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Here, we provide information on how to master mathematics, and what does it mean to master mathematics.

1.
Welcome to our 2020 Maths

Mastery Presentation

What is mastery?

What happens in a maths lesson?

What calculation methods are the children taught?

How can parents can help at home?

Mastery Presentation

What is mastery?

What happens in a maths lesson?

What calculation methods are the children taught?

How can parents can help at home?

2.
What does it mean to master

• You have a wealth of knowledge on the subject

• You have relevant skills at your disposal

• You can problem solve and know which method works best

• You don’t expend much energy on the basics – they become

second nature.

• You can explain and teach someone else effectively

• You can apply your knowledge and skills to slightly different

variations

• You have a wealth of knowledge on the subject

• You have relevant skills at your disposal

• You can problem solve and know which method works best

• You don’t expend much energy on the basics – they become

second nature.

• You can explain and teach someone else effectively

• You can apply your knowledge and skills to slightly different

variations

3.
THE MASTERY APPROACH FOR MATHS

(and other subjects):

• Fluency: the ability to recall and apply knowledge rapidly and

accurately.

• Reasoning: explain their mathematical thinking

• Problem solving: apply their knowledge to solve problems in

varied contexts.

(and other subjects):

• Fluency: the ability to recall and apply knowledge rapidly and

accurately.

• Reasoning: explain their mathematical thinking

• Problem solving: apply their knowledge to solve problems in

varied contexts.

4.
The National Curriculum states:

‘There is an expectation that the

majority of pupils will move through the

programme of study at broadly the same

pace and that pupils who grasp concept

rapidly should be challenged through rich

and sophisticated problems before any

acceleration to new content.’

‘There is an expectation that the

majority of pupils will move through the

programme of study at broadly the same

pace and that pupils who grasp concept

rapidly should be challenged through rich

and sophisticated problems before any

acceleration to new content.’

5.
OUR METHODOLOGY

• A high level of performance for all

• Keeping the class working together whilst addressing the

needs for all pupils to master the curriculum and for some to

gain greater depth and proficiency

• A mind-set that children can achieve with good teaching,

appropriate resources, effort and a ‘can-do’ attitude.

• Making use of in-depth, repetition and application.

• All pupils have access to the ideas and concepts.

• A high level of performance for all

• Keeping the class working together whilst addressing the

needs for all pupils to master the curriculum and for some to

gain greater depth and proficiency

• A mind-set that children can achieve with good teaching,

appropriate resources, effort and a ‘can-do’ attitude.

• Making use of in-depth, repetition and application.

• All pupils have access to the ideas and concepts.

6.
ALL ON BOARD THE SAME LIFT…

• NOT working on content from the next year group.

• More Able pupils NOT practising the same concept with

bigger numbers.

• Reasoning and problem solving NOT just the domain of ‘more

able’ pupils.

• Keeping the class working together: Quick intervention keep

up, not catch up.

• NOT working on content from the next year group.

• More Able pupils NOT practising the same concept with

bigger numbers.

• Reasoning and problem solving NOT just the domain of ‘more

able’ pupils.

• Keeping the class working together: Quick intervention keep

up, not catch up.

7.
WHY THE MASTERY APPROACH?

• It develops the ability to reason about a concept and make

connections

• It cuts down on the amount I need to learn eg relating

concepts of division, fractions and ratio

• It deepens conceptual understanding, conceptual and

procedural fluency

• It moves maths from one context to another.

• It helps us recognise concepts in unfamiliar situations.

• It ensures we know our number facts and tables and have

efficient procedures.

• It develops the ability to reason about a concept and make

connections

• It cuts down on the amount I need to learn eg relating

concepts of division, fractions and ratio

• It deepens conceptual understanding, conceptual and

procedural fluency

• It moves maths from one context to another.

• It helps us recognise concepts in unfamiliar situations.

• It ensures we know our number facts and tables and have

efficient procedures.

8.
A SHIFT IN OUR EXPECTATIONS

• Complete change in mindset for teachers, parents and the

children themselves

• The belief and expectation that all pupils can achieve.

• Growth mindset – “I can’t do it yet!” rather than “I’ll never

be good at maths!”

• Children discuss and share learning together so all can

access and master maths.

• Complete change in mindset for teachers, parents and the

children themselves

• The belief and expectation that all pupils can achieve.

• Growth mindset – “I can’t do it yet!” rather than “I’ll never

be good at maths!”

• Children discuss and share learning together so all can

access and master maths.

9.

10.
A typical maths lesson structure…

• Warming up – quick maths activity to revisit/ practise a

maths skill

• Sharing a problem together and discussing ways to tackle it

• Paired practice of the skills required for the problem

through 2 or 3 questions – broken down into small steps with

the teacher guiding the pupils through carefully

• Independent time – pupils given time to work alone on similar

questions that build in difficulty. During this time, the

adults monitor the learning through live marking and

questioning pupils to check understanding.

• Warming up – quick maths activity to revisit/ practise a

maths skill

• Sharing a problem together and discussing ways to tackle it

• Paired practice of the skills required for the problem

through 2 or 3 questions – broken down into small steps with

the teacher guiding the pupils through carefully

• Independent time – pupils given time to work alone on similar

questions that build in difficulty. During this time, the

adults monitor the learning through live marking and

questioning pupils to check understanding.

11.
Hearing from the Horses’ Mouths!

• Miss Lemon (EYFS)

• Mr Tolson (Y2)

• Mr Lawson (Y4)

• Miss Lemon (EYFS)

• Mr Tolson (Y2)

• Mr Lawson (Y4)

12.
SOME TEACHING METHODS AND

• Develop reasoning with all

• What do you notice?

• What’s the same?

• What’s different?

• Convince me!

• Spot the odd one out!

• True or false….or sometimes both?

• Give an example of…

• The missing digit/number (empty box)

• Here's the answer, create the question

• Develop reasoning with all

• What do you notice?

• What’s the same?

• What’s different?

• Convince me!

• Spot the odd one out!

• True or false….or sometimes both?

• Give an example of…

• The missing digit/number (empty box)

• Here's the answer, create the question

13.
SOME TEACHING METHODS AND

• Use of precise language and speaking in full sentences gives

children the language in order to express the maths and

hang learning on – use of stem sentences

Eg There are _________ packets in ______boxes in the

shop.

• Memorisation – Rehearsal and repetition.

• Use of precise language and speaking in full sentences gives

children the language in order to express the maths and

hang learning on – use of stem sentences

Eg There are _________ packets in ______boxes in the

shop.

• Memorisation – Rehearsal and repetition.

14.
WHAT ABOUT DIFFERENTIATION?

• Emphasis on developing deep understanding

not pushing children on to new content

• Support for those struggling through‘ keep

up’ not ‘catch up’

• Use of resources to support/ scaffold

learning

• Use of pre-teaching

• Starting with a misconception from a

previous lesson to unpick errors.

• Emphasis on developing deep understanding

not pushing children on to new content

• Support for those struggling through‘ keep

up’ not ‘catch up’

• Use of resources to support/ scaffold

learning

• Use of pre-teaching

• Starting with a misconception from a

previous lesson to unpick errors.

15.
EXAMPLES

IN RECEPTION - Using Spot The Mistake:

What is wrong with this sequence of numbers?

IN YEAR ONE – Using True or False?

I start at 2 and count in twos. I will say 9. True or False?

IN RECEPTION - Using Spot The Mistake:

What is wrong with this sequence of numbers?

IN YEAR ONE – Using True or False?

I start at 2 and count in twos. I will say 9. True or False?

16.
EYFS – number sense 1-5

Numberblocks

5 frames

Real life objects

Numberblocks

5 frames

Real life objects

17.
EYFS – activities 1-5

Number stories

Comparison

Subitizing

Number songs

Number stories

Comparison

Subitizing

Number songs

18.

19.
Guided Practice

We give learning a context – we try and make it real, but simple

enough to understand and work with. Pictures are used to enhance

the children’s understanding. Children are beginning to put their

previously learnt skills into a new context.

We repeat these tasks with

different numbers and

pictures to develop children’s

confidence. Children are

targeted at this stage for

additional support. At this

time many misconceptions

can be eliminated.

We give learning a context – we try and make it real, but simple

enough to understand and work with. Pictures are used to enhance

the children’s understanding. Children are beginning to put their

previously learnt skills into a new context.

We repeat these tasks with

different numbers and

pictures to develop children’s

confidence. Children are

targeted at this stage for

additional support. At this

time many misconceptions

can be eliminated.

20.
Independent work

Children will complete similar tasks independently. This allows the

teachers and TA’s to provide additional support to children who

need further teaching and check that children are secure with

Children complete as many

problems as they can. There

isn’t a minimum / maximum

expectation (within reason!)

Children will complete similar tasks independently. This allows the

teachers and TA’s to provide additional support to children who

need further teaching and check that children are secure with

Children complete as many

problems as they can. There

isn’t a minimum / maximum

expectation (within reason!)

21.
What a typical Year 2 lesson looks

like;

A quick 2 minute

activity to wake the

child’s mind up ready

for the numeracy lesson

The activity chosen

builds upon an aspect

of previous learning

helping them to develop

their fluency.

like;

A quick 2 minute

activity to wake the

child’s mind up ready

for the numeracy lesson

The activity chosen

builds upon an aspect

of previous learning

helping them to develop

their fluency.

22.
What a typical Year 2 lesson looks

like;

A problem to generate

mathematical conversation.

Children work with a partner

to discuss and solve the

problems, this will then be

talked about as a class to

address any misconceptions

and develop rich

mathematical vocabulary.

like;

A problem to generate

mathematical conversation.

Children work with a partner

to discuss and solve the

problems, this will then be

talked about as a class to

address any misconceptions

and develop rich

mathematical vocabulary.

23.
What a typical Year 2 lesson looks

like;

Guided practice allows the children to move through a problem in a logical way. Problems

can be broken down and solved collectively, allowing children to offer reasoning and

explanations around the order or processes that need to be followed. This time also allows

the teacher to showcase potential problems and pit falls the children may fall into.

like;

Guided practice allows the children to move through a problem in a logical way. Problems

can be broken down and solved collectively, allowing children to offer reasoning and

explanations around the order or processes that need to be followed. This time also allows

the teacher to showcase potential problems and pit falls the children may fall into.

24.
What a typical Year 2 lesson looks

like;

Children will then be stretched by the

use of a challenge. This is not used in

every lesson but allows for the

teacher to deepen children’s

understanding and allow children to

offer a greater level of reasoning to

their problem solving.

like;

Children will then be stretched by the

use of a challenge. This is not used in

every lesson but allows for the

teacher to deepen children’s

understanding and allow children to

offer a greater level of reasoning to

their problem solving.

25.
EXAMPLES

IN YEAR TWO - Using Continue The Pattern

90 = 100 – 10 80 = 100 – 20

Can you make up a similar pattern starting with the numbers

74, 26 and 100?

IN YEAR THREE – using Make Up An Example

Create numbers where the digit sum is three.

E.g. 120, 300, 210

What is the largest/smallest number?

IN YEAR TWO - Using Continue The Pattern

90 = 100 – 10 80 = 100 – 20

Can you make up a similar pattern starting with the numbers

74, 26 and 100?

IN YEAR THREE – using Make Up An Example

Create numbers where the digit sum is three.

E.g. 120, 300, 210

What is the largest/smallest number?

26.
What equal groups match? Y3 examples

Show it using repeated addition.

Show it using repeated addition.

27.
Fluency focus

Match the representation to the multiplication.

Match the representation to the multiplication.

28.
EXAMPLES

IN YEAR FOUR – Using Do, Then Explain

5035, 5053, 5350, 5530, 5503

If you wrote these numbers in order starting with the

largest, which number would be third? Explain how you

ordered the numbers.

IN YEAR FIVE – Using Missing Numbers

□

6 x 0.9 = x 0.03 6 x 0.04 = 0.008 x □

Which numbers could be written in the boxes?

IN YEAR FOUR – Using Do, Then Explain

5035, 5053, 5350, 5530, 5503

If you wrote these numbers in order starting with the

largest, which number would be third? Explain how you

ordered the numbers.

IN YEAR FIVE – Using Missing Numbers

□

6 x 0.9 = x 0.03 6 x 0.04 = 0.008 x □

Which numbers could be written in the boxes?

29.
Year 4 examples

30.
10 10 1 1 1 Can you do some exchange

with the counters?

10 10 1 1 1 Start with the ones

10 10 1 1 1 There are 15 ones.

10 10 1 1 1 15 ones is the same

10 10 1 1 1 as 1 ten and 5 ones

with the counters?

10 10 1 1 1 Start with the ones

10 10 1 1 1 There are 15 ones.

10 10 1 1 1 15 ones is the same

10 10 1 1 1 as 1 ten and 5 ones

31.
Y5 Paired practice

Use both

methods to

work out 2 × 2

× 7.

b) Choose a

sign to

complete this

number

statement.

4×7 □ 2 × 14

Use both

methods to

work out 2 × 2

× 7.

b) Choose a

sign to

complete this

number

statement.

4×7 □ 2 × 14

32.
Y5 Paired practice

Where should you start?

What strategy will you

use?

What do you notice about

the tens column?

What is missing that

might have helped?

Where should you start?

What strategy will you

use?

What do you notice about

the tens column?

What is missing that

might have helped?

33.
EXAMPLES

IN YEAR SIX – Using Which Is Correct?

Which of these number sentences is correct?

3 + 6 x 2 =15 6 x 5 – 7 x 4 = 92 8 x 20 ÷ 4 x

3 = 37

Using Open-Ended Questions

Jack went into a shop with £10. He only got silver coins in his

change. What amount could he NOT have spent? Why?

IN YEAR SIX – Using Which Is Correct?

Which of these number sentences is correct?

3 + 6 x 2 =15 6 x 5 – 7 x 4 = 92 8 x 20 ÷ 4 x

3 = 37

Using Open-Ended Questions

Jack went into a shop with £10. He only got silver coins in his

change. What amount could he NOT have spent? Why?

34.

35.

36.

37.
PROGRESSION IN ADDITION METHODS AND

STRATEGIES

STRATEGIES

38.

39.

40.
PROGRESSION IN MULTIPLICATION

41.

42.

43.
PROGRESSION IN DIVISION

44.

45.

46.
How To Help At Home - EYFS

• Cooking – measure out ingredients and use a timer together.

• Practise counting to 20 and back to 1.

• Find the same amount of different items eg 3 socks, 3 pens,

3 cups etc.

• Play shops using real or pretend Monopoly money

• Cooking – measure out ingredients and use a timer together.

• Practise counting to 20 and back to 1.

• Find the same amount of different items eg 3 socks, 3 pens,

3 cups etc.

• Play shops using real or pretend Monopoly money

47.
Helping At Home – Yrs 1-3

• Use playing cards to add together 2 cards. Try with

subtraction and multiplication too.

• Keep cooking!

• Play traditional board games.

• Explore different ways to make money totals.

• Use playing cards to add together 2 cards. Try with

subtraction and multiplication too.

• Keep cooking!

• Play traditional board games.

• Explore different ways to make money totals.

48.
Helping At Home – Yrs 4-6

• Keep cooking – develop ideas of what time food needs

to go into the oven/ come out based on cooking times

and when the meal is required.

• Use TV schedules to look at duration of programmes.

• Look at weather APPs to explore the probability of rain

etc.

• Compare and find differences in salaries in the jobs

sections of newspapers.

• When on the move, discuss journey lengths and how the

speed can affect the time of arrival etc.

• Keep cooking – develop ideas of what time food needs

to go into the oven/ come out based on cooking times

and when the meal is required.

• Use TV schedules to look at duration of programmes.

• Look at weather APPs to explore the probability of rain

etc.

• Compare and find differences in salaries in the jobs

sections of newspapers.

• When on the move, discuss journey lengths and how the

speed can affect the time of arrival etc.

49.