How to . . .
measure at
Key Stage 3
Introduction
Pupils who start secondary school with a poor
grasp of numeracy will experience difficulties, not
only in mathematics, but also in other subjects. If
these pupils then leave school still struggling with
basic numeracy skills, they will face significant
disadvantage in the workplace and will be illequipped to face the challenges of everyday life.
Helping to improve pupils’ numeracy skills can
enhance their learning, not just in mathematics,
but right across the curriculum, as well as
significantly improving their life chances.
Section 1
Most pupils in secondary school spend little
more than three hours a week studying
mathematics. It is, therefore, unrealistic to
place the responsibility for improving
standards in numeracy solely on those
teaching mathematics. Teachers in all subject
areas need to be committed to helping pupils
develop their numeracy skills. Pupils who
struggle with mathematics do not always have
sufficient opportunity during mathematics
lessons to consolidate their learning. Regular
opportunities to revisit numeracy skills across
a range of subjects can provide this much
needed additional practice.
• Offers teaching strategies to support
and develop pupils’ understanding of
measurement across the curriculum.
Many pupils fail to make the link between what
they learn in mathematics lessons and the
mathematics that they use and apply in other
areas of the curriculum. A common approach
to important aspects of numeracy, such as
measurement, handling data and calculation,
can help pupils make this vital link. This booklet
is designed to help teachers provide a common
approach to measurement at Key Stage 3.
The guidance offered in the booklet was
written with a specific target group in mind,
namely pupils at Key Stage 3 who have not
yet achieved a solid Level 4 in mathematics. It
is important to recognise, however, that all
pupils will benefit from regular opportunities to
revisit and rehearse their measuring skills in a
variety of contexts across the curriculum.
The booklet is divided into three sections.
• Highlights the problems faced by
pupils when using measuring
instruments.
• Offers practical ways of helping pupils
to measure with greater accuracy.
Section 2
• Outlines the problems faced by pupils
when reading calibrated scales and
digital displays.
Section 3
• Contains two photocopiable resource
sheets* that can be used to produce
individual pupil reference sheets,
laminated ‘maths mats’ or posters:
Resource sheet 1 illustrates common
mistakes made when using
measuring instruments.
Resource sheet 2 contains useful
information about metric units.
What problems do pupils face when using measuring
instruments?
Choosing the correct measuring
instrument for the task
Pupils need to learn how to choose the most
appropriate measuring instrument for the task. It
is all too easy to overlook the need to develop
such independence, particularly when working
with pupils in the target group. Wherever
possible, pupils should be given the opportunity
to select from a range of measuring instruments.
Common mistake
• Choosing instruments with an inappropriate
measuring range, e.g. a spring balance
calibrated from 0 to 500g to find the mass of
an object less than 50g.
0
grams
00
grams
grams
0
100
10010
10
200
20020
20
300
30030
30
400
40040
40
500
50050
50
grams
Action
• Ask pupils to make an estimate of the weight of
the object first and then check the range of each
instrument before deciding which one to use.
Preparing to use measuring
instruments
Measuring skills are often taught initially in the
context of mathematics. It is wrong to assume
that once a particular skill has been taught,
pupils will automatically be able to transfer it to
different contexts across the curriculum.
Common mistake
• Forgetting to set weighing scales to zero
before using them.
0 kg
0 kg
0 kg
1
0 kg
1
1
6
6
1
6
6
2
2
25
5
5
2
5
3
4
3
4
4
3
4
Action
• Remind pupils to ‘zero’ weighing scales before
using them.
• Check that pupils know how to set other
measuring instruments such as trundle wheels
and stopwatches.
Using rulers and tape measures
The ruler is a very familiar measuring instrument
and yet, surprisingly, it is often used incorrectly
by pupils in the target group. It is important that
pupils are given an opportunity to familiarise
themselves with any new piece of equipment
before they start measuring. Rulers and tape
measures are no exception.
Pupils need to be aware that not all rulers are
the same. The scale on most everyday rulers is
indented whilst on others, such as the metal
rulers used in design and technology, the scale
starts at the end.
Common mistake
• Starting to measure from the end of the ruler
rather than the ‘0’ mark on the actual scale.
3
Action
Common mistake
• Remind pupils to check where the scale starts
before using a ruler or tape measure.
• Ignoring the number of whole units and
focusing on the final fraction of a unit, e.g.
reading 3m 75cm as 75cm or 75m.
Using a protractor
Using a protractor can be even more confusing
than using a ruler. Some are circular in shape
whilst others are semicircular. The scales are
marked both clockwise and anticlockwise.
Action
• Encourage pupils to estimate lengths
before measuring as this will allow them to
check whether or not their answer is
reasonable.
Common mistakes
• Placing the edge of the protractor on one of the
lines defining the angle rather than the 0˚ line.
• Reading the angle from the wrong scale.
40
0
14
40
0
14
30
15
0
30
15
0
Measuring liquids and reading
thermometers
13
50
0
0
15
30
160
20
160
20
20
160
12
0
60
0
15
30
20
160
40
0
50
0
40
40
110
70
13
0
180
0
180
0
180
0
180
0
170
10
170
10
170
10
170
10
10
170
100
180
20
60
14
160
20
160
20
0
180
0
13
90
90
100
80
80
110
70
90
80
100 90
100 70
110
60
0
12
40
0
50
0
14
70
110
14
30
15
0
0
60
0
12
13
0
15
30
0
15
30
20
160
50
0
40
14
13
0
30
15
0
12
0
60
50
40
20
160
50
0
0
10
170
110
70
13
14
0
180
0
13
100
180
20
60
14
13
90
90
100
80
80
110
70
90
80
100 90
100 70
110
60
0
12
10
170
50
10
170
70
110
0
180
0
60
0
12
0
180
50
• Help pupils to develop their own personal
references for common metric units, e.g. ‘The
length of my stride is approximately one
metre.’ Encourage pupils to use these when
making an estimate.
Action
• Remind pupils to position the 0˚ line correctly.
• Ask pupils to estimate the angle first as this
will allow them to check whether or not their
answer is reasonable.
Using a long tape measure
Many science and technology tasks require a
high degree of accuracy when taking
measurements. The way you position your eye
when reading a scale can make a difference to
the reading. As with any skill, the ability to use
measuring instruments accurately requires
regular practice. Time spent at the beginning of
the lesson ensuring that pupils have the
necessary measuring skills will save time later.
Common mistake
• Not positioning the eye correctly when reading
the scale on a measuring instrument.
Pupils are often required to measure lengths
greater than a metre, e.g. the dimensions of the
classroom in geography, or the length of javelin/
discus throws in athletics. Pupils in the target
group may have difficulty reading lengths when
using a long tape measure.
1m
2m
Action
3m
60
70
80
• Remind pupils to read the meniscus at eye
level when using a graduated cylinder or
thermometer.
What problems do pupils face when reading scales and
digital displays?
Problem
Teaching strategies
Pupils find it difficult to work out the value
of the unnumbered markers on a scale.
• Remind pupils that reading a scale on a
measuring instrument is like reading a
number line. There are numbers in between
those numbers that are marked.
• Remind pupils that the unnumbered markers
usually represent obvious numbers such as
multiples of 2, 5, 10 or 100. They may also
represent fractional parts of a metric unit, e.g.
0.1kg or 0.25l.
• Demonstrate how pupils can use division to
work out the size of the interval between
each unnumbered marker.
The reading on
the weighing
scale is 2.2kg.
Step 1: Find the size of the labelled intervals.
Step 2: Count the number of subintervals
or spaces (not the lines) between each
labelled interval.
Step 3: Divide the first by the second to
find the size of the subintervals.
The scale is labelled every 100g.
There are five spaces between each label.
100 divided by five is 20. So the smaller
marks represent 20, 40, 60, 80g.
It is common here for pupils to assume that the
gaps on the scale are 100g (or 0.1kg) as they
are most familiar with scales marked in steps of
1, 10 or 100.
The scale is labelled every
one litre. There are four
spaces between each label.
One divided by four is 0.25.
So the smaller marks
represent 0.25, 0.5, 0.75l.
• Use a counting stick or a blank number line
(see Teaching resources) to practise this
method before asking pupils to use the
actual measuring equipment.
Problem
Teaching strategies
Pupils make mistakes when reading decimal
displays on measuring instruments.
• Ask pupils to estimate before they measure.
The reading
on the balance
is 65g.
That can’t be right. A packet of crisps
only weighs 30g. A drawing pin is lighter
than a packet of crisps. It must be 6.5g.
• Help pupils to ‘learn by heart’ and use
specific reference items as a basis for their
estimations.
An A4 piece of paper is roughly 21cm by
30cm.
The height of the classroom door is
about 2m.
The mass of a packet of crisps is about
30g.
A standard can of drink holds 330ml.
The capacity of a standard milk carton is
1l.
It is common here for pupils to ignore the
decimal point, treating the reading as a whole
number.
• Remind pupils to check whether their
readings make sense in the context of the
task.
Pupils have difficulty interpreting
measurements involving decimals.
• Use a number line to demonstrate how the
‘zooming process’ can be used when
comparing awkward measurements such as
2.38m and 2.4m.
David took part in three events at his school’s
sports day. Here is his record sheet.
SPORTS DAY
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
2.3
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.4
Long jump 2.32m 2.4m 2.38m
Javelin
19.52m19.48m19.6m
Discus
14.5m 14.55m14.05m
In the long jump, what
was David’s best
distance?
David’s third
attempt was
his best.
• Use place value cards to help pupils identify
the value of each digit in a decimal fraction.
Ensure that pupils know the equivalent of
one tenth and one hundredth of 1m, 1kg and
1l in cm, g and ml respectively.
2.38m
0.3m or
Many pupils are able to read and record
measurements correctly but lack the ability to
interpret them. Their knowledge of whole
numbers will often lead them to believe that
2.38m is greater than 2.4m.
Pupils need to understand the relative values of
the digits in a measurement involving decimals.
This will not only help to avoid errors like the
one illustrated here, but will give pupils a better
sense of what is being measured.
30cm
3
10
m
0.08m or
8
100
m
8cm
• Demonstrate how to convert measurements
involving decimals into smaller units, e.g.
convert 2.38m into cm.
Hundreds Tens Units TenthsHundredths
2 3 8
2 3 8
N.B. When multiplying decimal numbers by 100, the digits
move two places to the left. The decimal point does not
move.
Teaching resources
Counting stick
A counting stick can be made from a broom
handle or a length of dowelling. Mark the
divisions with electrician’s tape. The stick can
be used to represent part of a scale on a
measuring instrument. The teacher can point
to markers on the stick and ask pupils to say
what values they represent. Pupils can also
count along the scale in unison as the teacher
points to each mark in turn.
What does this marker
represent?
Number lines
Number lines can also be used to represent scales. Blank number lines can be drawn on the
board or on an OHP transparency. Toolboxes designed for use with the interactive whiteboard
often contain number lines. It is also possible to purchase laminated number lines that can be
used with dry-wipe pens. Large number lines are best for whole-class demonstrations, whilst the
desktop varieties are ideal for short interactive teaching sessions.
Show me 3.2m.
How many cm is that?
3m
4m
Place value cards
Place cards can be used to construct and partition decimal fractions. They can be used to
illustrate the principle that the value of a digit depends on its position in a number. In the context of
measures, it is essential to ensure that pupils not only understand that the places after the decimal
point represent tenths, hundredths and thousandths of a whole unit but are also able to express
these as centimetres, grams and millilitres.
2
3
7
2
0.2kg
2
10 kg
200g
0
3
0.03kg
3
100 kg
30g
0
0
7
0.007kg
7
1000 kg
7g
USING WEIGHING SCALES?
200
300
400
500
300
400
500
grams
10
20
30
40
50
10
30
40
50
grams
0
20
0
0
40
14
20
160
30
15
0
50
0
13
40
60
0
12
grams
6
5
0 kg
90
90
100
80
80
110
70
90
80
100 90
100 70
110
60
0
12
100
180
20
60
110
70
13
0
50
12
0
60
13
0
50
50
0
13
60
0
12
50
0
13
70
110
90
90
100
80
80
110
70
90
80
100 90
100 70
110
60
0
12
100
180
20
60
110
70
13
0
50
12
0
60
13
0
50
170
10
180
0
40
170
10
180
0
170
10
180
0
40
170
10
180
0
Remember to estimate the angle first. Use your estimate to check whether or not you have read the correct scale.
50
0
13
40
70
110
0
14
30
15
0
10
170
160
20
0
180
0
15
30
20
160
40
14
30
15
0
0
160
20
10
170
40
0
180
0
15
30
20
160
0
160
20
10
170
0
4
3
2
6
5
0 kg
4
1
3
2
5
6
4
0 kg
USING A LONG TAPE MEASURE?
1
3
1
25
2m
60
3m
70
80
6
Remember to make an estimate first. Use your estimate to check whether or not your reading is sensible.
1m
Make sure you position the 0˚ line correctly.
Make sure your reading includes the whole
metres.
USING A PROTRACTOR?
100
200
grams
0
100
0
Remember to check the range of each
Remember to ‘zero’ the scales before using
instrument.them.
CHOOSING A MEASURING INSTRUMENT?
Resource sheet 1
0
14
14
0
15
30
160
20
0
180
0
30
15
0
14
0
15
30
20
160
14
40
10
170
0
0
180
14
4
0 kg
3
2
You also need to position your eye correctly
when reading a thermometer.
Make sure you read the meniscus at eye level.
MEASURING LIQUIDS?
1
Make sure you start from zero.
USING A RULER?
km
m
cm
x 1000
x100
x 10
The classroom door is about
2m high.
1000m = 1km
100cm = 1m
10mm = 1cm
30cm
A sheet of A4 paper is
about 30cm in length.
kilometre (km)
metre (m)
centimetre (cm)
millimetre (mm)
The distance from
my nose to my outstretched
finger-tip is about 1m.
1m
The diameter
of a 2p coin
is 25mm.
÷1000
÷100
÷10
mm
2m
kg
g
x 1000
x 1000
kilogram (kg)
gram (g)
milligram (mg)
A standard bag of
sugar is 1kg.
1kg
The mass of a packet of crisps
is 30g.
The mass of a drawing
pin is approximately 6g.
÷1000
÷1000
mg
Crisps
30g
1000g = 1kg
1000mg = 1g
LENGTHMASS
Resource sheet 2
l
x 1000
litre (l)
millilitre (ml)
A standard carton of
milk holds 1l.
A can of soft drink
contains 330ml.
5ml
330ml
Cola
A medicine spoon holds 5ml.
1 litre = 1000 cubic centimetres (cm3)
1 ml = 1 cubic centimetre (cm3)
÷1000
ml
CAPACITY/VOLUME
1000ml = 1l
For further information and copies contact:
Basic Skills Cymru
Welsh Assembly Government
Ty’r Afon
Bedwas Road
Bedwas
Caerphilly
CF83 8WT
© The National Institute of Adult Continuing Education
(England and Wales)
ISBN 978 0 7504 5003 4
CMK-22-07-344
D4090809
For a full catalogue of all NIACE’s publications visit:
www.niace.org.uk/publications