The open end of the sign faces the bigger length.

Noah200 cmLeo180 cmZainab165 cm
The jumps in cm: Noah 200 cm, Leo 180 cm and Zainab 165 cm.

Key ideas

  • Change lengths to the same unit before you compare them.
  • The smaller unit gives the bigger number: 2 m is the same as 200 cm.
  • > means greater than. < means less than.
  • To put lengths in order, write them all in one unit first.
Worked example 5.2.1
Write < or > to make it true: 2 m [ ] 150 cm

Key words. < means less than. > means greater than. The open end of the sign faces the bigger amount.

Method. Change both amounts to the same unit. Then compare the numbers.

  1. Change both amounts to the same unit. We use cm for both, because it is the smaller unit.
    2 m = 200 cm; 150 cm is already in cm
  2. Compare the two numbers. The bigger number is the bigger amount.
    200 > 150
  3. Write the sign. The open end of the sign faces the bigger amount.
    >

Check. In cm, the two amounts are 200 and 150. ✓

Watch out. Do not compare the numbers before you change the units. A small number in a big unit can be the bigger amount.

Worked example 5.2.2
Write these lengths in cm, shortest first: 2 m, 150 cm, 90 cm.

Key words. < means less than. > means greater than. The open end of the sign faces the bigger amount.

Method. Change every amount to cm, then put the numbers in order from smallest to largest.

  1. Change every amount to the same unit. We use cm for all of them.
    2 m = 200 cm; 150 cm is already in cm; 90 cm is already in cm
  2. Put the numbers in order. The smallest number is the shortest or the lightest amount.
    90 < 150 < 200
  3. Write the answer. Write each amount in cm, smallest first.
    90, 150, 200

Check. Each number is smaller than the one after it. ✓

Watch out. Change the units first. The number 2 looks smaller than 150, but 2 m is longer than 150 cm.

Worked example 5.2.3
Noah jumps 2 m. Leo jumps 180 cm. Who jumps further?

Key words. < means less than. > means greater than. The open end of the sign faces the bigger amount.

Method. Change everything to cm, then pick the bigger amount.

  1. Change every amount to the same unit. We use cm for all of them.
    2 m = 200 cm; 180 cm is already in cm
  2. Find the bigger amount. We want the bigger amount, so we look for the biggest number.
    200 cm is the bigger amount
  3. Write the answer. The answer is Noah.
    Noah

Check. The other amount is the other way round, so the answer is Noah. ✓

Watch out. Change to the same unit first. Otherwise the numbers can point the wrong way.

Watch out

Watch out: 2 is less than 150, but 2 m is longer than 150 cm. Always change to the same unit before you compare the numbers.

Exam tip

The smaller unit gives the bigger number. Change to centimetres or millimetres, then compare.

Exercise 5B  Comparing and ordering lengths

Non-calculator
1
FWrite < or > to make it true: 4 cm [ ] 6 cm
2
FWrite < or > to make it true: 35 mm [ ] 4 cm
3
FWrite < or > to make it true: 3 m [ ] 250 cm
4
FWrite < or > to make it true: 500 ml [ ] 1 l
5
FWrite these lengths in mm, shortest first: 5 cm, 45 mm, 1 cm.
6
FWrite these amounts in ml, smallest first: 2 l, 750 ml, 900 ml.
7
FAnswer each question.
(a)Which is longer: 2 m or 180 cm?
(b)Which is shorter: 80 cm or 1 m?
8
FLook at the bars. Which pencil is the longest? Write the name.
Ali6 cmBen9 cmCara4 cm
9
PSNoah jumps 245 cm. Leo jumps 2 m 60 cm. Who jumps further?
10
PSMei's pencil is 14 cm long. Tom's pencil is 145 mm long. Whose pencil is longer?
11
RAli says that 1 m is shorter than 120 cm, because 1 is smaller than 120. Is he right? Explain.
12
RAlways, sometimes or never? The same length has a bigger number in mm than in cm.
5.3

Adding and subtracting lengths

Year 3
Measure, compare, add and subtract lengths (m, cm, mm)
Video lesson: Adding and subtracting lengthsComing soon
Jack has a ribbon 3 m long. He cuts off 45 cm to tie a card. How much ribbon is left? Give the answer in cm.

We can add or subtract lengths once they are in the same unit. Change any amount in metres to centimetres or millimetres first.

3 m is the same as 300 cm. So 3 m plus 45 cm is 300 cm plus 45 cm, which is 345 cm.

A bar model helps us see the parts. The whole ribbon is 300 cm. The part cut off is 45 cm. The part left is the missing part.

255 cm45 cm3 m = 300 cm
The whole ribbon is 300 cm. The 45 cm piece is cut off, and 255 cm is left.

Key ideas

  • Change every length to the same unit before you add or subtract.
  • For a whole, use the parts: whole = part + part, or part = whole − part.
  • 1 m = 100 cm, so 3 m = 300 cm.
  • The answer is in the unit the question asks for.
Worked example 5.3.1
Work out 245 cm + 130 cm.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in cm.
    245 cm is already in cm; 130 cm is already in cm
  2. Add the numbers. Both amounts are in the same unit, so we can add the numbers.
    245 + 130 = 375
  3. Write the answer. The answer is in cm.
    375

Check. 375 − 130 = 245. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Worked example 5.3.2
Work out 3 m + 45 cm. Give your answer in cm.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in cm.
    3 m = 300 cm; 45 cm is already in cm
  2. Add the numbers. Both amounts are in the same unit, so we can add the numbers.
    300 + 45 = 345
  3. Write the answer. The answer is in cm.
    345

Check. 345 − 45 = 300. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Worked example 5.3.3
Jack has a ribbon 3 m long. He cuts off 45 cm. How much ribbon is left? Give your answer in cm.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in cm.
    3 m = 300 cm; 45 cm is already in cm
  2. Subtract the numbers. Both amounts are in the same unit, so we can take one number away from the other.
    300 − 45 = 255
  3. Write the answer. The answer is in cm.
    255

Check. 255 + 45 = 300. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Watch out

Watch out: 3 m + 45 cm is not 48. You cannot add metres and centimetres until both are in the same unit.

Exam tip

Change both amounts to the same unit first. Then add or subtract the numbers.

Exercise 5C  Adding and subtracting lengths

Non-calculator
1
FWork out 128 mm + 46 mm.
2
FWork out 350 cm − 120 cm.
3
FWork out 2 m + 60 cm. Give your answer in cm.
4
FWork out 5 m − 80 cm. Give your answer in cm.
5
FWork out 67 cm + 58 cm.
6
FWork out each calculation.
(a)84 cm + 19 cm
(b)400 cm − 176 cm
7
PSBen runs 60 m on Monday and 85 m on Tuesday. How far does he run altogether? Give your answer in m.
60 m85 m? m altogether
8
PSA rope is 2 m long. Sam uses 175 cm. How much rope is left? Give your answer in cm.
9
PSMia joins three pieces of ribbon: 40 cm, 25 cm and 60 cm. How long is the ribbon altogether? Give your answer in cm.
10
PSFind the missing length: 3 m − [ ] = 1 m 40 cm. Give your answer in cm.
11
RRuby says 5 m − 90 cm is 4 m 10 cm. Is she right? Explain.
12
RAlways, sometimes or never? If you add 30 cm to 2 m, the answer is longer than 2 m.
5.4

Mass: kilograms and grams

Year 3
Measure, compare, add and subtract mass (kg, g)
Video lesson: Mass: kilograms and gramsComing soon
At the greengrocer's, Priya buys 2 kg of potatoes and 500 g of carrots. How many grams of vegetables does she buy altogether? Give your answer in g.

Mass tells us how heavy something is. We measure small things in grams (g) and heavy things in kilograms (kg).

One kilogram is 1000 grams: 1 kg = 1000 g. So 2 kg is 2000 g.

A balance helps us compare masses. The heavier side goes down.

2 kg1500 g
The 2 kg bag is heavier than the 1500 g bag, so its pan goes down.

Key ideas

  • 1 kg = 1000 g.
  • Use kg for heavy things, such as a bag of potatoes, and g for light things, such as an apple.
  • Change to the same unit before you add, subtract or compare masses.
  • Compare the numbers only after the units are the same.
Worked example 5.4.1
Write 3 kg in g.

Key words. To convert means to write the same amount in a different unit. The amount stays the same.

Method. A bigger unit is worth more small units, so we multiply by 1000 to change kg into g.

  1. Find how many small units make one big unit. 1 kg is the same as 1000 g.
    1 kg = 1000 g
  2. Multiply by the number of big units. We have 3 kg, so we have 3 groups of 1000 g.
    3 × 1000 = 3000
  3. Write the answer. The answer is in g.
    3000

Check. 3000 ÷ 1000 = 3, so the change is right. ✓

Watch out. Ask first: is the new unit bigger or smaller? A smaller unit needs more of them.

Worked example 5.4.2
Which is heavier: 2 kg or 1500 g?

Key words. < means less than. > means greater than. The open end of the sign faces the bigger amount.

Method. Change everything to g, then pick the bigger amount.

  1. Change every amount to the same unit. We use g for all of them.
    2 kg = 2000 g; 1500 g is already in g
  2. Find the bigger amount. We want the bigger amount, so we look for the biggest number.
    2000 g is the bigger amount
  3. Write the answer. The answer is 2 kg.
    2 kg

Check. The other amount is the other way round, so the answer is 2 kg. ✓

Watch out. Change to the same unit first. Otherwise the numbers can point the wrong way.

Worked example 5.4.3
Priya buys 2 kg of potatoes and 500 g of carrots. How many grams of vegetables does she buy altogether? Give your answer in g.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in g.
    2 kg = 2000 g; 500 g is already in g
  2. Add the numbers. Both amounts are in the same unit, so we can add the numbers.
    2000 + 500 = 2500
  3. Write the answer. The answer is in g.
    2500

Check. 2500 − 500 = 2000. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Watch out

Watch out: 1 kg is 1000 g, not 100 g. Many children think a kilogram is 100 grams because they see the number 100 in the word. A kilogram is 1000 grams.

Exam tip

Small things are weighed in grams. Heavy things are weighed in kilograms.

Exercise 5D  Measuring and comparing mass

Non-calculator
1
FWrite 4 kg in g.
2
FWrite 6000 g in kg.
3
FChange each mass.
(a)Write 8 kg in g.
(b)Write 3000 g in kg.
4
FWrite < or > to make each statement true.
(a)2 kg [ ] 1900 g
(b)750 g [ ] 1 kg
5
FWrite these masses in g, lightest first: 1 kg, 750 g, 980 g.
6
FWork out 400 g + 250 g.
7
FWork out 3 kg − 800 g. Give your answer in g.
8
FWork out each calculation. Give your answers in g.
(a)1 kg + 300 g
(b)2 kg − 500 g
9
PSA bag of rice weighs 2 kg. Jack uses 750 g. How many grams of rice are left?
10
PSA cake mix weighs 1 kg. Ali uses 350 g and Zainab uses 275 g. How many grams are left?
11
RTom says a 1 kg bag and a 999 g bag weigh the same. Is he right? Explain.
5.5

Capacity: litres and millilitres

Year 3
Measure, compare, add and subtract volume and capacity (l, ml)
Video lesson: Capacity: litres and millilitresComing soon
Aisha is making lemonade for the school fair. Her jug holds 1 litre. She pours in some juice, and then she needs to know how much is in the jug.

Capacity is how much a container can hold. We measure capacity in millilitres (ml) and litres (l).

One litre is 1000 millilitres: 1 l = 1000 ml. A small spoon holds about 5 ml. A cup holds about 200 ml. A bottle may hold 1 l or 2 l.

Use millilitres for small amounts and litres for bigger amounts.

0 ml200 ml400 ml600 ml800 ml1000 ml
This jug holds 1 litre, which is 1000 ml. The blue liquid is at 600 ml.

Key ideas

  • 1 l = 1000 ml.
  • Use ml for small amounts, such as a cup, and l for bigger amounts, such as a jug.
  • Change to the same unit before you add, subtract or compare amounts.
  • Read the scale on a jug from the bottom up.
Worked example 5.5.1
How many ml is 2 l?

Key words. To convert means to write the same amount in a different unit. The amount stays the same.

Method. A bigger unit is worth more small units, so we multiply by 1000 to change l into ml.

  1. Find how many small units make one big unit. 1 l is the same as 1000 ml.
    1 l = 1000 ml
  2. Multiply by the number of big units. We have 2 l, so we have 2 groups of 1000 ml.
    2 × 1000 = 2000
  3. Write the answer. The answer is in ml.
    2000

Check. 2000 ÷ 1000 = 2, so the change is right. ✓

Watch out. Ask first: is the new unit bigger or smaller? A smaller unit needs more of them.

Worked example 5.5.2
Aisha pours 350 ml of juice into a jug that already has 450 ml. How much juice is in the jug now? Give your answer in ml.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in ml.
    450 ml is already in ml; 350 ml is already in ml
  2. Add the numbers. Both amounts are in the same unit, so we can add the numbers.
    450 + 350 = 800
  3. Write the answer. The answer is in ml.
    800

Check. 800 − 350 = 450. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Worked example 5.5.3
A bottle holds 2 l. Aisha pours out 750 ml. How much is left? Give your answer in ml.

Key words. Length is how long something is. We measure length in millimetres (mm), centimetres (cm) and metres (m).

Method. Change both amounts to the same unit. Then add or subtract the numbers.

  1. Change both amounts to the same unit. We will give the answer in ml.
    2 l = 2000 ml; 750 ml is already in ml
  2. Subtract the numbers. Both amounts are in the same unit, so we can take one number away from the other.
    2000 − 750 = 1250
  3. Write the answer. The answer is in ml.
    1250

Check. 1250 + 750 = 2000. ✓

Watch out. Change to the same unit first. Adding the numbers without changing the units gives a wrong answer.

Watch out

Watch out: 1 l is 1000 ml, not 100 ml. A litre is a bigger unit, so the same amount has a much bigger number of millilitres.

Exam tip

Ask yourself: is this a small amount or a big amount? Small amounts use ml. Bigger amounts use litres.

Exercise 5E  Measuring and comparing capacity

Non-calculator
1
FWrite 3 l in ml.
2
FWrite 4000 ml in l.
3
FChange each amount.
(a)Write 7 l in ml.
(b)Write 6000 ml in l.
4
FWrite < or > to make each statement true.
(a)2 l [ ] 1900 ml
(b)750 ml [ ] 800 ml
5
FWrite these amounts in ml, smallest first: 5 l, 4500 ml, 4 l.
6
FWork out 1 l − 400 ml. Give your answer in ml.
7
FWork out 2 l + 500 ml. Give your answer in ml.
8
FWork out each calculation. Give your answers in ml.
(a)800 ml + 350 ml
(b)2 l − 900 ml
9
PSA jug holds 1 l of water. Leo pours 275 ml into a glass. How much water is left in the jug? Give your answer in ml.
10
PSFatima has 2 l of milk. She uses 600 ml for a cake and 750 ml for pancakes. How many ml of milk is left?
11
RSam says a 1 l bottle holds less than a 900 ml bottle. Is he right? Explain.
12
RAlways, sometimes or never? Half of 1 l is 500 ml.
5.6

Perimeter of 2-D shapes

Year 3
Measure the perimeter of simple 2-D shapes
Video lesson: Perimeter of 2-D shapesComing soon
Leo wants to put a fence round his square vegetable patch. To know how much fencing to buy, he needs to find how far it is all the way round.

The perimeter of a shape is the distance all the way round its outside. To find it, we add the lengths of all the sides.

A rectangle has four sides. The opposite sides are the same length, so a rectangle that is 5 cm long and 2 cm wide has sides of 5 cm, 2 cm, 5 cm and 2 cm.

A shape made of squares can be measured by counting the edges on the outside. Edges where two squares touch are inside the shape, so we do not count them.

Each square is 1 cm. The orange line goes all the way round the outside: 5 + 2 + 5 + 2 = 14 cm.

Key ideas

  • The perimeter is the distance all the way round a shape.
  • Add the lengths of all the sides to find the perimeter.
  • Opposite sides of a rectangle are equal.
  • The perimeter is a length, so give the answer in cm or m.
Worked example 5.6.1
What is the perimeter of this shape? Each square is 1 cm.

Key words. The perimeter is the distance all the way round the outside of a shape.

Method. Count the outside edges of the squares, then add them up. Edges between two squares are inside the shape.

  1. Count the top edges. Count each square edge that has no square above it.
    top: 3
  2. Count the bottom edges. Count each square edge that has no square below it.
    bottom: 3
  3. Count the left and right edges. Count the edges down each side of the shape.
    left: 3, right: 3
  4. Add all the outside edges. Each edge is 1 cm, so the total is the perimeter in cm.
    3 + 3 + 3 + 3 = 12
  5. Write the answer. The perimeter is measured in cm.
    12

Watch out. Do not count the edges where two squares touch. They are inside the shape, so they are not part of the perimeter.

Worked example 5.6.2
A triangle has sides of 3 cm, 4 cm and 5 cm. What is its perimeter?4 cm3 cm5 cm

Key words. The perimeter is the distance all the way round the outside of a shape.

Method. The perimeter is the distance all the way round, so add the lengths of all the sides.

  1. Find the length of every side, going all the way round. Each amount is in cm.
    3 cm, 4 cm, 5 cm
  2. Add all the sides together. Add the numbers together.
    3 + 4 + 5 = 12
  3. Write the answer. The answer is in cm.
    12

Check. Add the numbers again in a different order. You get 12 again. ✓

Watch out. Count every side once. Do not leave a side out, and do not count the squares inside the shape.

Worked example 5.6.3
A triangle has a perimeter of 20 cm. Two of its sides are 6 cm and 8 cm. How long is the third side?

Key words. The perimeter is the distance all the way round the outside of a shape.

Method. The perimeter is all the sides added together. Take the sides you know away from the perimeter.

  1. Add the sides you know. Find the total of the known sides.
    6 + 8 = 14
  2. Take that total away from the perimeter. What is left must be the missing side.
    20 − 14 = 6
  3. Write the missing side. The missing side is in cm.
    6

Check. 14 + 6 = 20, so all the sides make the perimeter. ✓

Watch out. Check that you have used every side. A shape with 3 sides has 3 lengths to add.

Watch out

Watch out: the perimeter counts only the outside edges. Do not count the squares inside the shape, and do not count the edges where two squares touch.

Exam tip

Mark each side as you count it. Then you cannot miss one out or count one twice.

Exercise 5F  Perimeter of shapes

Non-calculator
1
FWhat is the perimeter of this rectangle? Each square is 1 cm.
2
FA rectangle is 7 cm long and 4 cm wide. What is its perimeter?
7 cm7 cm4 cm4 cm
3
FEach side of a square is 5 cm. What is its perimeter?
4
FA triangle has sides of 6 cm, 8 cm and 10 cm. Find its perimeter.
8 cm6 cm10 cm
5
FFind the perimeter of each triangle. The triangles are not drawn to scale.
(a)Sides of 2 cm, 3 cm and 4 cm
(b)Three equal sides of 4 cm
6
FWhat is the perimeter of this shape? Each square is 1 cm.
7
PSWhat is the perimeter of this shape? Each square is 1 cm.
8
PSA triangle has a perimeter of 18 cm. Two of its sides are 5 cm and 7 cm. How long is the third side?
9
PSA square has a perimeter of 16 cm. How long is each side?
10
PSMia walks once round the edge of a square field. Each side is 25 m. How far does she walk? Give your answer in m.
11
RBen makes a rectangle 5 cm by 3 cm. Ruby makes a square with sides of 4 cm. Do they have the same perimeter? Explain.
12
RSam says that if you cut the top right corner square off this rectangle, the perimeter gets smaller. Is he right? Explain.

Chapter summary

SkillMethod
Measuring lengthPut the zero mark at one end and read the mark at the other end. Or subtract the start mark from the end mark.
Changing units1 cm = 10 mm, 1 m = 100 cm, 1 m = 1000 mm, 1 kg = 1000 g, 1 l = 1000 ml. To change to a smaller unit, multiply. To change to a bigger unit, divide.
Comparing measuresChange both amounts to the same unit. Then the bigger number is the bigger amount.
Adding and subtractingChange to the same unit first. Then add or subtract the numbers.
Mass and capacityMeasure mass in grams and kilograms, and capacity in millilitres and litres, using the same methods as for length.
PerimeterAdd the lengths of all the sides. On a grid of squares, count the outside edges of the squares.

Can you…?

  • I can measure a length with a ruler in mm, cm and m.
  • I can change between mm, cm and m, between g and kg, and between ml and l.
  • I can compare two lengths, masses or capacities in the same unit.
  • I can put measures written in different units in order.
  • I can add and subtract measures, changing to the same unit first.
  • I can choose a sensible unit for a length, a mass or a capacity.
  • I can find the perimeter of a rectangle, a square, a triangle and a shape made of squares.

Key terms

Length
How long something is. We measure it in mm, cm and m.
Millimetre (mm)
A small unit of length. There are 10 mm in 1 cm.
Centimetre (cm)
A unit of length. There are 100 cm in 1 m.
Metre (m)
A unit of length. There are 1000 mm in 1 m.
Mass
How heavy something is. We measure it in g and kg.
Kilogram (kg)
A unit of mass. There are 1000 g in 1 kg.
Capacity
How much a container can hold. We measure it in ml and l.
Litre (l)
A unit of capacity. There are 1000 ml in 1 litre.
Perimeter
The distance all the way round the outside of a shape.
Convert
To write the same amount in a different unit.

Exercise 5Z  Check-up

Non-calculator
1
How long is the bar? Give your answer in cm.
012345678910
2
Write 9 cm in mm.
3
Write 3000 g in kg.
4
Write < or > to make it true: 4 l [ ] 3900 ml
5
Work out 2 m + 36 cm. Give your answer in cm.
6
Work out 1 kg − 250 g. Give your answer in g.
7
A rectangle is 8 cm long and 3 cm wide. What is its perimeter?
8 cm8 cm3 cm3 cm
8
A triangle has a perimeter of 15 cm. Two of its sides are 4 cm and 6 cm. How long is the third side?
9
The jug shows 600 ml. How many ml more does it need to reach 1 litre? Give your answer in ml.
0 ml200 ml400 ml600 ml800 ml1000 ml
10
Write these lengths in mm, shortest first: 4 cm, 37 mm, 3 cm.

Total 19 marks. Allow about 19 minutes.

Exercise 5X  Practice test questions

Non-calculator
1
FHow long is the pencil? Give your answer in cm.[1 mark]
012345678910
2
FWrite 5 cm in mm.[1 mark]
3
FWrite 400 cm in m.[1 mark]
4
FWrite < or > to make it true: 2 kg [ ] 1900 g[2 marks]
5
FWrite these amounts in ml, smallest first: 3 l, 2500 ml, 2 l.[2 marks]
6
FWork out 4 m + 80 cm. Give your answer in cm.[2 marks]
7
FWork out 3 kg − 650 g. Give your answer in g.[2 marks]
8
FA bottle holds 2 l. It has 1250 ml of water in it. How many ml of space is left in the bottle?[2 marks]
9
FA rectangle is 6 cm long and 2 cm wide.[3 marks]
6 cm6 cm2 cm2 cm
(a)What is its perimeter?
(b)A square has the same perimeter as this rectangle. How long is each side of the square?
10
FAli has 2 l of juice. He pours 750 ml into one cup and 600 ml into another cup.[3 marks]
(a)How much juice does Ali pour altogether? Give your answer in ml.
(b)How much juice is left in the bottle? Give your answer in ml.
← Chapter 4: FractionsChapter 6: Money →

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