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