1. Part A
Consider which other aspects of arithmetic are relevant and the pre-requisite number skills and
understanding that are necessary before/to support conceptual work on your chosen area
References should be made to literature which explores the learning journey as well as literature
which explores the importance of secure conceptual understanding (ofsted, piaget)does not have
to be specific to fractions but more general on the learning journey.
Learning Journey
What knowledge/skills are needed to do fractions?
KS1 – yr1
Pupils should be taught – recognise, name and write ½ as one of two equal parts of an
object, shape or quantity
Recognise, name and write ¼ and ¾ as parts of two equal parts of an object, shape or
quantity
And find ½, ¼ and ¾ as parts of an object, shape or quantity.
Ensure pupils are taught all of the above fractions as objects and then as operators on discrete and
continuous quantities. As objects pupils recognise and combine fractions as part of a whole. As
operators, pupils recognise and find, for example, half of a length, container, set of objects and
shapes.
KS1 YR2
NUMBER AND PLACE VALUE -They should be introduced to counting in multiples of 3 to support
their understanding of a 3rd
Locate fractions on a number line and use them to find fractions of shapes and quantities solve
simple problems involving ratio and direct proportion NC
Pupils should be taught to recognise, name and write fractions ¼, 1/3, ½, 2/3 and ¾ of a
whole
Count in halves or quarters to ten
Start using the ½ and 2/4 equivalence
Reinforce that fractions can add up to more than one 1 ¼, 1 ½, 1 ¾, 2
Division and multiplication is taught through pupils sharing out quantities, finding simple
fractions of objects, numbers and quantities, doubling numbers and quantities and find
related halves.
KS2 YR3
COMPARE & ORDER unit fractions and fractions with the same denominator

2. Recognise fractions that are equivalent to 1 and ones that add up to 1
Perform calculations with addition and subtraction with the same denominator e.g.
( 5/7 + 1/7 = 6/7)
KS2 YR4
BE AWARE OF MULTIPLICATION AND DIVISION TABLES UP TO 12X12
Reduce fractions to their simplest form
Add and subtract two fractions with common denominators within one whole
Write equivalent fractions when just given the denominator or numerator for one fraction
Pupils practise counting fractions and decimal fractions - should be taught that ½ = 0.5
Ks2 yr 5
Prime numbers
Accurately multiply and divide numbers mentally - drawing upon known facts
Recognise improper fractions and convert them
Writing remainders as a fraction
Division using remainders e.g. 94/4 = 24 r2 = 24.5 = 25 and rounding off
Read and write decimal numbers as fractions e.g. 0.71 – 71/100
Recognise the % symbol and it relates to number as part of 100 e.g. 1/100 is 1%
Write simple fractions as percentages and decimals e.g. ½ = 50% = 0.5).
KS2 YR6 – UPPER
Use of brackets 2+1 x3 = 5 (2+1) x 3 = 9
Divide numbers using long division (4 digits by 2 digits) and interpret remainders as fractions
, decimals or rounding
Add and subtract mixed numbers and fractions with different denominators
Divide proper fractions by whole numbers
Associate fractions with division to calculate decimal fraction equivalents e.g. 0.375 for a
simple (3/8)
E.g. if ¾ of a length is 36 then the whole length is 36 x 4 = 144cm - pupils should understand
the relationship between unit fraction and division to work backwards by multiplying a
quantity that represents a unit fraction to find the whole quantity

3. WHAT DOES PIAGET SAY???
Sensorimotor skills (link numbers to objects)
Preoperitalstage - problem solving with water or blocks – squash www.tlrp.org context
specific. The importance of hands-on experiences cannot be overemphasized. (Burns and
sibly, 2000,p.60)
These activities Gives them the opportunity to test and confirm their learning.
Manipulative materials :pattern blocks, paper folding
Application –connecting mathematical concepts to real-life situations – pizza, chocolate
The numbers and quantities used to teach children should be meaningful to them – piaget
children asked to divide objects among the class.
Children learn that 1/3 of a pizza and 2/6 of a pizza are equivalent but not understand that 1
glass of orange with 2 glasses of water is the same as 2 glasses of orange is the same as 4
glasses of water
Barmby,P., Bilsborough, L., Harries, T and Higgins, S., (2009) Fractions in primary
mathematics Teaching for understanding : Maidenhead: OUP
Multiplying fractions – 2/5 x3/4 In this case, this is where the notion of repeated addition of
starts to break down. It does not mean anything to add 2/5 by ¾ times.
The counting technique DOES NOT REQUIRE THE APPLICATION OF ANY CONCEPTS OF
FRACTIONS AS PART OF A WHOLE.
Number lines – children have difficulties in placing 1/3 at a third of the distance along the
number line however long the number line happens to be.
Relative = part –whole relationship where parts and wholes are made up of discrete objects
Equivalent fractions comparing them e.g. ¾ / 6/8 and 9/12 how do we make comparison
with situations easier? 100 counters and 75 of them are shaded we know that that 75%. %
means out of 100. This is the percentage format for proportions and we can make a direct
link between fractions and percentages using equivalent fractions:
Teaching and learning; research briefing - www.tlrp.org
Most pupils in year 4 and 5 have not grasped the relative nature of fractions as numbers.
This difficulty is primarily conceptual. Teaching pupils fractions must include a focus on the
logical relations involved in this concept.
Pupils have some intuitive of the relative nature of fractions from their experiences with
division. Teaching logical relations should build on pupil’s intuitions.

4. The same fraction may refer to different quantities ½ of 6 or ½ of 8 and that different
fractions may be equivalent because they refer to the same quantity 1/3 and 3/9.It is not
possible for pupils to make further progress in mathematics without a sound grasp of the
relative nature of rational numbers.
Part whole fractions are used to introduce fractions. Denominator shows the number of
equal parts into which a whole was cut and the numerator indicates the number of parts
that were taken. E.g. choc bar cut into 4 equal parts and I ate 1 = ¼
Division situations
If one chocolate is shared among four children, the number 1 refers to the number of
chocolates being shared and 4 refers to the number of recipients. ¼ indicates both the
division 1 divided by 4 and the portion that each child receives
Children performed better at solving fractions problems about division. They compared
fractions and explanations to each other. The arguments were based on the logic of division.
Drawings, through group work showed use of logic division. However, a concern with
partitioning and perceptual comparison often left children confused due trouble drawing
with suffient precision. It moved them away from logic of division.
Division situations provide a sound starting point for pupils
Counting and natural numbers need to be taught in early yrs. as a basis for fractions.
Sharing problems

5. Pre – requisite understanding (required as a prior condition for something else to happen.)
Concept mapping - find out what they know
Mooney , C et al Teaching Theory and practice
Division situations provide a sound starting point for pupils understanding of the logic to
rational numbers but they must not be seen as the only context in which rational numbers
should be taught. Further lessons of fractions should be taught with different situations and
do not remain context specific
Must focus on logical relations involved in teaching fractions
Pupils have some intuitive understanding of the relative nature of fractions from their
experiences
EYFS – NEED TO KNOW number names in order “stable order principle” pg 112
ONE TO ONE CORRESPONDENCE (Counting each item)
Multiplication is inverse to division
Number lines help
Put half of these 10 animals in the ark
Common error with addition fractions is; ½ + 2/3 = 3/5 – because of prior knowledge for
addition
Rational numbers