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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?
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
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.
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.’
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.
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.
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.
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.
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.
11.
Hearing from the Horses’ Mouths!
• 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
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.
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.
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?
16.
EYFS – number sense 1-5
Numberblocks
5 frames
Real life objects
17.
EYFS – activities 1-5
Number stories
Comparison
Subitizing
Number songs
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.
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!)
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.
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.
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.
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.
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?
26.
What equal groups match? Y3 examples
Show it using repeated addition.
27.
Fluency focus
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?
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
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
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?
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?
37.
PROGRESSION IN ADDITION METHODS AND
STRATEGIES
40.
PROGRESSION IN MULTIPLICATION
43.
PROGRESSION IN DIVISION
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
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.
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.
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