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Fractions, Decimals, Percentages,
Ratio and Proportion
affectionately known as “FDPRP”
%
2:3
Common misconceptions about
fractions, decimals and
percentages
• Fractions are always parts of 1, never bigger than 1
• Fractions are parts of shapes and not numbers in their
own right
• A fraction such as ¾ is always seen as “three lots of a
quarter”, without recognition that it can also be “a quarter
of three”
• Decimals with more digits are bigger
• Percentages can never be bigger than 100%
Common difficulties with FDPRP in
school
• Many teachers are unaware of their place
within the progression within FDPRP
• Some teachers lack the subject knowledge
to teach FDPRP and are unaware of the
whole progression
• As FDPRP is difficult to teach it suffers
from poor coverage as less confident
teachers sometimes leave it out
• Early building blocks are often not in place
Back in School
• How might you use this progression back
in school?
• Who needs it?
• How will it support your planning and
delivery of lessons?
• Are there complex ideas that could be
started earlier than the progression
document suggests?
FDPRP in practice
• Children often consider fractions in terms
of fractions of shapes and often complete
the same types of activities
• Children rarely embrace fractions within
counting from an early age
• Children often deal with unitary fractions
• Children rarely see fractions within
traditional number activities for example,
15 – 5 ½ = ?
Building Up Visual Pictures of
Fractions
Children need to have a visual picture of the ¼
times table, for example:
1 whole
1/4
1/4
1/4
1/4
2 wholes
1/4
1/4
1/4
1/4
3 wholes
1/4
1/4
1/4
1/4
So what would you have if you had 7 quarters or 14 or
9?
A Fraction Wall as a Visual Image
Children need a visual picture of a fraction
wall. They can use a fraction wall to:
• Compare fractions
• Consider equivalence
• Help as a visual aid within problems
A flexible fraction wall can be found within
the interactive teaching programs
Fractions ITP
Building Up Parallel Models for
Fractions, Decimals and Percentages
Research suggests that when children learn
fractions, decimals and percentages
together then their understanding is better.
One way of doing this is to complete
fraction, decimal and percentage walls in the
same way.
Paper folding activity.
Finding Fractions
Children need opportunities to find fractions
of numbers and shapes in a range of
contexts.
One way of doing this is to consider sets
and make fraction statements about them.
Talking about sets
This frequent quick practice can incorporate
work on percentages and ratio and proportion.
Using and Applying with fractions
There is one chocolate bar on one chair, two
chocolate bars on the second and three on
the third. Take it in turns to go and stand
behind the chair that gives you the biggest
share of chocolate bars.
Speaking and Listening Opportunities
Would you rather type activities.
“Would you rather have 2/5 of £35 or 3/9 of
£27?”
Fractional group problem solving situations
Fraction games such as 4 in a row.
Fraction Munchers
Deriving additional statements from a single
Statement, “ I I know x then ……..”
Percentages
What are the strengths of Emma’s
approach?
How does Emma’s lesson develop the
children’s understanding of percentages?
Could the same approach be used for
fractions “ If ¼ of £2.40 is 60p. What else
do you know?”
The Percentage Board
The Percentage board is good strategy for
calculating percentages . It involves
dividing the total by 100 to find 1%. This is
also referred to as the unitary method. For
example wanted to find 7% of £2.00 I
would imagine 2p sitting on every board of
the hundred square. So 7% is 7 lots of 2p
or 14p.
Ratio and Proportion
Many teachers are confused by the
difference between ratio and proportion.
Ratio describes the part to part
relationship.
Proportion describes the part to whole
relationship. So proportion is much more a
fractional measure.
Proportion
What are the strengths of the year 4
teachers approach?
How does the year 4 teachers approach
help the children to develop their
understanding of proportion?
It is essential that the use of ICT and
practical models supports the teaching of
ratio and proportion as shown in this example.