Parent Workshop

Fractions, Decimals &

Percentages (Bar Modelling)

James Smyth

Year 6 Teacher and Maths Coordinator

Liz Martin

Year 1 Teacher

Charlotte Griffith

Year 3 Teacher

Ruth Scott

Year 5 Teacher

Programme of Study – Year 1 & 2

- Number and Place Value

- Addition and Subtraction

- Multiplication and Division

- Fractions

- Measure

- Geometry

- Statistics

Programme of Study – Year 3 & 4

- Number, Place Value & Rounding

- Addition & Subtraction

- Multiplication & Division

- Fractions & Decimals

- Measure

- Geometry

- Statistics

Programme of Study – Year 5-6

- Number, Place Value & Rounding

- Addition & Subtraction

- Multiplication & Division

- Fractions, Decimals & Percentages

- Measure

- Geometry

- Statistics

- Ratio & Proportion (Year 6 only)

Programme of Study (Website)

New Curriculum 2014

Focus on:

- Fluency

- Reasoning

- Problem Solving

Fluency

To be fluent in mathematics children should be

able to… - grasp the fundamentals of mathematics

- practice arithmetic skills

- make connections

- become more confident with written and mental

methods

- be confident with what they are doing and why

- recall and apply their knowledge rapidly and

accurately

Fluency

Examples of fluency in fractions, decimals and

percentages:

- Find ½ of 8 (Year 1)

- Find 1/3 of 30 (Year 2)

- Find 2/5 of 45 (Year 4)

- Find 5 equivalent fractions of ¾ (Year 5)

- 4/7 ÷ 5 (Year 6)

- 75% of £1340 (Year 6)

Reasoning

Through reasoning problems children should…

- be able to explain why an answer is right or

wrong

- follow a line of enquiry to a logical conclusion

- prove theories using mathematical language

Can be thought of as the ‘glue’ that helps maths

makes sense.

Reasoning

Examples

- Which would you rather have, three quarters

of £2.40 or one quarter of £6? Explain your

reasoning. (Year 4)

- Sophie thinks 1.007 is bigger than 1.01 because

7 is bigger than 1. Do you agree? Explain why.

(Year 5)

Problem Solving

Children should be able to…

- apply their mathematics to a variety of routine

and non-routine situations

- put maths into context

- break down problems into a series of manageable

steps

This is fundamental to the mathematical

development of all children

Problem Solving

Examples:

-Look at 20 toy cars. Is it possible to find ½, 1/3

and ¼ of them without breaking any of them? (Year 2)

- Find the smallest number that can be added to

92.7 to make it exactly divisible by 7. (Year 6)

Fluency Time

-To support the basic

arithmetic skills

- Short sessions (5 minutes)

alongside day-to-day maths

lessons

Problem Solving Pineapple

I’m here to set

children

mathematical

problems and help

them with their

reasoning and

problem solving.

Concrete – Pictorial - Abstract

At Lindfield Primary Academy we believe

that all students, when introduced to a

key new concept, should have the

opportunity to build competency in this

topic by taking this approach.

This is why we work through a Concrete –

Pictorial – Abstract approach

Concrete

Students have the opportunity to use

concrete objects and manipulatives to help

them understand what they are doing.

Concrete

Pictorial

Students build on this concrete approach

by using pictorial representations. These

representations can then be used to reason

and solve problems.

Pictorial

Bar Modelling

4 + 11 = ?

4 11

?15 - 4 = ?

4

15

?

5 x 4 = ?

4

?

4 4 4 4

20 ÷ 5 = ?

?

20

? ? ? ?

2 of 20 = ?5 20

?

Share 20 in the ratio 2:3

20

? ?

Using the bar model

Using the bar model

Early Years

Aliya had 4 oranges, Alfie had 3 oranges.

How many oranges did they have altogether?

Using the bar model

Using the bar model

Key Stage 1

Using the bar model

Using the bar model

Key Stage 2

Matthew has a 300g block of cheese. He eats 2

5of the cheese

and puts the rest back in the fridge.

How much cheese did Matthew put back in the fridge?

Pictorial

Eats Put back

60 60 60 60 60

Abstract

300 ÷ 5 =60

3 x 60 = 180

Abstract

With the foundations firmly laid, students

should be able to move to an abstract

approach using numbers and key concepts

with confidence.

Abstract

Halving of sets of objects begins as early as EYFS and Year 1.

It is vital that children know

halves and quarters must be

equal in size.

In Year 2 children begin to use ½, ¼, ¾ and 1/3 ; find simple fractions of amounts (½ of £12 = £6) and know equivalence of ½ = 2/4

.

FDP Progression in School

In Year 3 children begin to use the terms denominator

and numerator in writing proper fractions.

They recognise, find and write fractions of objects and

begin to compare and order them.

They begin to add and subtract them and solve problems.

In Year 4 children read and write fractions, ordering them

and recognising equivalent fractions. Children also find

fractions of amounts (3/5 of 25Kg = 15Kg).

They continue to add and subtract fractions and

understand more equivalences, including tenths and

hundredths.

Progression in KS2

By Year 5 children simplify fractions. They relate fractions to decimals and percentages, and begin to multiply them.

They begin to convert mixed numbers to improper and vice versa.

In Year 6 we ask children to find common factors in numerators and denominators.

They multiply and divide fractions and associate them with division. Children convert between F, D and P and recall and use equivalences.

Progression KS2

Fractions - what are they?

Part of a whole.

When an object or number is

divided into a number of

equal parts, then each part

is called a fraction.

12

A fraction is a part of a whole

Slice a pizza, and you will have fractions:

1/2

1/43/8

(One-Half) (One-Quarter) (Three-Eighths)

The top number tells how many slices you have

The bottom number tells how many slices the pizza was cut into.

Fractions

Parts of a Fraction

Numerator25 Denominator

The number of parts the whole is divided into (total).

The denominator is downstairs!

How many parts you have.

Language of fractions

Language of fractions is used all around children, “here’s

my half.” “I’ll cut this cake into equal parts for the four

of us.” etc

We would encourage correct use of terms from early on -

not “My half is bigger than yours!”

Improper Fraction

Equivalent fractions

Equivalent fractions are fractions that are

equal in size but have different

denominators or numerators.

1 = 2

2 4

There are many more!

We use a fraction wall as well

as lots of images and models to

aid understanding.

Decimals, Fractions and Percentages are just different

ways of showing the same value:

A Half can be written...

As a fraction: 1/2

As a decimal: 0.5

As a percentage: 50%

Fractions, Decimals and

Percentages

Fraction terminology

Numerator: the number on the top of a fraction showing the number of

equal parts in the fraction eg 3/4

Denominator: the number on the bottom of the fraction showing the total

number of equal parts in the whole eg 3/4

Proper fraction: the numerator is less than the denominator eg 2/3

Improper fraction: the numerator is larger than the denominator indicating

that the parts come from more than one whole (top-heavy fractions) eg9/5

Mixed fraction: has a whole number and a fraction eg 8 ½

Equivalent fraction: the same fraction written in different ways so each

one gives the same answer in a calculation, even though they look

different eg ½ and 3/6

Common denominator: a number that can be divided by the denominators

of all of the fractions eg 2/3 5/8

7/12 all the denominators divide

into 24 so 2/3 becomes 16/24, 5/8 becomes 15/24,

7/12 becomes 14/24.

So 24 is the lowest common denominator as this is the smallest number

that 3, 8 and 12 will divide into.

End of Key Stage Assessment

For Year 2 children – SATs

- Arithmetic Paper

- Reasoning & Problem Solving Paper

For Year 6 children – SATs

- Arithmetic Paper (30 mins)

- Two Reasoning & Problem Solving

Papers (40 mins)

Academy Website – Maths Section

- Year Group Overviews

- Times table challenge support

- Calculation Policy

- Key Vocabulary

- Maths Websites

Maths WebsitesSuper Maths World

Supermathsworld (Username:1010lpa)

My Maths

My Maths -https://www.mymaths.co.uk/

USER NAME: lindfieldpsPASSWORD: nine

Times Table Rockstars

Times Tables Rockstars - https://ttrockstars.com

Books

Maths for Mums and Dads Rob Eastaway and Mike Askew Maths on the Go

Rob Eastaway and Mike Askew

Pupil Demonstrations

Key Stage 1:

Jumaima Choudhury

Jess Tingley

Millie Farbrother

Year 3:

Charlie Kell

David Boyer

Finley Piddington

Pupil Demonstrations

Year 4:

Charlotte Smith

Sam Mercer

Ava Burnage

Year 5:

Ellie Martin

Beth Simmons

Alice Anderson

Year 6:

Hannah Bryan

Tess Marshallsay

Martha Gibson

Maria Forrest

Any questions please feel free

to talk to any of us afterwards