Part-whole concept - to understand what
fractions actually are
1. Real-life contexts with continuous wholes;
identifying the parts and the whole (pair of
gloves, lanes in a swimming pool, pieces of a
pizza. Can use practical and pictorial
representations as appropriate
(consider the language of ‘fair sharing’)
2. Then looking at discrete wholes – e.g. a group of marbles, beads on a piece of string: what is
the whole? What is one part? (children need to understand it’s not all about being split into
pieces)
3. Then looking at more than definite wholes – what about when it is the group of shapes?
What about when we just look at the stars? What is the new whole? What is the new part?
NOTE: Use concrete objects alongside pictorial representations throughout this initial phase so that
children really grasp the part-whole concept and don’t just think of fractions as a pizza being split up.
Don’t keep concrete objects purely for less confident children, they are valuable for all children!
Progression through Comparing and ordering fractions (Recognising
fractions)
1. Start with same denominator so they can just identify which has more parts – use pictures
and shading in.
2. Then move on to different denominators so they need to consider what the whole needs to
be out of
3. Comparing unitary fractions – this will really test that they understand
what fractions are and the part-whole relationship!
Progression through finding Fractions of number/shape (Calculating with
Fractions)
1. Simpler fractions of number (1/2, ¼) – Lower school to show using arrays, then times tables
facts, using what they know (1/3 of 210) then division methods (YR5)
2. Unitary fractions of shape
– start with colouring in simple unitary fractions of the shape. Use objects as well! (count to find
out the whole)
3. Trickier unitary fractions of number (1/3, 1/7) – can still be done using arrays if needed
4. Non-unitary fractions of number (e.g. 3/5, 7/8) – can be done pictorially
5. Non-unitary
fractions of shape
6. Use shapes with trickier parts
Applying ideas: Use inverse to show mastery
Apply through 2- step/multi-step problems.
Progression through Equivalents (Recognising fractions)
1. This will come naturally once the children understand the
part-whole concept, so they start to recognise basic fractions such as
½, ¼, etc. Use fraction cylinders and fraction walls to help with
spotting basic equivalents – e.g. 1/3 = 2/6
2. Children then need to be able to understand which fractions are equivalent to one another
so they can recognise that a half does not always have to look like ½. Start with exploring so
they can spot patterns for themselves. Pictures, shapes, etc.
This diagram proves that 2/3 is equivalent to
10/15. The children can then move on to
recognising that you need to multiply the
numerator and denominator by the same number
to get an equivalent fraction.
3. Simplifying fractions (Year 6)
Progression through adding, subtracting (Calculating with Fractions)
Use pictorial representations to teach this so that children understand why it works rather than just
learning tricks: they should have a really secure understanding of what fractions are
1. Making up the whole
Start with concrete resources
e.g. Numicon to show this
relationship
Then move on to presenting it
pictorially!
2. adding and subtracting – same denominator. Use pictures (vary the shapes so they don’t
always just think of a circle) to help prove understanding of why the denominator does not
change!
3. Adding and subtracting – different denominator/ includes unitary fractions. Brings in
knowledge of equivalent fractions
Progression multiplying, dividing (Calculating with Fractions)
1. Multiplying a fraction by a whole number – show through pictures
2. Multiplying a fraction by another fraction: visually proving why
you can multiply the numerators and then multiply the
denominators
3. Dividing a fraction by a whole number
4. Dividing fractions by each other
Progression converting between Mixed Numbers and improper fractions
(Recognising Fractions)
1. Mixed to improper
2. Improper to mixed
Progression through adding and subtracting with Mixed Numbers
(Calculating with Fractions)
1. Calculations where the fractions have the same denominator so the children
only need to add the wholes then add the fractions separately
2.
Calculations where the fractions have different denominators so the mixed
numbers need to be converted into improper fractions
Phase 9: Multiplying and dividing with Mixed Numbers (Calculating with
Fractions)
1. Multiplying a mixed number by a whole number
2. Multiplying a mixed number by a mixed number using knowledge of
converting to improper fractions
3. Dividing mixed numbers by a whole number
4. Dividing a mixed number by a mixed number
Use Maths No Problem books as a modelling tool
– NOTE: see year group below your own as pitched at a higher level than our curriculum