Year 4 · Chapter 7

Year 4 Perimeter, Area and Measures: worked examples and questions with answers

By the end of this chapter you will be able to

Read rulers to the nearest centimetre and millimetre, and write a length in cm and mm, in mm or as a decimal of a cm
Read weighing scales, measuring jugs and other scales, working out what each small mark is worth
Change between km and m, m and cm, cm and mm, kg and g, and litres and millilitres, in both directions
Use simple decimals of measures, like 2.5 m = 250 cm and 1.5 kg = 1,500 g
Compare and order measures in different units, and choose a sensible unit or estimate
Add and subtract measures, and solve measure word problems
Find the perimeter of squares, rectangles and L-shapes, including shapes with missing sides
Find the area of a shape by counting squares, and use rows and columns for rectangles

You should already know

Place value and rounding (Chapter 1)
Column addition and subtraction (Chapter 2)
Times tables and multiplying and dividing by 10, 100 and 1,000 (Chapters 3 and 4)
Halves, quarters, tenths and hundredths as decimals (Chapters 5 and 6)

Where this leads

Time: hours, minutes and seconds (Chapter 8)
Shapes and symmetry (Chapter 9)
Converting units and the area of rectangles in Year 5
Volume and area of triangles in Year 6

National Curriculum for England, Key Stage 2 mathematics, Year 4. Content: Read scales on rulers, weighing scales and measuring jugs, including scales with different step sizes, Measure length to the nearest centimetre and millimetre, Convert between different units of measure: kilometre to metre, metre to centimetre, centimetre to millimetre, kilogram to gram, litre to millilitre, Write simple decimals of measures, for example 2.5 m = 250 cm, Estimate, compare and calculate different measures; choose a sensible unit, Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres, Find the area of rectilinear shapes by counting squares.

Printable worksheets. Every lesson in this chapter has a free worksheet and an answer sheet to download and print.

7.1 Reading a ruler: centimetres and millimetres: Worksheet (PDF) · Answers (PDF) · lesson page
7.2 Reading scales, weighing scales and jugs: Worksheet (PDF) · Answers (PDF) · lesson page
7.3 Changing units: km, m, cm, mm, kg, g, l and ml: Worksheet (PDF) · Answers (PDF) · lesson page
7.4 Comparing, ordering and estimating measures: Worksheet (PDF) · Answers (PDF) · lesson page
7.5 Calculating with measures: Worksheet (PDF) · Answers (PDF) · lesson page
7.6 Perimeter: Worksheet (PDF) · Answers (PDF) · lesson page
7.7 Area: counting squares: Worksheet (PDF) · Answers (PDF) · lesson page
Check-up and SATs-style questions: Worksheet (PDF) · Answers (PDF) · lesson page

Exercise P Do you remember?

Non-calculator

FWork out 7 × 100.

Done

FWhat is half of 1,000?

Done

FWork out 346 + 278.

Done

FWork out 1,000 − 450.

Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
1 0 0 0
− 4 5 0
Subtract the ones. Always start with the ones, on the right.
0 − 0 = 0
Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
0 tens is not enough to take away 5. We need to exchange.
The hundreds has 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 1 thousand become 0 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
10 − 5 = 5
Subtract the hundreds. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5
Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.
(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 0.
We do not write a 0 at the front of an answer, so leave this space empty.
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
01 90 100 0
− 4 5 0
5 5 0

1,000 − 450 = 550

Check. Use the opposite (inverse) operation: 550 + 450 = 1,000. ✓
Estimate: 1,000 − 500 = 500 (rounding to the nearest 100). It is close to the exact answer. ✓

Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.

Done

FWrite 0.5 as a fraction in its simplest form.

Done

7.1

Reading a ruler: centimetres and millimetres

Year 4
Read scales on rulers, Measure to the nearest cm and mm, Length in cm and mm

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Reading a ruler: centimetres and millimetresComing soon

We measure length with a ruler. A ruler has a scale: a line of marks with numbers. The big numbered marks are centimetres (cm). Between two numbers there are 10 tiny marks. Each tiny mark is a millimetre (mm). 10 mm = 1 cm. The middle mark between two numbers is longer. It is 5 mm.

Zoomed in. From 0 to 1 there are 10 gaps: each gap is 1 mm. A is at 1 cm. B is at 1 cm 5 mm (the long middle mark). C is at 2 cm 4 mm.

How to read a ruler. Put the 0 mark at the start of the thing you measure. Then look at where the other end is.

Read the last whole centimetre before the end.
Count the small marks after it. Each one is 1 mm.
Say the length: centimetres and millimetres.

The pencil ends 4 small marks after the 7 cm mark. Its length is 7 cm 4 mm.

Different ways to write a length. The pencil is 7 cm 4 mm. There are 7 × 10 = 70 mm in 7 cm, so it is also 74 mm. Each millimetre is one tenth of a centimetre (0.1 cm), so we can write it as 7.4 cm.

To the nearest centimetre. Look at the millimetres. If there are 5 or more, round up to the next centimetre. If there are fewer than 5, stay on the same centimetre. 7 cm 4 mm is about 7 cm. And 7 cm 5 mm is about 8 cm.

When the object does not start at 0. Sometimes a strip starts at another mark. Read both ends, then take the smaller reading away from the bigger one.

The strip starts at 2 cm 3 mm (23 mm) and ends at 9 cm 6 mm (96 mm). Its length is 96 − 23 = 73 mm = 7 cm 3 mm.

Key words. The length is how long something is. A millimetre is a very small unit (about the thickness of a coin). A centimetre is about the width of your little fingernail.

Key ideas

10 mm = 1 cm. Big marks are cm. Tiny marks are mm. The long middle mark is 5 mm.
Start at 0. Read the whole cm first, then count the mm.
7 cm 4 mm = 74 mm = 7.4 cm.
To the nearest cm: 5 mm or more rounds up. Less than 5 mm stays the same.
If a strip does not start at 0, read both ends and subtract.
Always write the unit: cm or mm.

Worked example 7.1.1

Read the length of the ribbon. Give your answer in cm and mm.

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

Find where the end of the ribbon is on the ruler. The left end of the ribbon is at 0, so the number at its right end is its length.
the end of the ribbon is just after the 7 cm mark, with 4 small marks to go.
Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre.
4 small marks = 4 mm
Write the length. Say the centimetres, then the millimetres.
7 cm and 4 mm = 7 cm 4 mm

Check. 7 cm = 70 mm and 70 mm + 4 mm = 74 mm. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Worked example 7.1.2

How long is the pencil? Give your answer in millimetres.

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

Find where the end of the pencil is on the ruler. The left end of the pencil is at 0, so the number at its right end is its length.
the end of the pencil is just after the 12 cm mark, with 6 small marks to go.
Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre. The long middle mark is 5 mm.
6 small marks = 6 mm
Change the centimetres to millimetres. 1 cm = 10 mm, so multiply the centimetres by 10.
12 × 10 = 120 mm
Add the extra millimetres.
120 + 6 = 126 mm

Check. 126 ÷ 10 = 12 remainder 6, which is 12 cm 6 mm. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Worked example 7.1.3

What is the length of the line to the nearest centimetre?

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

Find where the end of the line is on the ruler. The left end of the line is at 0, so the number at its right end is its length.
the end of the line is just after the 9 cm mark, with 5 small marks to go.
Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre. The long middle mark is 5 mm.
5 small marks = 5 mm
Look at the extra millimetres. To round to the nearest cm, look at the millimetres. 5 mm or more rounds UP.
5 mm is 5 or more, so round up from 9 cm to 10 cm

Check. The length is 9 cm 5 mm. It is closer to 10 cm than to the other whole centimetre. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Worked example 7.1.4

Write the length of the ribbon as a decimal number of centimetres.

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

Find where the end of the ribbon is on the ruler. The left end of the ribbon is at 0, so the number at its right end is its length.
the end of the ribbon is just after the 8 cm mark, with 3 small marks to go.
Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre.
3 small marks = 3 mm
Write the millimetres as a part of a centimetre. 1 mm is one tenth of a cm, so 1 mm = 0.1 cm.
3 mm = 3 tenths of a cm = 0.3 cm
Put the centimetres and the part together. The whole centimetres go before the decimal point.
8 + 0.3 = 8.3 cm

Check. 8.3 cm × 10 = 83 mm. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Worked example 7.1.5

The strip does not start at 0. How long is the strip?

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. When an object does not start at 0, read both ends and subtract the smaller reading from the bigger one.

Read the left end. The strip does not start at 0, so we need both ends.
The left end is at 2 cm 3 mm = 23 mm
Read the right end. Do the same for the other end.
The right end is at 9 cm 6 mm = 96 mm
Take the left end away from the right end. The length is the distance between the two ends.
96 − 23 = 73 mm
Write the length in the unit asked. 10 mm = 1 cm.
73 mm = 7 cm 3 mm

Check. Count on from the left end: 23 mm + 73 mm = 96 mm. ✓

Watch out. Do not just read the right end. That would be the distance from 0, not the length of the strip.

Worked example 7.1.6

What length does the arrow point to? Give your answer in cm and mm.

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler where the arrow points: whole centimetres first, then the small marks.

Find where the arrow is on the ruler. Read the number at the big mark just before it.
the arrow is just after the 4 cm mark, with 7 small marks to go.
Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre. The long middle mark is 5 mm.
7 small marks = 7 mm
Write the length. Say the centimetres, then the millimetres.
4 cm and 7 mm = 4 cm 7 mm

Check. 4 cm = 40 mm and 40 mm + 7 mm = 47 mm. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Worked example 7.1.7

Which letter is at 6 cm 5 mm?

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at every pointer. Pick the pointer that matches the measurement.

Find the measurement we want on the ruler. 6 cm 5 mm means go to the 6 cm mark, then count 5 small marks.
6 cm 5 mm = 65 mm
Read each letter. Read the big mark just before the pointer, then count the small marks.
D is at 4 cm
A is at 5 cm 6 mm
B is at 6 cm 5 mm
C is at 7 cm 1 mm
Choose the matching letter.
The letter at 6 cm 5 mm is B.

Check. B is at 6 cm 5 mm. ✓

Watch out. Count the small marks carefully. 6 cm 5 mm is not the same as 5 cm 6 mm.

Watch out

Start at 0, and count the tiny marks. There are 10 tiny marks in each centimetre, so after the 7 cm mark the first tiny mark is 7 cm 1 mm. 6 cm 5 mm is not the same as 5 cm 6 mm. And 4.5 cm is 45 mm, not 4.5 mm.

7.2

Reading scales, weighing scales and jugs

Year 4
Read scales on weighing scales and measuring jugs, Scales with different step sizes, Mass and capacity

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Reading scales, weighing scales and jugsComing soon

Mass is how heavy something is. We measure it in grams (g) and kilograms (kg). Capacity is how much a container can hold, or how much liquid is in it. We measure it in millilitres (ml) and litres (l). A weighing scale and a measuring jug both have a scale, which works just like a number line.

Two weighing scales. The pointer shows how heavy the thing is.

Step 1: find the unit (g or kg, ml or l). Step 2: work out the step. Different scales have different steps, so never guess. Look at two numbers next to each other. Count the gaps between them and divide. On the first scale there are 5 gaps from 300 to 400, so each small mark is 100 ÷ 5 = 20 g. On the second scale there are 2 gaps from 3 to 4, so each small mark is 1 ÷ 2 = 0.5 kg.

Step 3: count on. The first pointer is 2 small marks after 300. So it shows 300 + 20 + 20 = 340 g. The second pointer is 1 small mark after 3 kg, so it shows 3 + 0.5 = 3.5 kg.

Two measuring jugs. Read the scale at the top of the liquid. The first jug has 4 gaps from 600 to 800, so each mark is 50 ml: the jug has 750 ml. The second has 5 gaps from 1 to 1.5, so each mark is 0.1 l: the jug has 1.3 l.

Reading a jug. Look at the top of the liquid and read the mark level with it. A scale can also be a straight line, like a tiny ruler. Here each mark is 2 mm. The numbers are 0, 10, 20 … and there are 5 gaps between them, so each mark is 10 ÷ 5 = 2 mm.

A straight scale with marks every 2 mm. The arrow points 2 marks after 10, so the reading is 14 mm.

Key words. The scale is the line of marks. The step (or interval) is the amount between two small marks. Mass is measured in g and kg. Capacity is measured in ml and l.

Key ideas

Mass: grams (g) and kilograms (kg). Capacity: millilitres (ml) and litres (l).
Find the unit first.
Count the gaps between two numbered marks and divide to find the step.
Read the number below the pointer, then count on in steps.
For a jug, read at the top of the liquid.
Do not assume each mark is 1. Always work out the step.

Worked example 7.2.1

Each scale mark is not always 1. Here is a weighing scale. What is each small mark worth?

Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).

Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.

Look at two numbered marks next to each other. We need two marks where we know the numbers.
The marks 0 and 100 are next to each other.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 0 to 100 there are 5 gaps.
100 − 0 = 100 g
100 ÷ 5 = 20 g for each small mark
Write the answer.
Each small mark is 20 g.

Check. 5 small marks × 20 g = 100 g, which is the gap from 0 to 100. ✓

Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.

Worked example 7.2.2

How heavy is the flour?

Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.

Find the unit on the scale. The unit tells us what the numbers mean.
The unit is g (grams).
Find the two numbered marks either side of the pointer. We read the number below it first, then count on.
The pointer is between 300 and 400.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 300 to 400 there are 5 gaps.
400 − 300 = 100 g
100 ÷ 5 = 20 g for each small mark
Count on from 300. Count how many small marks the pointer is past 300.
2 small marks × 20 g = 40 g
300 + 40 = 340 g
Write the reading with its unit. A measure always needs a unit.
340 g

Check. Count back from 400: 3 small marks below it. 400 − 60 = 340. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Worked example 7.2.3

The scale shows the mass of a bag of potatoes. Write the mass.

Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.

Find the unit on the scale. The unit tells us what the numbers mean.
The unit is kg (kilograms).
Find the two numbered marks either side of the pointer. We read the number below it first, then count on.
The pointer is between 3 and 4.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 3 to 4 there are 2 gaps.
4 − 3 = 1 kg
1 ÷ 2 = 0.5 kg for each small mark
Count on from 3. Count how many small marks the pointer is past 3.
1 small mark × 0.5 kg = 0.5 kg
3 + 0.5 = 3.5 kg
Write the reading with its unit. A measure always needs a unit.
3.5 kg

Check. Count back from 4: 1 small mark below it. 4 − 0.5 = 3.5. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Worked example 7.2.4

How much water is in the jug?

Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.

Find the unit on the scale. The unit tells us what the numbers mean.
The unit is ml (millilitres).
Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.
The top of the liquid is between 600 and 800.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 600 to 800 there are 4 gaps.
800 − 600 = 200 ml
200 ÷ 4 = 50 ml for each small mark
Count on from 600. Count how many small marks the top of the liquid is past 600.
3 small marks × 50 ml = 150 ml
600 + 150 = 750 ml
Write the reading with its unit. A measure always needs a unit.
750 ml

Check. Count back from 800: 1 small mark below it. 800 − 50 = 750. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Worked example 7.2.5

How much juice is in the jug? Give your answer in millilitres.

Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.

Find the unit on the scale. The unit tells us what the numbers mean.
The unit is l (litres).
Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.
The top of the liquid is between 1 and 1.5.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 1 to 1.5 there are 5 gaps.
1.5 − 1 = 0.5 l
0.5 ÷ 5 = 0.1 l for each small mark
Count on from 1. Count how many small marks the top of the liquid is past 1.
3 small marks × 0.1 l = 0.3 l
1 + 0.3 = 1.3 l
Change to millilitres. 1 l = 1,000 ml, so multiply by 1,000.
1.3 l = 1,300 ml

Check. Count back from 1.5: 2 small marks below it. 1.5 − 0.2 = 1.3. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Worked example 7.2.6

What does the arrow show?

Method. Look at the scale. Find the numbered marks either side of the arrow, work out what each small mark is worth, then count on.

Find the unit on the scale. The unit tells us what the numbers mean.
The unit is mm (millimetres).
Find the two numbered marks either side of the arrow. We read the number below it first, then count on.
The arrow is between 10 and 20.
Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 10 to 20 there are 5 gaps.
20 − 10 = 10 mm
10 ÷ 5 = 2 mm for each small mark
Count on from 10. Count how many small marks the arrow is past 10.
2 small marks × 2 mm = 4 mm
10 + 4 = 14 mm
Write the reading with its unit. A measure always needs a unit.
14 mm

Check. Count back from 20: 3 small marks below it. 20 − 6 = 14. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Worked example 7.2.7

Dev needs 1 litre (1,000 ml) of water. The jug has the amount shown. How much more water must he add?

Method. Read the scale, then find the difference between the two amounts.

Read the amount now. First we need to know how much there is.
650 ml
Take the smaller amount away from the bigger. The difference is how much more (or less) there is.
1000 − 650 = 350 ml
Write the answer with its unit.
350 ml

Check. 650 + 350 = 1000. ✓

Watch out. Write the unit in the answer.

Worked example 7.2.8

Which jug has 340 ml of water in it?

Method. Work out the step of the scale, read every jug, then pick the one that matches.

Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
From 0 to 100 there are 5 gaps.
100 − 0 = 100 ml
100 ÷ 5 = 20 ml for each small mark
Read each one. Count on from the numbered mark below.
A: 200 + 3 × 20 = 260 ml
B: 300 + 2 × 20 = 340 ml
C: 400 + 1 × 20 = 420 ml
Choose the jug that shows 340 ml.
B

Check. B shows 340 ml. ✓

Watch out. Check the step first. A different scale can make the same-looking pointer mean a different amount.

Watch out

Count the gaps, not the marks. Between 300 and 400 there are 5 gaps (and 6 marks). Do not say each mark is 1 or 10 without checking. Also keep an eye on the unit: a scale marked in kg gives an answer in kg.

7.3

Changing units: km, m, cm, mm, kg, g, l and ml

Year 4
Convert between units of measure, Decimals of measures, Kilometres, metres, centimetres, millimetres, Kilograms and grams, litres and millilitres

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Changing units: km, m, cm, mm, kg, g, l and mlComing soon

We use different units for different sizes. A kilometre (km) is for long distances. A metre (m) is for the size of a room. A centimetre (cm) and a millimetre (mm) are for small things. For mass we use kilograms (kg) and grams (g). For capacity we use litres (l) and millilitres (ml).

Going right (to a smaller unit) we multiply. Going left (to a bigger unit) we divide.

Length	Mass	Capacity
10 mm = 1 cm	1,000 g = 1 kg	1,000 ml = 1 l
100 cm = 1 m
1,000 m = 1 km

Kilo means 1,000. Centi means one hundredth. Milli means one thousandth. These words help you remember the facts.

Big unit to small unit: multiply. A cm is small, so you need lots of cm to make 3 m. 3 m = 3 × 100 = 300 cm. The number gets bigger. Small unit to big unit: divide. It takes only a few big units to make the same length. 600 cm = 600 ÷ 100 = 6 m. The number gets smaller.

The same idea for mass (kg and g) and capacity (l and ml): multiply by 1,000 or divide by 1,000.

Decimals of measures. Half of a metre is 50 cm, and half is 0.5, so 0.5 m = 50 cm. For 2.5 m, change 2 m and 0.5 m separately: 200 cm + 50 cm = 250 cm. A double number line shows both units at once.

2.5 m is the same distance as 250 cm. Each whole metre is 100 cm.

More decimals: 1.5 kg = 1,500 g. 0.25 l = 250 ml (a quarter of 1,000). 0.75 l = 750 ml. 4.5 km = 4,500 m. And going the other way, 1,500 g = 1.5 kg and 250 cm = 2.5 m.

Mixed units. 3 m 40 cm means 3 m and 40 cm. To write it in cm, change the 3 m to 300 cm and add 40 cm: 340 cm. And 1,450 ml is 1 l and 450 ml.

Key words. To convert is to change from one unit to another. The unit is the name we give a measure (cm, kg, ml...). A decimal uses a point, like 2.5.

Key ideas

10 mm = 1 cm 100 cm = 1 m 1,000 m = 1 km 1,000 g = 1 kg 1,000 ml = 1 l.
Big unit to small unit: multiply (the number gets bigger).
Small unit to big unit: divide (the number gets smaller).
Halves and quarters: 0.5 = half, 0.25 = a quarter, 0.75 = three quarters.
2.5 m = 250 cm and 1.5 kg = 1,500 g.
Mixed units: 3 m 40 cm = 300 cm + 40 cm = 340 cm.

Worked example 7.3.1

Change 3 m to centimetres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 100 centimetres in 1 metre, so multiply by 100 to change metres to centimetres.

Remember the fact. 1 m is the same as 100 cm. A centimetre is a much smaller unit, so we will have a bigger number.
1 m = 100 cm
Multiply by 100. Each m is 100 cm. So 3 m is 3 lots of 100 cm. (Multiplying by 100 moves every digit 2 places to the left.)
3 × 100 = 300
Write the answer with its unit. A measure always needs its unit.
3 m = 300 cm

Check. Go back: 300 ÷ 100 = 3. ✓

Watch out. Changing to a smaller unit gives a bigger number: 3 m is 300 cm, not 0.03.

Worked example 7.3.2

Change 5 kg to grams.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
1 kg = 1,000 g
Multiply by 1,000. Each kg is 1,000 g. So 5 kg is 5 lots of 1,000 g. (Multiplying by 1,000 moves every digit 3 places to the left.)
5 × 1,000 = 5,000
Write the answer with its unit. A measure always needs its unit.
5 kg = 5,000 g

Check. Go back: 5,000 ÷ 1,000 = 5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 5 kg is 5,000 g, not 0.005.

Worked example 7.3.3

A bottle holds 4 litres. How many millilitres is that?

Method. There are 1,000 millilitres in 1 litre, so multiply by 1,000 to change litres to millilitres.

Remember the fact. 1 l is the same as 1,000 ml. A millilitre is a much smaller unit, so we will have a bigger number.
1 l = 1,000 ml
Multiply by 1,000. Each l is 1,000 ml. So 4 l is 4 lots of 1,000 ml. (Multiplying by 1,000 moves every digit 3 places to the left.)
4 × 1,000 = 4,000
Write the answer with its unit. A measure always needs its unit.
4 l = 4,000 ml

Check. Go back: 4,000 ÷ 1,000 = 4. ✓

Watch out. Changing to a smaller unit gives a bigger number: 4 l is 4,000 ml, not 0.004.

Worked example 7.3.4

Change 600 cm to metres.

Method. There are 100 centimetres in 1 metre, so divide by 100 to change centimetres to metres.

Remember the fact. 1 m is the same as 100 cm. A metre is a much bigger unit, so we will have a smaller number.
100 cm = 1 m
Divide by 100. Every 100 cm make 1 m. We find how many lots of 100 there are.
600 ÷ 100 = 6
Write the answer with its unit. A measure always needs its unit.
600 cm = 6 m

Check. Go back: 6 × 100 = 600. ✓

Watch out. Changing to a bigger unit gives a smaller number. 600 cm is 6 m, not 60,000.

Worked example 7.3.5

A box has a mass of 7,000 g. What is its mass in kilograms?

Method. There are 1,000 grams in 1 kilogram, so divide by 1,000 to change grams to kilograms.

Remember the fact. 1 kg is the same as 1,000 g. A kilogram is a much bigger unit, so we will have a smaller number.
1,000 g = 1 kg
Divide by 1,000. Every 1,000 g make 1 kg. We find how many lots of 1,000 there are.
7,000 ÷ 1,000 = 7
Write the answer with its unit. A measure always needs its unit.
7,000 g = 7 kg

Check. Go back: 7 × 1,000 = 7,000. ✓

Watch out. Changing to a bigger unit gives a smaller number. 7,000 g is 7 kg, not 7,000,000.

Worked example 7.3.6

Change 2.5 m to centimetres.

Method. There are 100 centimetres in 1 metre, so multiply by 100 to change metres to centimetres.

Remember the fact. 1 m is the same as 100 cm. A centimetre is a much smaller unit, so we will have a bigger number.
1 m = 100 cm
Split the number into whole metres and a part. It is easier to change the whole metres and the part separately.
2.5 m = 2 m + 0.5 m
Change the whole metres. Multiply by 100.
2 × 100 = 200 cm
Change the part. Think about what fraction of a m it is.
0.5 m is half of 1 m. Half of 100 = 50 cm
Add the two answers together.
200 + 50 = 250 cm

Check. Go back: 250 ÷ 100 = 2.5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 2.5 m is 250 cm, not 0.025.

Worked example 7.3.7

Change 1.5 kg to grams.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
1 kg = 1,000 g
Split the number into whole kilograms and a part. It is easier to change the whole kilograms and the part separately.
1.5 kg = 1 kg + 0.5 kg
Change the whole kilograms. Multiply by 1,000.
1 × 1,000 = 1,000 g
Change the part. Think about what fraction of a kg it is.
0.5 kg is half of 1 kg. Half of 1,000 = 500 g
Add the two answers together.
1,000 + 500 = 1,500 g

Check. Go back: 1,500 ÷ 1,000 = 1.5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 1.5 kg is 1,500 g, not 0.0015.

Worked example 7.3.8

A path is 2,500 m long. Write its length in kilometres.

Method. There are 1,000 metres in 1 kilometre, so divide by 1,000 to change metres to kilometres.

Remember the fact. 1 km is the same as 1,000 m. A kilometre is a much bigger unit, so we will have a smaller number.
1,000 m = 1 km
Divide by 1,000 and keep the remainder. The whole kilometres come from the lots of 1,000 m. The remainder is the part left over.
2,500 ÷ 1,000 = 2 remainder 500
Write the remainder as a part of 1 km. 500 m out of 1,000 m is 500/1,000 of a km.
500 m is half of 1,000 m, so 500 m = 0.5 km
Put the whole kilometres and the part together. The whole number goes before the decimal point.
2 + 0.5 = 2.5 km

Check. Go back: 2.5 × 1,000 = 2,500. ✓

Watch out. Changing to a bigger unit gives a smaller number. 2,500 m is 2.5 km, not 2,500,000.

Worked example 7.3.9

How many millilitres is 0.75 litres?

Method. There are 1,000 millilitres in 1 litre, so multiply by 1,000 to change litres to millilitres.

Remember the fact. 1 l is the same as 1,000 ml. A millilitre is a much smaller unit, so we will have a bigger number.
1 l = 1,000 ml
Split the number into whole litres and a part. It is easier to change the whole litres and the part separately.
0.75 l is just a part of 1 l.
Change the part. Think about what fraction of a l it is.
0.75 l is three quarters of 1 l. 1,000 ÷ 4 = 250, then 250 × 3 = 750 ml
So 0.75 l = 750 ml

Check. Go back: 750 ÷ 1,000 = 0.75. ✓

Watch out. Changing to a smaller unit gives a bigger number: 0.75 l is 750 ml, not 0.00075.

Worked example 7.3.10

Change 45 mm to centimetres.

Method. There are 10 millimetres in 1 centimetre, so divide by 10 to change millimetres to centimetres.

Remember the fact. 1 cm is the same as 10 mm. A centimetre is a much bigger unit, so we will have a smaller number.
10 mm = 1 cm
Divide by 10 and keep the remainder. The whole centimetres come from the lots of 10 mm. The remainder is the part left over.
45 ÷ 10 = 4 remainder 5
Write the remainder as a part of 1 cm. 5 mm out of 10 mm is 5/10 of a cm.
5 mm is half of 10 mm, so 5 mm = 0.5 cm
Put the whole centimetres and the part together. The whole number goes before the decimal point.
4 + 0.5 = 4.5 cm

Check. Go back: 4.5 × 10 = 45. ✓

Watch out. Changing to a bigger unit gives a smaller number. 45 mm is 4.5 cm, not 450.

Worked example 7.3.11

Write 3 m 40 cm in centimetres.

Method. Change the metres to centimetres, then add the centimetres that are left over.

Change the whole metres to cm. 1 m = 100 cm, so multiply by 100.
3 × 100 = 300 cm
Add the extra cm. Put the two parts together.
300 + 40 = 340 cm
Write the answer. Use the small unit only.
3 m 40 cm = 340 cm

Check. 340 ÷ 100 = 3 remainder 40. ✓

Watch out. Change the metres first. 3 m is 300 cm, not 3 cm. Then add the 40 cm.

Worked example 7.3.12

Write 1,450 ml in litres and millilitres.

Method. Divide by 1,000 to find the whole litres. The remainder is the millilitres that are left over.

Divide by 1,000. Every 1,000 ml make 1 l.
1,450 ÷ 1,000 = 1 remainder 450
Say what the answer means. The whole number is the litres. The remainder is the millilitres left over.
1 l and 450 ml
Write the answer. Put the big unit first, then the small unit.
1,450 ml = 1 l 450 ml

Check. 1 × 1,000 + 450 = 1,450. ✓

Watch out. The remainder is not a decimal. It is the part left over, written in the smaller unit.

Watch out

Multiply or divide? Ask yourself: am I going to a smaller unit (more of them: multiply) or a bigger unit (fewer of them: divide)? Check the answer makes sense: 3 m is 300 cm, not 0.03 cm. And 3 m 40 cm is 340 cm, not 3.40 cm and not 34 cm.

7.4

Comparing, ordering and estimating measures

Year 4
Compare and order measures, Estimate measures, Choose a sensible unit, Round measures

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Comparing, ordering and estimating measuresComing soon

Comparing measures. Which is longer: 3 km or 2,500 m? The numbers 3 and 2,500 look different, but the units are different too. We can only compare measures when they are in the same unit. Change both to the smaller unit: 3 km = 3,000 m. Now compare 3,000 m and 2,500 m. So 3 km is longer.

After changing to metres, 3,000 is more than 2,500.

Ordering measures. Change every measure to the same unit. Put the numbers in order. Then write the original measures in that order. Ascending order is smallest first. Descending order is biggest first.

Choosing a sensible unit. Picture the thing and compare it with a size you know.

Unit	About the size of…
1 mm	the thickness of a coin
1 cm	the width of your little fingernail
1 m	one big step
1 km	a 12-minute walk
1 g	a paper clip
1 kg	a bag of sugar
5 ml	a teaspoon
1 l	a big carton of juice

Estimating. An estimate is a sensible guess. Use these sizes to help. A pencil is about 15 cm (about the length of your hand). A door is about 2 m tall. An apple is about 150 g. A cup of tea is about 250 ml.

This block is 1 cm. About how many blocks fit along the line? The line is about 8 cm long.

Rounding measures. We can round a measure just like any number. 2,450 g to the nearest 100 g: the digit to the right of the hundreds is 5, so round up to 2,500 g. We use ≈ to mean “is about”.

Key words. To compare is to say which is bigger. To order is to put in a list. To estimate is to make a sensible guess. To round is to change to a nearby number.

Key ideas

Change measures to the same unit (the smaller one) before comparing or ordering.
3 km > 2,500 m because 3,000 > 2,500.
Order: smallest first (ascending) or biggest first (descending).
Know some sizes: 1 cm is a fingernail, 1 m is a big step, 1 kg is a bag of sugar, 1 l is a big carton.
A sensible estimate has the right size and the right unit.
To round to the nearest 100, look at the tens digit: 5 or more rounds up.

Worked example 7.4.1

Write <, > or = in the box. 3 km [ ] 2,500 m

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change both measures to the same unit (the smaller one). Then compare the numbers.

Look at the units. We can only compare measures that are in the same unit.
3 km and 2,500 m: the units are different.
Change both to the smaller unit, metres. Changing to the smaller unit gives whole numbers that are easy to compare.
3 km = 3 × 1,000 = 3,000 m
2,500 m
Compare the numbers. Compare the digits from the left, starting with the biggest place value.
3,000 > 2,500
Write the answer. Put the sign between the two original measures.
3 km > 2,500 m

Check. 3,000 m and 2,500 m: the bigger number is the bigger measure. ✓

Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.

Worked example 7.4.2

Which is the bigger mass: 1.5 kg or 1,450 g?

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change both measures to the same unit (the smaller one). Then compare the numbers.

Look at the units. We can only compare measures that are in the same unit.
1.5 kg and 1,450 g: the units are different.
Change both to the smaller unit, grams. Changing to the smaller unit gives whole numbers that are easy to compare.
1.5 kg = 1.5 × 1,000 = 1,500 g
1,450 g
Compare the numbers. Compare the digits from the left, starting with the biggest place value.
1,500 > 1,450
Write the answer. Pick the measure with the bigger number.
1.5 kg is the bigger measure.

Check. 1,500 g and 1,450 g: the bigger number is the bigger measure. ✓

Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.

Worked example 7.4.3

Write these lengths in order, smallest first. 2.5 m, 240 cm, 2 m, 260 cm

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.

Change every measure to centimetres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.
2.5 m = 2.5 × 100 = 250 cm
240 cm
2 m = 2 × 100 = 200 cm
260 cm
Put the whole numbers in order. Compare the digits from the left. Order them smallest first.
200, 240, 250, 260
Write the original measures in that order. Match each number back to its measure.
2 m, 240 cm, 2.5 m, 260 cm

Check. Read the ordered list again in centimetres: 200, 240, 250, 260. Each one is bigger than the one before. ✓

Watch out. Keep the original units in your final answer. Do not write the changed numbers.

Worked example 7.4.4

Write these capacities in order, biggest first. 1.5 l, 1,200 ml, 0.75 l, 1,050 ml

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.

Change every measure to millilitres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.
1.5 l = 1.5 × 1,000 = 1,500 ml
1,200 ml
0.75 l = 0.75 × 1,000 = 750 ml
1,050 ml
Put the whole numbers in order. Compare the digits from the left. Order them biggest first.
1,500, 1,200, 1,050, 750
Write the original measures in that order. Match each number back to its measure.
1.5 l, 1,200 ml, 1,050 ml, 0.75 l

Check. Read the ordered list again in millilitres: 1,500, 1,200, 1,050, 750. Each one is smaller than the one before. ✓

Watch out. Keep the original units in your final answer. Do not write the changed numbers.

Worked example 7.4.5

Which unit would you use to measure the length of a pencil: mm, cm, m or km?

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.

Think about the size. Picture the thing. How big, heavy or full is it?
The length of a pencil.
Compare with something you know. These are good sizes to remember.
Sizes to know:
1 mm is about the thickness of a coin
1 cm is about the width of your little fingernail
1 m is about one big step, or the height of a door handle
1 km is about a 12-minute walk
Choose the unit. A pencil is about as long as your hand.
The best unit is cm (centimetres).

Check. A measure like 5 cm makes sense for this. Another unit would give a number that is far too big or too small. ✓

Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.

Worked example 7.4.6

Which unit would you use to measure the mass of a bag of sugar: g or kg?

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.

Think about the size. Picture the thing. How big, heavy or full is it?
The mass of a bag of sugar.
Compare with something you know. These are good sizes to remember.
Sizes to know:
1 g is about a paper clip
1 kg is about a bag of sugar
Choose the unit. A bag of sugar is the example of 1 kg.
The best unit is kg (kilograms).

Check. A measure like 5 kg makes sense for this. Another unit would give a number that is far too big or too small. ✓

Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.

Worked example 7.4.7

What is the mass of an apple?
A 15 g B 150 g C 1.5 kg

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.

Picture the thing. Use something you know to help you.
An apple is a bit lighter than a bag of sugar (1 kg). 150 g is sensible.
Test each answer. Ask whether the number and unit are sensible.
A: 15 g is too small.
B: 150 g is sensible.
C: 1.5 kg is too big.
Choose the sensible estimate.
150 g

Check. 150 g is about the right size, while the other two are far too big or far too small. ✓

Watch out. An estimate does not need to be exact, but it must be sensible.

Worked example 7.4.8

The block is 1 cm long. Estimate the length of the line.

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Use the 1 cm block as a ruler. Count how many blocks fit along the line.

Look at the block. The block shows 1 cm. It has the same size as one centimetre on this picture.
One block = 1 cm
Compare the line with the block. Picture the block placed end to end along the line. Count how many blocks it takes.
About 8 blocks fit along the line.
Write the estimate. Each block is 1 cm, so the number of blocks is the number of centimetres.
The line is about 8 cm long.

Check. 8 × 1 cm = 8 cm. ✓

Watch out. An estimate needs the unit as well as the number.

Worked example 7.4.9

Round 2,450 g to the nearest 100 g.

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Round to the nearest 100 g: look at the digit in the next place to the right.

Find the hundreds digit and the digit to its right. We round to the nearest 100, so we look at the digit one place to the right of the hundreds.
2,450 g: the digit to look at is 5
Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.
5 is 5 or more, so round UP
Write the rounded measure. The numbers between are 2,400 and 2,500.
2,450 g ≈ 2,500 g

Check. 2,450 is between 2,400 and 2,500. It is closer to 2,500. ✓

Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).

Worked example 7.4.10

Round 3,260 ml to the nearest 1,000 ml (the nearest litre).

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Round to the nearest 1,000 ml: look at the digit in the next place to the right.

Find the thousands digit and the digit to its right. We round to the nearest 1,000, so we look at the digit one place to the right of the thousands.
3,260 ml: the digit to look at is 2
Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.
2 is less than 5, so round DOWN
Write the rounded measure. The numbers between are 3,000 and 4,000.
3,260 ml ≈ 3,000 ml

Check. 3,260 is between 3,000 and 4,000. It is closer to 3,000. ✓

Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).

Watch out

Do not compare the numbers as they are. 2,500 g is less than 3 kg, even though 2,500 is bigger than 3. Always change to the same unit first. And when you choose a unit, check that the number makes sense: a pencil that is “15 m long” is silly.

7.5

Calculating with measures

Year 4
Add and subtract measures, Multiply and divide measures, Measure word problems, Estimate answers

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Calculating with measuresComing soon

We can add, subtract, multiply and divide measures. The golden rule is: the units must be the same. We cannot add 1 m and 45 cm as 1 + 45. First change them both to centimetres: 100 cm + 45 cm = 145 cm.

Adding and subtracting. Use the column method from Chapter 2. Line up the digits, with ones under ones. Add or subtract one column at a time and carry or exchange when you need to. Write the unit in the answer.

For 346 cm + 278 cm the columns look like this.

	H	T	O
	3	4	6
+	2	7	8
	6	2	4
	1	1

Changing back. If the question uses two units (like m and cm), give the answer in two units too. 425 cm is 4 m 25 cm. If it uses decimals (like 2.5 kg), give a decimal. Multiplying and dividing. Work in the smaller unit. 4 × 350 ml = 1,400 ml = 1.4 l. And 1 l ÷ 4 = 1,000 ml ÷ 4 = 250 ml.

Word problems. Read the problem slowly. Draw a bar model. Decide which calculations you need and in what order. Change the units first. Then check that the answer is sensible.

A bar model: a 2 m (200 cm) ribbon. 75 cm and 60 cm are used. How much is left?

Key words. The total is all the amounts added together. The difference is how much bigger or smaller one amount is than another. To estimate is to round first to get a quick check.

Key ideas

The units must be the same before you add or subtract.
Change to the smaller unit. 1 m 45 cm = 145 cm.
Use column addition and subtraction. Carry and exchange when you need to.
Multiply and divide in the smaller unit, then change back if you need to.
Draw a bar model for word problems.
Check: use the inverse, or estimate by rounding.

Worked example 7.5.1

Work out 346 cm + 278 cm.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.

Check the units. We can only add or subtract measures that are in the same unit.
Both measures are in centimetres, so we can go straight to the calculation.
Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.
346 cm + 278 cm = 624 cm
H T O
3 4 6
+ 2 7 8
6 2 4
1 1
Write the answer with its unit. A measure always needs its unit.
624 cm

Check. Use the inverse: 624 − 278 = 346. ✓

Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.

Worked example 7.5.2

Work out 1 m 45 cm + 2 m 80 cm. Give your answer in metres and centimetres.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.

Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.
1 m 45 cm = 1 × 100 + 45 = 100 + 45 = 145 cm
2 m 80 cm = 2 × 100 + 80 = 200 + 80 = 280 cm
Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.
145 cm + 280 cm = 425 cm
H T O
1 4 5
+ 2 8 0
4 2 5
1
Write the answer in metres and centimetres. 100 cm = 1 m, so divide by 100 and keep the remainder.
425 ÷ 100 = 4 remainder 25
425 cm = 4 m 25 cm

Check. Use the inverse: 425 − 280 = 145. ✓

Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.

Worked example 7.5.3

A jug holds 1 litre. Mia pours out 350 ml. How much is left in the jug?

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.

Change both measures to millilitres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.
1 l = 1 × 1,000 = 1,000 ml
Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.
1,000 ml − 350 ml = 650 ml
Th H T O
01 90 100 0
− 3 5 0
6 5 0
Write the answer with its unit. A measure always needs its unit.
650 ml

Check. Use the inverse: 650 + 350 = 1,000. ✓

Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.

Worked example 7.5.4

Work out 3 kg − 1.25 kg.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.

Change both measures to grams. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.
3 kg = 3 × 1,000 = 3,000 g
1.25 kg = 1.25 × 1,000 = 1,250 g
Take the smaller measure away from the bigger. Subtract column by column. Exchange when a top digit is too small.
3,000 g − 1,250 g = 1,750 g
Th H T O
23 90 100 0
− 1 2 5 0
1 7 5 0
Write the answer in kilograms. 1,000 g = 1 kg, so divide by 1,000.
1,750 g = 1,750 ÷ 1,000 = 1.75 kg

Check. Use the inverse: 1,750 + 1,250 = 3,000. ✓

Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.

Worked example 7.5.5

A glass holds 350 ml. How much do 4 glasses hold? Give your answer in litres.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Multiply the measure by 4. Keep the unit.

Multiply each part of 350 by 4. Splitting the number into hundreds, tens and ones makes the times tables easier (the distributive law).
4 × 300 = 1,200
4 × 50 = 200
1,200 + 200 = 1,400
Write the total with its unit.
1,400 ml
Write the answer in litres. 1,000 ml = 1 l.
1,400 ÷ 1,000 = 1.4 l

Check. Divide back: 1,400 ÷ 4 = 350. ✓

Watch out. The unit stays the same when you multiply by a number. 4 lots of 350 ml is still in ml.

Worked example 7.5.6

Share 1 litre of juice equally between 4 friends. How much does each friend get?

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Share by dividing. Work in the small unit and keep the unit.

Change the measure to millilitres. Work in the smaller unit so we have a whole number.
1 l = 1 × 1,000 = 1,000 ml
Divide 1,000 by 4. Use a times-table fact. 100 ÷ 4 = 25, and 1,000 is 100 × 10.
100 ÷ 4 = 25
25 × 10 = 250 ml
Write the answer with its unit. A measure always needs its unit.
250 ml

Check. Multiply back: 4 × 250 = 1,000. ✓

Watch out. Change to the small unit first, so you have a whole number to divide. 1 l shared between 4 is 1,000 ml ÷ 4 = 250 ml.

Worked example 7.5.7

Priya has a ribbon 2 m long. She uses 75 cm for a bow and 60 cm for a card. How much ribbon is left?

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the ribbon to centimetres. Add up what was used. Then take it away from the whole ribbon.

Change 2 m to centimetres. The pieces are in cm, so we use cm for everything.
2 m = 2 × 100 = 200 cm
Add the two pieces used. Find out how much ribbon was used in total.
75 + 60 = 135 cm
Subtract the total used from the whole ribbon. What is left is the whole ribbon take away what was used.
200 − 135 = 65 cm
Write the answer.
65 cm of ribbon is left.

Check. Add back: 75 + 60 + 65 = 200. ✓

Watch out. Take away the TOTAL used (135 cm), not just one piece.

Worked example 7.5.8

A box has a mass of 850 g. It holds 3 books. Each book has a mass of 450 g. What is the total mass of the box and the books? Give your answer in kg and g.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. First find the mass of the 3 books. Then add the mass of the box. Finally change to kilograms and grams.

Find the mass of 3 books. Each book is 450 g. Multiply by 3.
3 × 450 = 3 × 400 + 3 × 50 = 1,200 + 150 = 1,350 g
Add the mass of the box. The total mass is the books plus the box.
1,350 + 850 = 2,200 g
Change to kilograms and grams. 1,000 g = 1 kg.
2,200 ÷ 1,000 = 2 remainder 200, so 2,200 g = 2 kg 200 g

Check. 2 kg 200 g = 2,200 g. And 850 + 1,350 = 2,200. ✓

Watch out. Work out the 3 books first, then add the box.

Worked example 7.5.9

Estimate 598 g + 407 g, then work it out exactly.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Round each number to the nearest 100 to make an estimate. Then work out the exact answer.

Round each mass. 598 is close to 600 and 407 is close to 400.
598 g ≈ 600 g and 407 g ≈ 400 g
Add the rounded numbers. These are easy to add. This is our estimate.
600 + 400 = 1,000 g
Work out the exact answer. Use the column method.
598 + 407 = 1,005 g
Th H T O
5 9 8
+ 4 0 7
1 0 0 5
1 1 1
Compare. The exact answer should be close to the estimate.
1,005 is close to 1,000. The answer is sensible.

Check. 1,005 − 407 = 598. ✓

Watch out. An estimate does not give the exact answer. It tells you if your answer is sensible.

Watch out

Same units first! 1 m + 45 cm is not 46 cm and not 1.45 cm. Change to cm: 100 cm + 45 cm = 145 cm. Also, when you subtract from 1 litre or 1 kilogram, change it to 1,000 ml or 1,000 g first, then use the column method.

7.6

Perimeter

Year 4
Perimeter of rectilinear shapes in cm and m, Perimeter of squares and rectangles, Missing sides

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: PerimeterComing soon

The perimeter of a shape is the distance all the way round its edge. Imagine walking round the edge of a field and ending up where you started. The length of your walk is the perimeter. We measure it in cm or m (the same units as length).

Each side of a square is 1 cm. The orange dots show the edges on the outside. Count them all the way round: that is the perimeter.

Rectangles. A rectangle has 2 long sides and 2 short sides. Opposite sides are equal. So we only need to know two sides. Add all four sides, or add the length and the width and double it.

The top is 9 cm, so the bottom is 9 cm. The right side is 4 cm, so the left side is 4 cm. Perimeter = 9 + 4 + 9 + 4 = 26 cm.

Squares. A square has 4 equal sides. For a square with sides of 6 m, the perimeter is 6 + 6 + 6 + 6 = 4 × 6 = 24 m.

Shapes with missing sides. Some sides are not labelled. We can work them out. Imagine walking all the way round and back to the start. You go right exactly as far as you go left. And you go down exactly as far as you go up. In this shape, the top is 8 cm. The sides along the bottom must also add up to 8 cm. One of them is 4 cm, so side a = 8 − 4 = 4 cm.

An L-shape. Sides a and b are not labelled. Going right = 8. Going left = 4 + a. Going down = 3 + 3. Going up = b. So a = 4 cm and b = 6 cm.

Key words. The perimeter is the distance round a shape. A rectilinear shape has straight sides that meet at right angles. A square has 4 equal sides. A rectangle has 2 pairs of equal sides.

Key ideas

Perimeter = the distance all the way round the edge. Units: cm or m.
Rectangle: add all four sides, or double (length + width).
Square: 4 × the side.
Missing sides: you go right as far as you go left, and down as far as you go up.
Add ALL the sides, including the ones you worked out.
Perimeter is a length, so it is in cm or m (not cm²).

Worked example 7.6.1

Each square has sides of 1 cm. What is the perimeter of the shape?

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.

Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.
Count only the edges on the OUTSIDE.
Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.
Top: 4
Right: 4
Bottom: 4
Left: 4
Add them.
4 + 4 = 8
8 + 4 = 12
12 + 4 = 16
Write the perimeter with its unit.
Perimeter = 16 cm

Check. The top (4) matches the bottom (4), and the left (4) matches the right (4). That is a good sign. 2 × (4 + 4) = 16. ✓

Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.

Worked example 7.6.2

Find the perimeter of the rectangle.

Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.

Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.
9 cm, 4 cm, 9 cm, 4 cm
Add the sides, one at a time. The perimeter is all the sides added together.
9 + 4 = 13
13 + 9 = 22
22 + 4 = 26
Write the perimeter with its unit.
Perimeter = 26 cm

Check. Another way: double the length and the width. 2 × (9 + 4) = 2 × 13 = 26. ✓

Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.

Worked example 7.6.3

A square playground has sides of 6 m. What is the perimeter of the playground?

Method. A square has four equal sides, so the perimeter is 4 times the side length.

Remember: a square has 4 equal sides. We only need one side length.
Each side is 6 m.
Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.
6 + 6 + 6 + 6 = 4 × 6 = 24 m
Write the perimeter with its unit.
Perimeter = 24 m

Check. Half way: 6 + 6 = 12 and 12 + 12 = 24. ✓

Watch out. Do not just give one side. The perimeter goes all the way round.

Worked example 7.6.4

Amira wants to put a fence all the way round her rectangular garden. The garden is 20 m long and 8 m wide. How long does the fence need to be?

Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.

Add the length and the width. These two sides are half of the way round.
20 + 8 = 28 m
Double it. The other two sides are the same, so we go round twice.
2 × 28 = 56 m
Write the perimeter with its unit.
Perimeter = 56 m

Check. Add all four sides: 20 + 8 + 20 + 8 = 56. ✓

Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.

Worked example 7.6.5

Find the perimeter of the L-shape.

Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.

Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.
8 cm, 3 cm, 4 cm, 3 cm, a, b
Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.
Going right: 8
Going left: 4 + a
These are equal, so: a = 8 − 4 = 4 cm
Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.
Going down: 3 + 3
Going up: b
These are equal, so: b = 6 cm
Add all the sides. Now every side has a length. Add them one at a time.
8 + 3 = 11
11 + 4 = 15
15 + 3 = 18
18 + 4 = 22
22 + 6 = 28
Write the perimeter with its unit.
Perimeter = 28 cm

Check. The shape fits inside a 8 cm by 6 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (8 + 6) = 28. ✓

Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.

Worked example 7.6.6

Find the perimeter of this L-shape. Work out the missing sides first.

Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.

Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.
10 cm, 4 cm, 4 cm, 3 cm, a, b
Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.
Going right: 10
Going left: 4 + a
These are equal, so: a = 10 − 4 = 6 cm
Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.
Going down: 4 + 3
Going up: b
These are equal, so: b = 7 cm
Add all the sides. Now every side has a length. Add them one at a time.
10 + 4 = 14
14 + 4 = 18
18 + 3 = 21
21 + 6 = 27
27 + 7 = 34
Write the perimeter with its unit.
Perimeter = 34 cm

Check. The shape fits inside a 10 cm by 7 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (10 + 7) = 34. ✓

Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.

Worked example 7.6.7

Find the perimeter of the T-shape.

Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.

Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.
9 cm, 2 cm, 3 cm, 3 cm, 3 cm, 3 cm, a, b
Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.
Going right: 9
Going left: 3 + 3 + a
These are equal, so: a = 9 − 6 = 3 cm
Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.
Going down: 2 + 3
Going up: 3 + b
These are equal, so: b = 5 − 3 = 2 cm
Add all the sides. Now every side has a length. Add them one at a time.
9 + 2 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
20 + 3 = 23
23 + 3 = 26
26 + 2 = 28
Write the perimeter with its unit.
Perimeter = 28 cm

Check. The shape fits inside a 9 cm by 5 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (9 + 5) = 28. ✓

Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.

Worked example 7.6.8

A rectangle has a perimeter of 38 cm. One side is 12 cm long. How long is the other side?

Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.

Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.
2 × 12 = 24 cm
38 − 24 = 14 cm
Share what is left between the two other sides. The two other sides are equal, so halve the answer.
14 ÷ 2 = 7 cm
Write the answer.
The other side is 7 cm.

Check. Check by adding: 12 + 7 + 12 + 7 = 38. ✓

Watch out. Do not halve the perimeter and stop. Take away the known sides first.

Worked example 7.6.9

A square has a perimeter of 36 cm. How long is each side?

Method. A square has 4 equal sides, so divide the perimeter by 4.

Remember: the 4 sides of a square are equal. So the perimeter is 4 times one side.
4 × side = 36 cm
Divide the perimeter by 4. Division is the opposite of multiplying.
36 ÷ 4 = 9 cm
Write the answer.
Each side is 9 cm.

Check. 4 × 9 = 36. ✓

Watch out. Divide by 4, not by 2.

Watch out

Do not forget the sides you cannot see numbers on. Count all the sides (an L-shape has 6). Do not multiply the length by the width: that gives the area, not the perimeter. And for a rectangle you need four sides, not two.

7.7

Area: counting squares

Year 4
Area of rectilinear shapes by counting squares, Rows and columns, Area and perimeter

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Area: counting squaresComing soon

The area of a shape is the amount of flat space inside it. To find the area, we cover the shape with squares that are all the same size and count them. If each square is 1 cm by 1 cm, then each square has an area of 1 square centimetre, written 1 cm².

Count the squares one by one. There are 16 squares, so the area is 16 cm². (Each square is 1 cm by 1 cm.)

Count in rows. Counting row by row is neat. In the shape above there are 4 + 4 + 4 + 2 + 2 = 16 squares.

Rectangles: rows and columns. In a rectangle every row has the same number of squares. So we can multiply: number of rows × squares in each row. This is an array, like in your times tables.

4 rows of 6 squares. 4 × 6 = 24 squares, so the area is 24 cm².

Area is not perimeter. Perimeter is the distance round the edge (in cm). Area is the space inside (in cm²). A shape can have a big area and a small perimeter, or the other way round.

Splitting shapes. To find the area of an L-shape, split it into rectangles, find the area of each one, and add. In the picture each rectangle has its own colour.

The L-shape is split into two rectangles. 8 × 3 = 24 and 4 × 3 = 12. The area is 24 + 12 = 36 cm².

Key words. Area is the space inside a shape. A square centimetre (cm²) is the area of a square with sides of 1 cm. A row goes across and a column goes down.

Key ideas

Area = the number of squares that cover a shape. Units: cm² (or m²).
Count carefully: row by row.
Rectangle: rows × squares in each row (length × width).
Split L-shapes into rectangles. Find each area and add.
Area is the space inside. Perimeter is the distance round the edge. They are different!
A bigger perimeter does not always mean a bigger area.

Worked example 7.7.1

Each square has an area of 1 cm². What is the area of the shape?

Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.

Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.

Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.
Each square has an area of 1 cm² (one square centimetre).
Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.
Row 1: 4 squares
Row 2: 4 squares
Row 3: 4 squares
Row 4: 2 squares
Row 5: 2 squares
Add the rows.
4 + 4 = 8
8 + 4 = 12
12 + 2 = 14
14 + 2 = 16
Write the area with its unit. Area is measured in square units.
Area = 16 cm²

Check. Count in columns instead: 5 + 5 + 3 + 3 = 16. ✓

Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.

Worked example 7.7.2

What is the area of the rectangle?

Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.

Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.
Each square has an area of 1 cm² (one square centimetre).
Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.
Row 1: 6 squares
Row 2: 6 squares
Row 3: 6 squares
Row 4: 6 squares
Add the rows.
6 + 6 = 12
12 + 6 = 18
18 + 6 = 24
Use rows and columns as a quick way. This is a rectangle, so every row has the same number of squares.
4 rows of 6 = 4 × 6 = 24
Write the area with its unit. Area is measured in square units.
Area = 24 cm²

Check. Count in columns instead: 4 + 4 + 4 + 4 + 4 + 4 = 24. ✓

Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.

Worked example 7.7.3

A rectangle is 7 cm long and 5 cm wide. Find its area.

Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)

Picture the squares. The rectangle is 7 cm long, so one row has 7 squares. It is 5 cm tall, so there are 5 rows.
5 rows of 7 squares
Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.
5 × 7 = 35
Write the area with its unit.
Area = 35 cm²

Check. Swap them: 7 × 5 = 35. The answer is the same. ✓

Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.

Worked example 7.7.4

Find the area of the L-shape.

Method. Split the shape into rectangles. Find the area of each one, then add the areas.

Split the shape into rectangles. Rectangles are easy: area = rows × columns. We colour each rectangle so we do not mix them up.
Find the area of each rectangle. Multiply the squares in a row by the number of rows.
Rectangle A: 8 cm by 3 cm, area = 8 × 3 = 24 cm²
Rectangle B: 4 cm by 3 cm, area = 4 × 3 = 12 cm²
Add the areas together.
24 + 12 = 36
Write the area with its unit.
Area = 36 cm²

Check. Count the squares one by one: there are 36. ✓

Watch out. Make sure the rectangles do not overlap and nothing is left out.

Worked example 7.7.5

Each square has an area of 1 cm². Find the area of the staircase shape.

Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.

Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.
Each square has an area of 1 cm² (one square centimetre).
Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.
Row 1: 1 square
Row 2: 2 squares
Row 3: 3 squares
Row 4: 4 squares
Add the rows.
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
Write the area with its unit. Area is measured in square units.
Area = 10 cm²

Check. Count in columns instead: 4 + 3 + 2 + 1 = 10. ✓

Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.

Worked example 7.7.6

Shape A and shape B each have an area of 12 cm². Do they have the same perimeter? Each square has sides of 1 cm.

Method. Find the area and the perimeter of each shape. Then compare.

Find the area of shape A. Count the squares: 2 rows of 6.
2 × 6 = 12 cm²
Find the area of shape B. 3 rows of 4.
3 × 4 = 12 cm²
Find the perimeter of each shape. Add the sides.
A: 6 + 2 + 6 + 2 = 16 cm
B: 4 + 3 + 4 + 3 = 14 cm
Compare. The areas are equal, but the perimeters are not.
Same area (12 cm²), but different perimeters (16 cm and 14 cm).

Check. A: 2 × (6 + 2) = 16. B: 2 × (4 + 3) = 14. ✓

Watch out. Shapes with the same area can have different perimeters.

Worked example 7.7.7

A rectangle has an area of 36 cm². It is 9 cm long. How wide is it?

Method. Area = length × width, so divide the area by the side you know.

Write what we know. Area = rows × columns, so the area is made from the two side lengths.
9 × ? = 36
Divide the area by the side we know. Division is the opposite of multiplication.
36 ÷ 9 = 4
Write the length with its unit. The answer is a length, so it is in cm (not cm²).
The other side is 4 cm.

Check. 9 × 4 = 36. ✓

Watch out. The answer is a length in cm, not an area in cm².

Worked example 7.7.8

A floor is 6 m long and 4 m wide. Square tiles 1 m by 1 m cover the floor. How many tiles are needed?

Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)

Picture the squares. The rectangle is 6 m long, so one row has 6 squares. It is 4 m tall, so there are 4 rows.
4 rows of 6 squares
Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.
4 × 6 = 24
Write the area with its unit.
Area = 24 m²

Check. Swap them: 6 × 4 = 24. The answer is the same. ✓

Watch out. Area is in square units (m²). The perimeter is the distance round the edge, in m. Do not mix them up.

Watch out

Area is in squares, perimeter is in lengths. Do not add the sides to find the area, and do not multiply the sides to find the perimeter. Count every square once only. For an L-shape, make sure your rectangles do not overlap.

Chapter summary

Skill	Method
Reading a ruler	10 mm = 1 cm. Start at 0. Read the whole cm, then count the mm. 7 cm 4 mm = 74 mm = 7.4 cm. If it does not start at 0, subtract the readings.
Nearest cm	Look at the mm: 5 or more rounds up, less than 5 stays. 7 cm 5 mm is about 8 cm.
Scales and jugs	Find the unit. Count the gaps between two numbered marks and divide to find the step. Read the number below the pointer, then count on in steps.
Units	10 mm = 1 cm 100 cm = 1 m 1,000 m = 1 km 1,000 g = 1 kg 1,000 ml = 1 l.
Converting	Big unit to small unit: multiply (3 m = 300 cm). Small unit to big unit: divide (600 cm = 6 m).
Decimals of measures	2.5 m = 250 cm. 1.5 kg = 1,500 g. 0.25 l = 250 ml. 3 m 40 cm = 340 cm.
Comparing and ordering	Change to the same unit (the smaller one) first. 3 km = 3,000 m, which is more than 2,500 m.
Sensible units	1 cm is a fingernail, 1 m is a big step, 1 kg is a bag of sugar, 1 l is a big carton of juice. Choose the unit that gives a sensible number.
Adding and subtracting measures	Same units first. Use columns. 1 m 45 cm + 2 m 80 cm = 145 cm + 280 cm = 425 cm = 4 m 25 cm.
Multiplying and dividing measures	Work in the smaller unit. 4 × 350 ml = 1,400 ml = 1.4 l. 1 l ÷ 4 = 1,000 ml ÷ 4 = 250 ml.
Perimeter	The distance all the way round. Rectangle: 2 × (length + width). Square: 4 × side. Add ALL the sides.
Missing sides	You go right as far as you go left, and down as far as you go up. Work out the missing sides, then add all the sides.
Area	The number of squares inside a shape, in cm². Rectangle: rows × squares in each row. Split L-shapes into rectangles and add.
Area or perimeter?	Area is the space inside (cm²). Perimeter is the distance round the edge (cm). They are different, and a bigger perimeter does not always mean a bigger area.

Can you…?

I can read a ruler in cm and mm, and write a length in cm and mm, in mm, or as a decimal.
I can measure to the nearest cm and mm.
I can read weighing scales, jugs and other scales, and work out what each small mark is worth.
I can change between km and m, m and cm, cm and mm, kg and g, and l and ml.
I can use decimals like 2.5 m = 250 cm and 1.5 kg = 1,500 g.
I can compare and order measures in different units.
I can choose a sensible unit and make a sensible estimate.
I can add and subtract measures, and solve measure problems.
I can find the perimeter of squares, rectangles and L-shapes, including missing sides.
I can find the area of a shape by counting squares, and use rows and columns for rectangles.
I know that area and perimeter are different.

Key terms

Length: How long something is, measured in mm, cm, m or km.
Mass: How heavy something is, measured in g or kg.
Capacity: How much a container holds, measured in ml or l.
Millimetre (mm): A very small unit of length. 10 mm = 1 cm.
Centimetre (cm): A unit of length. 100 cm = 1 m.
Metre (m): A unit of length. 1,000 m = 1 km.
Kilometre (km): A unit for long distances. 1 km = 1,000 m.
Gram (g): A small unit of mass. 1,000 g = 1 kg.
Kilogram (kg): A unit of mass. 1 kg = 1,000 g.
Millilitre (ml): A small unit of capacity. 1,000 ml = 1 l.
Litre (l): A unit of capacity. 1 l = 1,000 ml.
Scale: A line of marks with numbers on it, like on a ruler, scales or a jug.
Step (interval): The amount between two small marks on a scale.
Convert: To change a measure from one unit to another.
Estimate: A sensible guess, or an answer found by rounding.
Perimeter: The distance all the way round the edge of a shape.
Rectilinear: Having straight sides that meet at right angles, like a rectangle or an L-shape.
Area: The amount of flat space inside a shape, measured in square units such as cm².
Square centimetre (cm²): The area of a square with sides of 1 cm.
Row and column: A row goes across. A column goes down.

Total 17 marks. Allow about 17 minutes.

← Chapter 6: Decimals and money Chapter 8: Time →

Year 4 Perimeter, Area and Measures: worked examples and questions with answers

By the end of this chapter you will be able to

You should already know

Where this leads

Exercise P Do you remember?

Reading a ruler: centimetres and millimetres

Key ideas

Watch out

Exercise 7A Reading a ruler

Reading scales, weighing scales and jugs

Key ideas

Watch out

Exercise 7B Weighing scales

Exercise 7C Measuring jugs and straight scales

Changing units: km, m, cm, mm, kg, g, l and ml

Key ideas

Watch out

Exercise 7D Changing units

Comparing, ordering and estimating measures

Key ideas

Watch out

Exercise 7E Comparing, ordering and estimating

Calculating with measures

Key ideas

Watch out

Exercise 7F Adding, subtracting, multiplying and dividing measures

Exercise 7G Measure problems

Perimeter

Key ideas

Watch out

Exercise 7H Perimeter

Area: counting squares

Key ideas

Watch out

Exercise 7I Area

Chapter summary

Can you…?

Key terms

Exercise 7Z Check-up (non-calculator)

Exercise 7X SATs-style questions

	H	T	O
	01	101	122
−		4	7
		6	5

	Th	H	T	O
	01	155	0	0
−		9	0	0
		6	0	0