1. family and parenting
2. children

Teaching Guidance
For
Fractions, Decimals and
Percentages
(Overcoming Barriers
Moving Levels 1 to 2, 2 to 3, 3 to 4, 4 to 5)
1 of 2 The National Strategies  Primary
Overcoming barriers in mathematics – helping children move from level 1 to level 2
Can I use the position of both hands to tell the time to the quarterhour on a clock face?
Teaching guidance
Key vocabulary
time, clock, watch, analogue, hour (h), minute (min), o’clock, quarter to, quarter past, half past,
hands, long (minute) hand, short (hour) hand
Models and images, resources and equipment
Use a demonstration clock with geared hands
Analogue clock faces
Ensure that children have opportunities to read the time on a variety of clock faces.
Tell time ITP
Use the ITP to set the clock to a specific time, or to leave the clock running in real time. When using the
ITP ensure that children also have their own clock faces to manipulate.
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2 of 2 The National Strategies  Primary
Overcoming barriers in mathematics – helping children move from level 1 to level 2
Teaching tips
 When demonstrating times on an analogue clock, use a clock with geared hands.
Children should also have small geared clocks for their own use. Simple clock faces
without geared hands do not help children to understand how the long hand moves over
an hour.
 Provide plenty of opportunities to tell the time during the routine of the day. Put children
in charge of letting everyone know when it is lunch time, time to go to assembly, etc.
 Ensure that children apply their knowledge of half and quarter turns to reading the time to
half and quarter hours.
o’clock
quarter past
quarter to
half past





Give opportunities to relate times on clock faces to recognisable events in the day. This
would be particularly supportive of recently arrived EAL learners to help them gain
familiarity with and understanding of the school routine and day. Activities might be
based around matching significant events of the day to a basic timeline or asking
questions and modelling responses so that children hear and get the opportunity to
practise particular language structures, for example language structures used to describe
a point in time (‘What time does…?’, ‘When does…?’) and language structures to
describe the length of time (‘How long is…?’).
Emphasise the key physical features of the clock face, i.e. the significance of the 6, when
‘past’ times become ‘to’ times and the position of the hour hand as the change-over
occurs.
Make a large circle on the floor and place the numbers 1 to 12 around the edge to
represent a clock face. Ask two children to be the hands of the clock and lie down on the
clock face to show a given time. Take photographs for display.
Produce sets of matching cards that enable children to match pictures of everyday
events to clock faces showing the time, or to cards showing how the time is written.
While asking questions about the position of the hands at various times, include those
that cross the hour boundary, for example: ‘It is a quarter to three now. School will finish
in half an hour. What time will that be?’ As children become more confident with telling
the time and positioning the hands, questions like these will begin to establish the
concept of time intervals and lay the foundations of solving problems involving time.
00021-2009CDO-EN
© Crown copyright 2009
The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I use and explain decimal notation for tenths and
hundredths?
Teaching guidance
Key vocabulary
place value, partition, digit, ones, units, tens, hundreds, one-digit number, two-digit
number, three-digit number, tenths, hundredths, compare, order, read, write
Models and images
Number lines
Position decimal numbers on number lines to get a sense of the size and order of
decimals.
1.6
2.4
Decimal number line ITP
Use the Decimal number line ITP to explore
and expand the divisions between numbers
to get a sense of what the decimal parts of
the number represent (e.g. 3.6).
Decimal place value cards and charts
Use decimal place value cards to illustrate what the
different digits represent in decimal numbers (e.g. the 3 in
2.38 represents 3 tenths and is written as 0.3).
Ask children to suggest what number is formed on
the place value chart by combining units and tenths.
Alternatively, children can identify the parts to make
a given number.
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1
The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I use and explain decimal notation for tenths and hundredths? – Teaching guidance
Measuring stick or ruler
Relate decimals to measuring length by using rulers, tape measures and measuring sticks
with different scales to become familiar with decimal numbers written as units of length.
Bead string
If the bead string represents one whole then each set of ten coloured beads represent
a tenth and each individual bead represents a hundredth.
Teaching tips
• Make sure that children understand that the decimal point is used to separate whole
amounts and parts of the whole. You might use place value cards and the Decimal
number line ITP, or pounds and pence with money notation, to illustrate this point.
• Help children become aware of the relative size of decimal numbers by ordering a set
of amounts of money or lengths. Link this to ordering numbers on a number line. Make
sure that you include numbers to overcome misconceptions such as mistaking the
length of the number with its size, for example thinking that 4.05 is larger than 4.5.
• Ensure that as children are introduced to decimal notation they hear and use the
language of tenths and hundredths, i.e. they can read 3.6 as ‘three units and six tenths’
and not just as ‘three point six’.
• Use a simple number line marked in divisions of 0.5 to familiarise children with counting
forwards and backwards in steps of 0.5. Extend this to other number lines to develop
counting in other step sizes (e.g. 0.2).
• Use money and length as practical examples of decimals to place decimal numbers in
context and compare size of numbers. For example:
– Which is the larger amount, £0.75 or 90p?
– Which is longer, 3.06 m or 3.6 m?
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The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I find a unit fraction of a shape, number or quantity by
splitting it into the correct number of equal parts?
Teaching guidance
Key vocabulary
fraction, part, equal parts, one whole, parts of a whole, number of parts, divide, one half,
one third, one quarter, one fifth, one sixth, one tenth, unit fraction
Models and images
Link fractions of amounts and fractions of shapes
⅓ ⅓
⅓
Create shapes divided in halves, quarters,
thirds, etc. using card or paper plates.
Share objects onto the appropriate shape to
find fractions of an amount.
1
/3 of 6 = 2
Ensure that children can also talk about and
explain the inverse of this operation:
2 multiplied by 3 = 6
Counting stick
0
5
1/
4
10
20
of 20
Relate fraction notation to division
1 whole
5
1 whole
5
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5
© Crown copyright 2008
1
The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I find a unit fraction of a shape, number or quantity by splitting it into the correct number of equal parts?
– Teaching guidance
Teaching tips
•
Check that children are able to read and write fractions. (See the section: Can I read
and write fractions and explain their meaning?) Children are frequently able to read the
fractions 1/2 and 1/4 because they have seen them regularly, but may struggle to read
and write other fractions.
•
Ensure that children understand that the bottom number of a fraction (the denominator)
tells you how many pieces the whole is divided into. So 1/5 can be read as ‘one whole
divided into five equal parts’. Explore what happens when these five equal parts are
recombined to make the whole.
•
Reinforce that when a shape (or number) is divided into fractions such as quarters,
each piece must be the same size. This shape is divided into four pieces
but the pieces are not quarters because they are not the same size.
•
Give children practical experience of dividing shapes into fractions. For example:
– Give children a rectangle that is 10 cm long and access to a ruler.
– Explain that you want them to draw lines to divide the rectangle into fifths.
– Ask: How many fifths make one whole? How many pieces must we divide the
rectangle into?
– Ask children to think about how to make sure that each piece is the same size.
•
Use practical resources to link fractions of shapes and fractions of amounts.
– Make a set of card shapes/paper plates divided into halves, thirds, quarters, etc.
– To find, for example 1/3 of 12, ask children which shape shows the appropriate
fraction (thirds).
– Take 12 counters/objects and ask a child to place these onto the shape so that
there is the same number of counters/objects on each third.
– Ask: What is 1/3 of 12?
– Ask children to describe how they found 1/3 of 12. Ask: What number sentence
could we write?
•
Stress the link between fractions and division:
– to find 1/2 of an amount, divide it into two equal sets;
– to find 1/3 of an amount, divide it into three equal sets; etc.
•
Give children opportunities to find fractions of shapes where the shape is divided into
small pieces. These should not always be regular.
For example, say: Shade 1/3 of this shape.
– How many squares is it made from?
– What is 1/3 of 15? How do you know?
– How many squares do you need to shade?
•
Give children opportunities to find fractions of quantities, for example asking them to
divide a metre stick into tenths. Ask: What is 1/10 of 1 metre? Ensure that children
include an appropriate unit of measure in their answer.
00099-2008DOC-EN-27
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The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I read and write fractions and explain their meaning?
Teaching guidance
Key vocabulary
fraction, part, equal parts, one whole, parts of a whole, number of parts, one half,
one third, one quarter, one fifth, one sixth, one tenth, two thirds, three quarters,
unit fraction
Models and images
Use a range of representations
⅔
⅔
0
⅔
1
Fractions ITP
This interactive
program allows
children to create and
compare fractions.
Number lines
Counting in, for example, tenths
along a number line helps children
to understand that tenths
represent one whole divided into
ten equal pieces.
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© Crown copyright 2008
1
The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I read and write fractions and explain their meaning? – Teaching guidance
Teaching tips
• Use practical activities to give children opportunities of making halves, quarters, etc.
Make sure that children know how many of each fraction make one whole.
– Ask children to cut a piece of paper into quarters. Emphasise that quarters should
be exactly the same size. Ask: How many quarters make one whole?
– Ask children to make a strip of paper 1 metre long. Use a metre stick to help divide
the strip into ten equal pieces. Ask: What fraction is each piece? How many tenths
make one whole?
•
Ensure that children know that the bottom number (denominator) of a fraction tells you
how many equal parts the whole is divided into, for example a denominator of 5 tells
you that the pieces are fifths and so five pieces of that size would make one whole.
– Take equal strips of paper. Fold one into halves, one into quarters (half and half
again) and one into eighths (half, half and half again). Label each half, quarter and
eighth. Use this to discuss how many halves make one whole, how many quarters
make one whole, etc. Ask: How can you tell how many of each fraction make one
whole? (The denominator tells you.) Which is bigger, 1/4 or 1/8?
– Label the fractions on a fraction wall or use the Fractions ITP to create strips that
are divided into halves, thirds, quarters, etc. Compare the size of unit fractions –
ask: Which is bigger, 1/2 or 1/3? Which do you think would be bigger, 1/50 or 1/100?
How do you know?
•
Teach children that the top number (numerator) of a fraction tells you how many pieces
you have. In 3/5, the 3 tells you that you have three pieces and
the 5 tells you that each piece is one fifth of a whole. One way
to read 3/5 is ‘3 out of 5’.
•
Count in fractions, e.g. 1/10, 2/10, using
number lines, fraction walls or fractions
of shapes. This helps children to
understand non-unit fractions.
•
Some children are able to write fractions without being able to read them, so plan
activities that involve children in reading fractions aloud, for example the following.
– Matching game: Children pick a picture card, say the fraction that it shows and then
pick a fraction card to see whether it matches.
– Give pairs of children a set of 1–9 digit cards. Children take turns to pick two cards,
then place the smaller digit over the larger to make a fraction, e.g. 7/9, and say the
fraction made. Use a fraction wall to compare the fractions. Whoever has the larger
fraction wins a point. Replace the cards, shuffle them and continue playing.
•
Make sure that children experience a variety of representations for fractions, including
objects, shapes and number lines/strips.
•
Where possible, avoid saying a fraction on its own. Instead, try to say ‘3/5 of a metre’,
‘3/5 of the shape’, ‘3/5 of the line’, etc. Ask questions such as: Which is smaller – a
quarter of an elephant or a quarter of a mouse?
00099-2008DOC-EN-03
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The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I explain what each division means on a numbered or
partly numbered line and use this information to read a scale
to the nearest division or half-division?
Teaching guidance
Key vocabulary
measure, estimate, length, distance, height, depth, weight, capacity, temperature,
measuring scale, interval, division, unit, standard unit, metric unit, approximately, close,
about the same as, ruler, tape measure, balance, scales, measuring cylinder/jug,
thermometer, centimetre (cm), metre (m), millimetre (mm), kilogram (kg), gram (g), litre (l),
millilitre (ml), degree Celsius (°C)
Models and images
Counting stick
0
1 kg
0
200
400
600
800
1000 g
Use sticky notes to partly label the divisions. Discuss the missing numbers. Change the
labels to represent 0–1 litre. Hold the counting stick vertically to represent a thermometer
or a measuring jug.
Measurement ITPs
Measuring cylinder ITP
Use measurement ITPs to provide
examples of different types of scales and
demonstrate how to read them.
Settings can be changed to show various
ranges and intervals.
Measuring scales ITP
Thermometer ITP
00099-2008DOC-EN-19
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1
The National Strategies | Primary
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Can I explain what each division means on a numbered or partly numbered line and use this information to read a scale
to the nearest division or half-division? – Teaching guidance
Teaching tips
•
Plan practical activities that involve children using different types of measuring
equipment. Assess whether children have the skills they need to read scales
accurately.
•
Ensure that children have regular experience of placing numbers and reading numbers
on partly marked number lines.
•
A key skill that children need in order to read scales accurately is being able to work
out the value of each interval. In order to do this,
children need to:
– identify two labelled divisions such as 0 g and
50 g;
– count how many intervals lie between these
amounts
(Note: Make sure that children understand that they must count the number of
jumps between each labelled division rather than the number of marks);
– use division to work out the value of one interval;
– count along the scale to check that this interval is correct.
•
Ensure that children know relationships between units of measurement. See the
resource: Can I explain the relationship between km and m, m and cm, kg and g,
l and ml?
•
It is important to select equipment that is marked clearly enough for children to read.
For instance, ordinary kitchen equipment may have scales that are very difficult for
young children to make sense of, and rulers marked in millimetres can lead to
confusion.
•
Offer children as many experiences as possible to measure for a purpose, so it is
important to be accurate, for example following a recipe, carrying out an experiment in
science, making a scale model. Look for cross-curricular opportunities.
•
Images of scales on ITPs are useful for supporting
explanations and as a basis for discussion but are
no substitute for practical experience.
00099-2008DOC-EN-19
Measuring scales ITP
© Crown copyright 2008
2
Can I find simple equivalent fractions?
Teaching guidance
Key vocabulary
numerator, denominator, fraction, proper/improper fraction, equivalent,
reduced to, cancel
Models and images
Model how a fraction wall can be used to find equivalent fractions.
Fractions ITP
Demonstrate how a multiplication board can be used to scale up fractions.
Discuss with children what needs to happen, to change 3/4 into other
equivalent fractions.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I find simple equivalent fractions?
Teaching tips
• Children need the opportunity to practise finding equivalent fractions by
scaling simple fractions up or down.
• Use paper-folding to help establish equivalence; for example, fold a strip
of 20 squares into quarters and colour 3/4 of them to establish that 3/4 is the
same as 15 out of 20 or 15/20.
• Focus on recognising the patterns in sets of equivalent fractions and
making links between multiplication and division.
• Represent fractions on a number line. This can help show that the same
point on the number line can have more than one label, for example 1
could also be labelled as 2/2, 3/3, 4/4, 5/5, etc.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I multiply and divide by 10 and 100 and 1000?
Teaching guidance
Key vocabulary
digit, decimal, multiply, times, divide, share, scale up, scale down, increase,
decrease, factor, how many 100s in …?, tens of thousands, thousands,
hundreds, tens, units, ones, tenths, hundredths, thousandths
Models and images
Show children how multiplying a number by 10 moves the digits one place to
the left, and multiplying by 100 moves the digits two places to the left.
Demonstrate the effect of dividing a number by 10. Show children how the
digits move one place to the right, and when dividing by 100 the digits move
two places to the right.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I multiply and divide by 10 and 100 and 1000?
Use a calculator or the Moving digits ITP to model how the digits move when
we multiply or divide by powers of 10.
Moving digits ITP
Teaching tips
•
Help children to generalise correctly so that they can cope with decimals.
Multiplying by 10 gives an answer that is bigger than the original number
and all the digits move one place to the left. Dividing by 10 gives an
answer that is smaller than the original number and all the digits move one
place to the right.
•
Discuss why 4.6 × 10 is not the same as 4.60 and 40.3 ÷ 10 is not the
same as 4.3.
•
Explore with children the relationships between the operations and how to
simplify combinations of operations. For example, multiplying by 10 then
dividing by 100 is the same as dividing by 10. Help children to recognise
that dividing by 200 is the same as dividing by 10, dividing by 10 again
and then halving, by using a calculator to explore different examples.
•
Emphasise that a multiplication and division by 10, 100 and 1000 should
be a mental calculation.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I calculate a fraction of a number or quantity?
Teaching guidance
Key vocabulary
fraction, equal parts, numerator, denominator, divide, division, multiply,
multiplication
Models and images
Use models and images alongside oral work. For example, display 12 small
objects such as counters.
Ask questions such as:
‘What is one third of these 12 counters?’
‘What is two thirds of 12 counters?’
‘What is three thirds of 12?’
Arrange the counters in ways that help children to see the process and
gradually reduce the reference to the counters as the children become more
confident. Record the steps with the children and encourage them to
recognise the underlying counting in 4s.
1
/3 of 12 is 4
2
/3 of 12 is 8
3
/3 of 12 is 12
Link finding fractions of amounts to fractions of shapes, for example:
1
1
/6
/6
/6
1
/6
1
1
1
/6
/6
Find 5/6 of 18.
What is 1/6 of 18? (3 × 6 = 18)
If one sixth is 3, what is five sixths?
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I calculate a fraction of a number or quantity?
Ensure children have experience of finding fractions of a range of wholes.
Give children ‘bags of images to represent the whole’, of which they can then
find fractions, such as 5/6. This could include shapes, numbers, an amount of
money, a length of string, a set of counters and so on.
240
£1.80
Teaching tips
• Children need to be able to relate fractions to division, for example, to
understand that finding one tenth is equivalent to dividing by 10.
• Help children to understand that they are finding a fraction of a whole
amount by using practical equipment to explore a variety of different
wholes (see image box above).
• Use different models and images to help children understand that a
fraction such as 4/5 is 1/5 × 4, and finding 1/5 is the first step to finding 4/5.
This will help them begin to associate finding 4/5 with ‘divide the whole into
five equal parts and then group together four of these equal parts’.
• Introduce a scale or length to support the process, for example a length
representing 30 cm. Use this to ask questions such as: ‘What is one sixth
of 30 cm? What is two sixths of 30 cm? What is three sixths of 30 cm?’
Identify the steps of 5 cm and the counting process to establish that 1/6 of
30 is 5; 2/6 of 30 is 10; 3/6 of 30 is 15; 4/6 of 30 is 20; 5/6 of 30 is 25; 6/6 of 30
is 30. It is important to establish that 6/6 represents the whole. When they
are confident they can extend the idea beyond the whole to 7/6 and so on.
• When finding a fraction of a quantity, children will also need to consider
whether a unit of measurement is required in the answer. Ensure that they
know the relationships between familiar units of measure.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I express tenths and hundredths as percentages?
Teaching guidance
Key vocabulary
percentage, per cent, %, tenths, hundredths
Models and images
Represent a percentage, using practical resources such as money (£1, 10p
and 1p coins) or images, for example, a 10 by 10 square grid or the Area ITP.
Area ITP used to represent 35 shaded squares out of 100, or 35%.
Teaching tips
• Use ICT resources, such as the Fractions ITP, to explore and instantly
record the link between fractions and percentages.
• Use money to show how 10p can be expressed as a percentage and a
fraction of £1. Give children the opportunity to use coins to convince
themselves that, for example, 10p is 1/10 or 10% of £1 because they need
ten 10p coins to make £1.
• Refer to percentage as being the number of parts per hundred. Reinforce
that 100% represents 100 per 100 or a whole.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I read, write, partition and order decimal numbers?
Teaching guidance
Key vocabulary
decimal, decimal fraction, decimal point, decimal place, tenth, hundredth,
thousandth, significant digit
Models and images
Use the Decimal number line ITP to zoom into a number line and position decimal
numbers.
Decimal number line ITP
Use place-value charts to help identify the value of each digit in a decimal number.
Place-value chart spreadsheet
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I read, write, partition and order decimal numbers?
For decimal numbers with up to two places, use a 10 × 10 grid so that each square
represents 0.01 and each row represents 0.1. Discuss the effect of repeatedly adding
the same decimal number, for example 0.01.
Increasing number grid generator spreadsheet
Teaching tips
• Build on understanding of decimals in the contexts of money and
measures when working with decimal numbers with up to two places.
However, decimal place value should also be planned for and taught in its
own right and not just in those contexts.
• Use number lines to help children order decimals. Present children with
numbers that have different numbers of decimal places for ordering, to
tackle the common misconception that the more digits there are after the
decimal point, the bigger the number.
• Focus on the vocabulary of decimal fractions and encourage children to
read decimal numbers, using the language of tenths, hundredths and
thousandths so that, for example, they know the number comprising two
tenths, five hundredths and nine thousandths is written as 0.259.
• Reinforce the equivalence between fractions and decimals. Fraction
notation gives the language to help understand place value, for example,
knowing 0.01 is equivalent to 1/100 helps you to read this decimal number
as one hundredth and not just as zero point zero one.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I relate simple fractions to their decimal equivalents?
Teaching guidance
Key vocabulary
numerator, denominator, equivalent, proper fraction, decimal fraction, decimal
place, decimal point
Models and images
Use the Moving digits ITP to make links between fraction and decimal equivalents
of tenths, hundredths, and so on. For example, 3⁄10 = 0.3 and 13⁄100 = 0.13.
Moving digits ITP
Use number lines or the Fractions ITP to reinforce the decimal equivalent of fractions
such as 2⁄5 or 1⁄20.
Fractions ITP
Fractions ITP
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I relate simple fractions to their decimal equivalents?
Teaching tips
• Use a calculator and the language of fractions to find decimal and fraction
equivalents. For example, 2/5 is keyed into the calculator as 2 divided by 5
(2 ÷ 5) and shows a decimal equivalent of 0.4 (four tenths).
• Children can look for fraction equivalents by finding decimal equivalents.
Encourage them to make general statements about equivalent fractions.
• Use resources such as equivalent dominoes or washing lines with fraction
and decimal equivalent cards. Invite children to peg the cards on the line
and justify their choice of location.
• Present children with commonly confused fraction and decimal
equivalents, for example, 0.4 and 1/4. Ask them to use images or practical
resources to investigate whether these are actually equivalent; for
example they could use the Fractions ITP.
Fractions ITP
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I convert between units?
Teaching guidance
Key vocabulary
kilometre, metre, centimetre, millimetre, kilogram, gram, litre, millilitre
Models and images
Use the Converting measures spreadsheet to practise and reinforce the
conversion between different measures.
Converting measures spreadsheet
Use the Moving digits ITP to model the effect of multiplying and dividing by 10,
100 and 1000.
Moving digits ITP
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I convert between units?
Teaching tips
• Link converting units of measures to estimating, in order to help children
spot where they have made mistakes, for example, ‘1.5 m cannot equal
15 cm because I know 1.5 m is about my height but 15 cm is half the
length of a ruler.’
• Build the rehearsal of converting units into oral and mental starter
activities, and as a practical context in lessons focused upon calculation
where children are multiplying and dividing by 10, 100 and 1000.
• Explore the language of units, for example, roots from which ‘centi’ and
‘milli’ are derived and where else they are used (e.g. century, centurion).
• Provide regular practical opportunities for children to learn and understand
the relationship between units.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I calculate simple percentages of whole numbers or
quantities?
Teaching guidance
Key vocabulary
hundredths, percentage, equivalent, %, tenths
Models and images
Demonstrate how finding 10% can often be a useful starting point when finding
other percentages. For example, you can find 20% by doubling 10%, find 5%
by halving 10% or find 15% by adding 10% and 5%.
The diagram helps model how 20% of 50 is 10.
Area ITP
Links can be made between fractions and percentages, using the Fractions ITP.
This can help children realise that finding 50% is the same as halving, to find
25% they are finding one quarter, etc.
Fractions ITP
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I calculate simple percentages of whole numbers or
quantities?
Teaching tips
•
When finding a percentage of a quantity, remind children that:
– they might find it helpful to find 1% or 10% first;
– they may need to decide whether their answer needs rounding up or
down;
– if the question is in the context of money and measures, they will need to
remember to include the relevant unit in their answer.
•
Help children make links by creating webs of percentages of numbers and
then comparing the different amounts. For example, ‘What would £2.48
buy in comparison with £248?’
£186
75%
£62
25%
£2.48
1%
£248
100%
£124
50%
£24.80
10%
£74.40
30%
£49.60
20%
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I use my tables to work out multiplication and division facts
with decimals?
Teaching guidance
Key vocabulary
times, multiply, multiplied by, product, multiple of, divide, divided by, divisible by,
quotient, factor, inverse
decimal, decimal point, tenths, hundredths, thousandths
Models and images
Use the Number dials ITP to explore multiples of decimal numbers.
Explore known multiplication facts, such as multiples of 6, before exploring
related facts such as multiples of 0.6.
Number dials ITP
What multiplication table does this diagram represent? How do you know? What are
the missing numbers? What division facts do you know by using this diagram?
Teaching tips
•
Ensure children can confidently multiply and divide by 10 and 100 and that
they understand that multiplying by 10 gives an answer that is bigger than
the original number and all the digits move one place to the left, while
dividing by 10 gives an answer that is smaller than the original number
and all the digits move one place to the right. (See the teaching guidance
‘Can I multiply and divide by 10 and 100 and 1000?’, in the Calculating
strand).
•
Start with known multiplication facts before relating these to decimal
multiplication facts; for example, count on and back in steps of 3 before
relating this to counting on and back in steps of 0.3. Encourage children to
explain the relationship between the two sets of numbers.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
Can I use my tables to work out multiplication and division facts
with decimals?
•
Ensure that children meet and can interpret multiplication and division
calculations that are written in a variety of different ways, for example:
„ × 0.8 = 5.6
9 = 5.4 ÷ z
0.3 × 8 = 6 × 
•
Reinforce the division facts corresponding to multiplication facts; for
example:
8 × 0.7 = 5.6 0.7 × 8 = 5.6 5.6 ÷ 0.7 = 8 5.6 ÷ 8 = 0.7
When solving a missing number question, it is helpful to write down the
other three number sentences and then decide which one is most useful to
use to help find the missing number.
•
Model the use of jottings and encourage children to use jottings to help
keep track of the stages within a mental calculation.
Overcoming barriers in mathematics – helping children move from level 3 to level 4
00695-2007CDO-EN
Primary National Strategy
© Crown copyright 2007
1 of 3
The National Strategies  Primary
Overcoming barriers level 4-5
Can I solve simple problems involving ratio and
proportion?
Teaching guidance
Key vocabulary
problem, pattern, relationship, ratio, proportion, in every, for every, to every, fraction, equivalent,
simplify
Models, images and resources
Ratio and proportion ITP
Use this program to set the a ratio for yellow : pink liquid to
provide a visual image for the relationship between the two
quantities.
The yellow and pink liquid can be combined in a single
measuring cylinder to explore what proportion of the total
mixture is each colour.
Number lines and scales
Children need to be able to work out the
value of each interval on a number line
using the proportion that it represents of
a known amount.
120
B
200
Scale drawings, models and scaled maps
The ratio of a length on a drawing, model or map
to the equivalent length on the real item is given
by the scale.
Northcott
Westbury
Eastfield
Scale 1 cm : 5 km
00904-2009EPD-EN-01
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Line graphs
Graphs can be used to compare related
measurements. Where the measurements
are in a constant ratio, for example, in
conversions between units of
measurement or currencies, the graph
formed will be a straight-line graph.
Teaching tips
Proportion

Proportion describes the relationship between part of a quantity or measure and the whole. For
example:
o What proportion of the class is female? The class contains 25 children and ten out of the 25
are girls. Therefore 10/25, or 2/5, of the class are female.
Make sure children appreciate that where a proportion can be described as, for instance 3 out
of 4, this can be written as the fraction 3/ 4 .

Ensure that children meet proportion described in different ways:
o
o
o
o
o

Using everyday language: ten out of 25 children are girls; ten in 25 children are girls.
In simplified form: two out of every five children are girls; two in every five children are girls.
As a fraction: 2/ 5 of the class are female.
As a decimal: 0.4 of the class are female.
As a percentage: 40% of the class are female.
Rehearse scaling proportions up and down. This technique can be used to solve problems.
Provide visual images, for example:
one in four tiles is black
two in eight tiles is black
three in 12 tiles are black
Ratio

Ratio can describe a part to part relationship. For example:
The ratio of girls to boys in a class is two to every three (represented as 2:3).
Ratio can also describe the relationship between two comparable quantities/measures:
The ratio of a distance on a map to the distance on the ground is 1:10 000.

Ensure that children understand and can use ratios described in different ways:
o
o
Using everyday language: there is one black tile to three white tiles; there is one black tile
for every three white tiles.
Using a colon (use everyday language first, then the colon form):
The ratio of black tiles to white tiles is one to every three.
The ratio of black tiles to white tiles is 1:3.
The ratio of white tiles to black tiles is 3:1.
00904-2009EPD-EN-01
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
Ensure that children can use and describe ratios in their simplest form, for example 1:3 is the
simplest form of the relationship 3:9.

Rehearse scaling ratios up/down. This technique can be used to solve problems:
o
o
o
5 miles is approximately equal to 8 km
10 miles is approximately equal to 16 km
15 miles is approximately equal to 24 km.
Ratio and proportion

Where ratio is describing part to part, this can be linked to the proportion of the whole, for
example:
The ratio of black to white tiles on a wall is 1:3. This means that for every one black tile there
are three white tiles. Therefore there is one black tile in every four tiles and so ¼ of the tiles are
black.
00904-2009EPD-EN-01
© Crown copyright 2009
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The National Strategies  Primary
Overcoming barriers level 4-5
Can I explain and use ratio notation?
Teaching guidance
Key vocabulary
ratio, for every, to every, equivalent, simplify, problem, pattern, relationship, scale up/down
Models and images and resources
Ratio and proportion ITP
This program enables you to set the ratio for yellow:pink
liquid that is poured into two measuring cylinders. This
provides a visual image for the relationship between two
quantities in this ratio.
A scale factor can be used that scales up the amount of
each colour poured in.
Fraction ITP
This program allows you to break a strip
into different parts and to colour some of
the parts yellow. The program can
display the ratio of yellow to green parts.
Area ITP or tiles or squared paper
Rows of coloured tiles or squares can be displayed
in a given ratio to create a sequence of equivalent
ratios.
3 orange:2 pink
6 orange:4 pink
9 orange:6 pink...
Number lines or counting stick
12
10
8
6
4
2
18
15
12
9
6
3
00904-2009EPD-EN-01
A sequence of equivalent ratios is produced when a given ratio is scaled up
by a factor of one, then two, then three...
This can be represented on a number line or counting stick.
Encourage children to describe the patterns within the sequence.
© Crown copyright 2009
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The National Strategies  Primary
Overcoming barriers level 4-5
Teaching tips

Ratio can describe a part to part relationship. For example:
– The ratio of girls to boys in a class is two to every three (represented as 2:3).
Ratio can also describe the relationship between two comparable quantities/measures:
– The ratio of a distance on a map to the distance on the ground is 1:10 000.

Provide visual images for ratios then ask children to describe the scenario using the language
and notation of ratio, and vice versa:
–
Each cone has two scoops of chocolate ice cream to every one scoop of strawberry.

Ensure that children understand and can use ratios described in different ways:
– Using everyday language: there is one black tile to three white tiles; there is one black tile
for every three white tiles.
– Using a colon (use everyday language first, then the colon form):
The ratio of black tiles to white tiles is one to every three.
The ratio of black tiles to white tiles is 1:3.
The ratio of white tiles to black tiles is 3:1.

Ensure that children can use and describe ratios in their simplest form, for example 1:3 is the
simplest form of the relationship 3:9.
Demonstrate how ratios can be simplified in a similar way to fractions:

12 yellow:8 red
3 yellow:2 red
The following activity/activities available via the NRich site can be used to support use and
application of mathematics associated with this Can I sequence.
Pumpkin Pie Problem http://nrich.maths.org/public/viewer.php?obj_id=1026
00904-2009EPD-EN-01
© Crown copyright 2009
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The National Strategies  Primary
Overcoming barriers level 4-5
Can I work out the whole, having been given the
fraction?
Teaching guidance
Key vocabulary
fraction, numerator, denominator, unit fraction, whole, equivalent
Models and images and resources
Fractions of a whole set
Use objects to model fractions of a whole set. Show two
groups of cubes and explain that this shows 2/ 5 of the whole
set. Encourage children to use and extend this model to
explain how they can work out the number of cubes in the
whole set.
■■■■■
■■■■■
Counting stick or Counting stick with further options spreadsheet
Attach cards onto a counting stick to create a sequence of fractions. Show a given fraction of the
whole. Ask children what other fractions they can find using this piece of information. Alternatively,
annotate the spreadsheet Counting stick with further options.
Fraction number lines
Ask children to use given information to add details to the number line.
Masters of fraction number lines are provided in the Consolidation and practice section.
Diagrams
Model how to draw diagrams to show
information given about the fraction of an
amount and annotate these to find the whole.
Encourage children to develop their own
diagrams and explain their methods.
00904-2009EPD-EN-01
2
/ 5 of a number is 20. What is the number?
© Crown copyright 2009
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Overcoming barriers level 4-5
2 of 3
Pie chart spreadsheet
Reveal the number of children
represented by one segment. Discuss
what fraction of the pie chart represents
these children. Use this to work out the
total number of children.
Teaching tips

Ensure that children are confident in reading and writing fractions, and in recognising fractions
of amounts, shapes or objects. Clarify the role of the numerator and denominator of a fraction:
in other words, the denominator tells you how many equal parts a whole is divided into; the
numerator tells you how many of these equal parts are being considered.

In mental and oral starters, count in fractional steps and place fractions on a number line. Use
opportunities that arise to discuss equivalent forms of fractions:
0, 1/ 8 , 2/ 8 , 3/ 8 , 4/ 8 , 5/ 8 , 6/ 8 , 7/ 8 , 8/ 8 or 0, 1/ 8 , 1/ 4 , 3/ 8 , 1/ 2 , 5/ 8 , 3/ 4 , 7/ 8 , 1

Make sure that children have secure methods for finding fractions of amounts. For example,
children should be able to explain how they would find 3/ 5 of 200. Encourage them to explain
each step involved:
whole of 200 = 200 ÷ 5 1
/ 5 of 200 = 40 × 3 × 3 3
/ 5 of 200 = 120 ÷ 5 
Ensure that children can continue patterns in fractions of amounts:
1
/ 5 of 200 = 40
2
/ 5 of 200 = 80
3
/ 5 of 200 = 120...

Initially, give children unit fractions of an amount and ask them to tell you the whole:
1
/ 10 of a number is eight. What is the number?
o
Ensure that children can explain their reasoning. For example: 1/ 10 of a number is eight, so
2
/ 10 of the number is 16, 3/ 10 of the number is 24, and so on; the whole number is 10/ 10 , so it
will be 10 × 8, that is, 80.
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The National Strategies  Primary
Overcoming barriers level 4-5
When they are given a non-unit fraction and asked to find the whole, encourage children to find
the unit fraction first. For example:
3
÷ 3 × 5 / 5 of number = 120 1
/ 5 of number = 40 whole number = 200 ÷ 3 × 5 
Encourage children to draw diagrams to show the fraction they are given and to annotate this
to find the whole number.

Use real-life contexts for problems, including those that involve approximation:
o
There are about 36 000 000 people aged 16 to 65 in the UK. This is roughly 3/ 5 of the
population. What is the approximate population of the UK?
00904-2009EPD-EN-01
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1 of 2
The National Strategies  Primary
Overcoming barriers level 4-5
Can I solve multi-step problems involving
percentages and/or fractions?
Teaching guidance
Key vocabulary
per cent, hundredth, fraction, proper, numerator, denominator, equivalent, proportion
Models and images and resources
Fractions ITP
This ITP can be used to compare fractions and find equivalent fractions. It can also show
equivalence between fractions, decimals and percentages.
Counting sticks and number lines
Placing fractions, decimals and
percentages on counting sticks and
number lines helps children to
understand that these are different
ways of representing numbers.
They provide a visual means of
comparing and ordering fractions,
decimals and percentages, and of
identifying equivalents.
Spider diagrams
25% = £7.50
10% = £3
50% = £15
100% = £30
20% = £6
1% = 30p
30% = £9
2% = 60p
These can help children use known percentages or fractions of numbers to generate other
percentages or fractions through scaling and combining.
00904-2009EPD-EN-01
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The National Strategies  Primary
Overcoming barriers level 4-5
2 of 2
Teaching tips

When finding fractions of amounts, encourage children to find the unit fraction first and then to
scale this up to find a non-unit fraction if required. For example, to find 3/ 5 of 40:
1
/ 5 of 40 = 8
×3
×3
3

Encourage children to draw diagrams to represent situations or problems involving fractions.
Model how to do this, for example:
2

/ 5 of 40 = 24
/ 5 of a number is 20. What is the number?
When finding percentages of amounts, encourage children to work out key percentages such
as 50% and 10% to help them to find the required percentage.
For example, to find 15% of £40:
10% of £40 = £4
halving gives 5% of £40 = £2
adding these gives 15% of £40 = £6


Model how to record the steps in a multi-step problem so that each stage is clear. Encourage
children to develop confidence by writing down every calculation they do, even when they work
them out mentally or on a calculator.
For example: Charlie has saved £15 towards buying a computer game. This is 3/ 5 of the cost of
the game. How much does the game cost?
o We know that 3/ 5 of the cost = £15
o
So 1/ 5 of the cost = £15 ÷ 3 = £5
o
If 1/ 5 of the cost is £5, then the whole cost = £5 × 5 = £25
o
The game costs £25
Help children to be aware that there are two main types of problems involving fractions or
percentages of amounts:
(a)You are asked to find a given fraction or percentage of an amount.
For example Ian scores 80% in a test. There were 40 questions. How many did he get right?
Whole test = 100% = 40 questions
10% = 4 questions
80% = 32 questions
(b) You are told an amount and asked to work out what fraction or percentage it is of
another amount.
For example, I score 30 out of 50 in a test. What percentage is this?
Whole test = 50 questions = 100%
5 questions = 10%
30 questions = 60%

Both types can be solved by writing what you know and then using proportional reasoning as
shown above.
00904-2009EPD-EN-01
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1 of 2
The National Strategies  Primary
Overcoming barriers level 4-5
Can I extend my written methods for multiplying
whole numbers to multiplying decimals by whole
numbers?
Teaching guidance
Key vocabulary
place value, digit, column, decimal point, tenth, hundredth, thousandth, partition, integer, method,
strategy
Models, images and resources
Place-value cards
0.05
0.3
Use place-value cards to model how to partition decimal numbers before multiplying each part and
then recombining to get the final product.
Grid method or Multiplication grid ITP
Even where children are working with a
compact written method for multiplication, it is
sensible when first multiplying decimals to go
back to an expanded form such as the grid
method, to help them focus on the value of
each digit in the calculation.
Spider diagrams
42 ÷ 6 =
4.2 ÷ 6 =
0.7 × 6 = 4.2
7 × 6 = 42
0.07 × 6 =
0.007 × 6 =
To be successful at multiplying decimal numbers using a written method, children need to be
completely secure in using known multiplication facts to derive linked decimal facts. Spider
diagrams provide a visual way of recording these facts.
00904-2009EPD-EN-01
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The National Strategies  Primary
Overcoming barriers level 4-5
Teaching tips

Ensure that children know the value of each digit in decimal numbers and can state them as
decimals and fractions, for example, the value of the six in 3.69 is 0.6 or 6/10.

Help children to secure their understanding of place value in decimals. Use resources such as
base ten apparatus or money to represent wholes, tenths and hundredths to provide them with
a visual image. They need to know that ten thousandths = one hundredth, ten hundredths =
one tenth and ten tenths = one whole. Teach them to use this understanding to appreciate that,
for example, 0.06 × 4 = 24 hundredths = two tenths + four hundredths, and so is written as
0.24.

Give children regular practice in using known multiplication facts to derive linked decimal facts.
For example, children should be able to use 6 × 8 = 48 to derive:
0.6 × 8 = 4.8
0.06 × 8 = 0.48
0.006 × 8 = 0.048
0.6 × 0.8 = 0.48, and so on.

Make sure that children can explain each step of their whole-number written method for
multiplication before extending this into working with decimals. They should use the value of
the digit they are working with as part of their explanation, for example, by saying two tens or
20 rather than just two.

Compact methods for multiplication are efficient but often do not make the value of each digit
explicit. When introducing multiplication of decimals, it is sensible to take children back to an
expanded form such as the grid method where the value of each digit is clear, to ensure that
children understand the process.

Insist that children make an estimate for the answer to every written calculation before carrying
it out. This can then be used to check that the answer they get is reasonable.

Give children experience of calculations involving gaps. Ask children to work out the missing
number or digit:
?

Build on children’s understanding of written methods for whole numbers. Demonstrate
multiplication of a decimal number alongside its whole number equivalent: For example:
326
×
8
2400
160
48
2608
00904-2009EPD-EN-01
3.26
×
8
24.00
1.60
0.48
26.08
© Crown copyright 2009
1 of 2
The National Strategies  Primary
Overcoming barriers level 4–5
Can I make use of my understanding of place
value to explain how to mentally multiply or divide
a decimal number by an integer?
Teaching guidance
Key vocabulary
place value, digit, column, decimal point, tenth, hundredth, thousandth, partition, integer
Models and images and resources
Counting stick or Counting stick with further options spreadsheet
Use a counting stick to create related sequences, for example count in sixes and then in 0.6s. Ask
children to comment on the patterns and relationships between the numbers in the two counts and
to use this to predict and explain future terms. Alternatively use the spreadsheet Counting stick
with further options, showing one sequence above the counting stick and a related one below.
Moving digits ITP
Ensure that children are confident in
understanding the effect of multiplying
and dividing numbers by 10, 100 and
1000.
Children need to appreciate that 0.6 is
six divided by ten, in other words that
it is ten times smaller than six.
Place-value cards
0.1
X3
0.3
0.05
0.15
Carry out multiplication calculations involving decimals by partitioning the decimal number using
place-value cards and then multiplying each part separately before recombining to get the answer.
00904-2009EPD-EN-01
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The National Strategies  Primary
Overcoming barriers level 4–5
2 of 2
Teaching tips

Ensure that children understand the effect of multiplying or dividing whole numbers and
decimals numbers by 10, 100 and 1000. Reinforce understand by using visual images:
Put place value or column labels (..., tens, units, tenths, hundredths, ...) onto cards and
stick these onto the wall. Include a decimal point. Ask a group of children to create a
given number, for instance 1.35, by taking the necessary digit cards and standing in the
appropriate places. Ask what will happen when this number is multiplied by ten. Discuss
the effect on each digit – each child should jump a column to the left to show the effect
of multiplying by ten.
o Use the ITP Moving digits. Ask children to predict the answer when a given number is
multiplied or divided by ten, 100 or 1000, before using the program to check.
Check that children fully understand the relationship between the values of digits in different
columns in decimal numbers. For example, children need to appreciate that ten hundredths is
equivalent to one tenth, so 0.13 can be thought of as one tenth + three hundredths or as 13
hundredths.
o


Give children opportunities to identify missing operations and numbers in calculations. Ask
them to explain how they identified the missing number(s) or operation, for instance in:
5

= 0.05
0.6 ×
= 5.4
Give children experience in creating whole number then decimal sequences:
6, 12, 18, 24, 30, 36, ...
0.6, 1.2, 1.8, 2.4, 3, 3.6, ...

Encourage them to explain the relationship between corresponding numbers in the sequences,
in other words to recognise that each number in the second sequence is ten times smaller than
the equivalent number in the first sequence. They should use this information to answer related
calculation questions, for example: If 7 × 6 = 42, what is 7 × 0.6?

Spider diagrams are useful for rehearsing how to use known facts to work out unknown ones:
0.7 × 6 = 4.2
42 ÷ 6 =
4.2 ÷ 6 =
7 × 6 = 42
0.07 × 6 =
0.007 × 6 =

When asked to multiply or divide a decimal by a whole number, children need to identify a
linked whole number fact that can help them. For example, for 2.1 ÷ 3, they need to recognise
that it is linked to the fact 21 ÷ 3 = 7 and use this to help them. Encourage them to explain their
reasoning. For example: 21 ÷ 3 = 7, and 2.1 is ten times smaller than 21, so the answer will be
ten times smaller than seven, in other words 2.1 ÷ 3 = 0.7. Or 21 ÷ 3 = 7, so 21 tenths divided
by three is seven tenths, that is 0.7

In order to multiply decimal numbers with two or more digits, partition them and multiply each
part before recombining answers. The grid method is a clear way to record this thinking:

×
1
0.3
4
4
1.2
so 1.3 × 4 = 4 + 1.2
= 5.2
Always ask children to check that the size of their answer sounds reasonable. For example,
children should recognise that 0.18 ÷ 2 = 0.9 cannot be correct. Using a number line to locate
numbers such as 0.18 and then thinking about dividing by two could help children to check the
reasonableness of an answer.
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1 of 3 The National Strategies  Primary
Overcoming barriers level 4–5 Can I solve problems involving the conversion
of units?
Teaching guidance
Key vocabulary
units of measure and abbreviations, equivalent, length, mass, capacity, pound, ounce,
centilitre, yard, foot, inch
Models and images, resources
Range of measuring equipment using different scales Counting stick or Converting measures spreadsheet 00904-2009EPD-EN-01
© Crown copyright 2009
2 of 3 The National Strategies  Primary
Overcoming barriers level 4–5 Conversion graphs including miles to kilometres conversion
spreadsheet Give children experience of
creating and interpreting line
graphs that demonstrate the
relationships between metric and
imperial measures.
Teaching tips

Ensure that children have regular opportunities to solve practical problems that involve
measurement. This will involve choosing and using suitable equipment, considering
appropriate units and converting between them as appropriate. Draw on opportunities
provided in other curriculum areas such as science and food and design technology.

Make sure that children have ‘benchmarks’ to help them relate to key units of measure.
For example, children could find the distance in kilometres between their home and
school.

Give children experience of choosing suitable units for measurement activities, for
example, considering whether to measure the amount of water in a bath in centimetres
(depth) or litres (capacity). They should be able to list all known units for an aspect of
measure such as capacity and then select the most appropriate unit depending on the
circumstance.

Look at measuring equipment that uses two scales alongside each other to compare
units; for example use a measuring jug that has scales for litres and pints to find
equivalents.

Use a variety of activities, such as ‘loop cards’ and ‘fact of the week’ to help children to
learn the key conversion facts. Stress links with prefixes in spelling, establishing for
example that ‘kilo’ means ‘thousand’, so that 1 kg is the same as 1000 g. Children should
know approximate conversions between common imperial and metric units.

Use mental and oral activities to rehearse strategies for converting units of measure.
Children need plenty of experience of finding equivalents to decimal and fractional
measures such as 2.3 kg or 2 1/ 4 litres.

Make sure that children understand how, why and when to use multiplication or division
by ten, 100 and 1000 to convert between metric units. Encourage children to check that
their answer is reasonable to ensure that they have used the correct operation.
00904-2009EPD-EN-01
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The National Strategies  Primary
Overcoming barriers level 4–5 Establish links with work on ratio and
proportion. Starting from a known fact
such as 1 m = 1000 mm, ask children to
use scaling to generate other facts. The
Converting units of measure spreadsheet
can help children to find equivalent pairs
using scaling.
00904-2009EPD-EN-01
© Crown copyright 2009