1. 1A
MASTERY
M AT H E M AT I C S
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MEET THE TEACHERS AND JOIN A
MATHEMATICS MASTERY
LESSON

3. We believe that the UK needs a new approach to teaching maths. So we’ve drawn on the best of existing practice from
all over the world to create Mathematics Mastery. Initially developed with teachers in the ARK network of schools,
we are now partnered with over 100 primary and secondary schools in the UK and we’re excited to be bringing new
schools to the partnership
DEEP UNDERSTANDING
At its heart Mathematics Mastery is simple – maths at any level, be it aged 5 or 35, can be broken down into a few
core principles. Mathematics Mastery ensures pupils have a deep understanding of mathematical concepts; they explore
these using objects, pictures and through conversation as well as written symbols and numbers. Mathematics Mastery
puts problem solving and language at the centre of every maths lesson and we make sure that our pupils are resilient
learners. Read on to sample a Mathematics Mastery lesson to find out how this works in practice.
PROFESSIONAL COLLABORATION
We also believe that excellent maths teaching doesn’t begin and end in the classroom.Teachers both need and want
professional development and support that flows seamlessly into every aspect of their teaching. Mathematics Mastery
encourages teachers to develop their lessons and teaching techniques for themselves.We believe in our teachers as
contributors and researchers as well as practitioners – Mathematics Mastery is driven by the schools and teachers
within the partnership. Read on to hear one of our teachers explaining how her school’s membership of the Maths
Mastery partnership helps her become a better teacher.
ACTION LINKED TO EVIDENCE
Mathematics Mastery has grown out of respected research and we will continue to learn and adapt as the partnership
develops.We want to demonstrate the possibilities for mathematics teaching and learning in UK schools and show that
the UK can be great at maths.
SO WHAT’S IT REALLY LIKE?
So what’s it like to be a Mathematics Mastery partner? The best people to help you with that are our schools, teachers
and pupils…and I’m delighted to introduce just a few of them to you…
WELCOMETO
MATHEMATICS
MASTERY
My name is Helen Drury,
I’m a maths teacher and
Director of Mathematics Mastery

4. I’m a Headteacher at a primary school in West London.We became a
Mathematics Mastery partner school in 2012 – the very first cohort.
We joined Maths Mastery because we’re always looking for new approaches
that will have an impact on our pupils. I liked the fact that Maths Mastery was
cutting edge but would be monitored closely and is based on educational
research. Maths attainment in our school was already good but I wanted to
find ways to accelerate progress.
It’s not easy introducing a new classroom approach and I didn’t take the
decision lightly. It was helpful that we were able to introduce it just toYear 1
to start with. It gave us a chance to get to grips with the principles without
having to commit the whole school.
Maths Mastery asked us to show that we were committed to the programme
for the whole year – turning up to the cluster sessions and putting time
and effort into making the school visits worthwhile. Like making any
improvements, it certainly takes extra resources and time to make it work.
It’s been worth it though and I understand why there is such an emphasis on
engagement and commitment.
I don’t teach Maths Mastery myself, but I’ve got a great Maths Mastery
School Lead.TheYear 1 teacher worked really hard and enthusiastically at
introducing the programme. She spent a lot of time liaising with the Maths
Mastery core team to make sure that the programme worked for the school.
What’s been interesting for me is seeing how really experienced teachers
and more junior teachers can both use the materials and support in the way
that works best for them. It’s worked well with very different teachers. As a
Headteacher I’m always trying to make sure that my staff are supported and
getting interesting training and I’ve enjoyed seeing the teachers develop their
teaching.
One area of concern for me was how we would manage our Ofsted visits.
I was worried that to people who aren’t familiar with the Maths Mastery
approach, the units at the beginning ofYear 1 can look a bit easy. I was
concerned Ofsted would think we weren’t stretching the pupils enough.
However when you see what that initial teaching enables the pupils to do by
the end ofYear 1, then it’s really impressive. Now I’d be very happy to show
off Key Stage 1 to Ofsted.
We’ve had measurable improvement in maths attainment. For the first time
ever, ourYear 1 class are all on track with expected progress – that has
never happened before. MyYear 2s (who studied Maths Mastery inYear 1)
now make faster progress in maths than any other class in the school. And
perhaps even more importantly, my pupils seem to be enjoying maths more.
They get really excited when they find out that maths is next!
MEET A HEADTEACHER
Miles Chester
New King’s Primary School
MEET MORE HEADTEACHERS
“Over 80% of my pupils speak
English as an additional language
and I know how important it is to
have a real emphasis on language
and vocabulary – I was impressed by
Maths Mastery’s focus on language
and developing understanding through
talking. I also believe that the concrete-
pictorial-abstract approach is key to
maths teaching and I liked the way
this was embedded at every stage of
Maths Mastery. As an inner London
school we also have an inevitable
turnover of staff and Maths Mastery
ensures that our maths curriculum is
stable, consistent and well-established,
despite staff changes.”
Suzanne Parry, Headteacher
St Augustine’s Primary School
“We joined Mathematics Mastery
because we were interested to find
out more about the SE Asian ‘mastery’
approach but we didn’t just want to
purchase a scheme.What attracted
us was the support package: the
professional development, school visits
and the academic/research approach.
We haven’t followed it to the letter
but we have merged it with our
already excellent practice. Even as an
outstanding school, it has really helped
develop our pedagogy and practice for
the better.”
Kate Frood, Headteacher
Eleanor Palmer Primary School

5. I’m aYear 1 teacher at a primary school in Hammersmith. I was an NQT
when I started teaching Mathematics Mastery in 2012 and I was the first
teacher in the school to work with the Maths Mastery approach.
I was a bit apprehensive joining a new programme as an NQT. But I’m so
pleased I did – I love teaching maths.
At first I tended to plan my lessons one at a time. Now that I have more
experience I plan all the lessons for the week in one go. I log in to the online
toolkit and find the learning objectives and lesson principles. I go through and
add my own success criteria specific for my pupils. I adapt and differentiate
the tasks to suit my pupils and I write notes for the teaching assistant as to
how to support different children through the lesson. I also have an ongoing
bank of extensions that I create for the unit.
I definitely have more confidence now than when I started. It’s always been
clear that the whole point of the Maths Mastery principles and materials is
to provide a framework for each teacher to adapt creatively for their own
pupils. I’m now much more flexible and inventive about the way I teach. I like
that I’m paart of a new approach to teaching maths that gives you the time,
space and tools to really understand not just what you’re teaching, but why
you’re teaching it.
It’s been great working with other Maths Mastery teachers in the school.The
Year 2 teacher is a much more experienced teacher than me and I’ve enjoyed
working collaboratively.We have discussions about Maths Mastery everyday –
it’s definitely a team effort!
MEET ATEACHER
Rebecca Carver
ARK Conway Primary School
One of the hardest things about being a teacher is making sure that you keep developing and learning whilst also fitting
in a busy teaching schedule. Maths Mastery makes it easy for me to bring my own new learning into the classroom.
When we signed up, I went for a day’s launch training.We had really intensive sessions on the principles of the
programme and I was there with teachers from other schools.
At first I was a bit daunted trying to implement everything we’d been taught. But because the principles are developed
so strongly in the curriculum and teaching materials, I’m always drawing on the training when I teach. I’ve found
the online tutorials particularly helpful. It’s like having a really keen teaching partner – a particular treat for me as
my school is one form entry! I revisit the tutorials frequently during the unit so that I’m constantly reinforcing the
principles.
I’ve been a regular at the cluster sessions, where we meet up with teachers in other schools to discuss different
aspects of the curriculum. It’s been reassuring and inspiring to find out what other people are doing. I’m also still
in touch with some of the teachers I met at launch training and we’ve been to visit each other in our schools and
observe each other’s lessons. It’s been great to make a new network of colleagues. Collaborating is effective because
we understand each other but can bring new ideas.We’ve also had school visits from the Maths Mastery team. I’ve had
some informative feedback and I like that they come to see us in our personal teaching environment.
“I like that I’m part
of a new approach
to teaching maths
that gives you the
time, space and tools
to really understand
not just what you’re
teaching, but why
you’re teaching it.”

6. MEET SAM DAVIES AND HER
YEAR 1 CLASS FROM KING
SOLOMON ACADEMY
My class has 30 children with a
really broad spread of low and high
attaining pupils. Most of them don’t
have English as a first language.
They have been learning with the
Maths Mastery approach for around
8 months.
Today’s lesson is all about comparing
numbers within 100.They all know
the numbers to 100 from previous
lessons and we’ve done lots of
work on place value, adding and
subtracting numbers up to 40.
They’re all confident using dienes
blocks and number lines because we
use them in every lesson.
The children always sit at their
tables at the start. First we go
through the lesson objectives so
I explain that we’re comparing
numbers within 100 and they tell
me that comparing numbers means
working out if a number is bigger or
smaller.
We also look at the key words for
each lesson – here they’re greater,
smaller, tens, ones and compare.
Maths Mastery lessons follow a 6 part structure.This keeps the lesson
pacey, gives flow and allows more opportunities to teach creatively, give
feedback and assess learning.
1 DO NOW
2 NEW LEARNING
3TALKTASK
4 DEVELOP LEARNING
5 INDEPENDENTTASK
6 PLENARY
PART LESSONS6
Whilst the principles are always the
same, no two Maths Mastery teachers
are! Check the speech bubbles for
ideas from other Maths
Mastery teachers!
JOIN AYEAR1
LESSON
Numbers within 100
Comparing numbers

7. This is a warm up task which the children do independently at their tables.
The material is a recap of previous learning and every child should be able to
do it. To get them all started I’ve given them each a 100 square. I ask them to
put a counter on a number greater than 59. And then on a number less than
15. And I do a few more examples. They’re already familiar with “greater
than” and “less than” so this is a great way to remind them of previous learn-
ing and make sure they’re all concentrating for today’s new learning.
The Do Now task lasts about 5 minutes and at the end the children will all
come together for the lesson’s New Learning.They’ve all got spaces on the
carpet in the centre of the classroom.Whilst the children are moving to the
carpet, they will do a TRANSITION song – the song for today’s lesson is the
Days of the Week Song!
SPOTLIGHT ON
TRANSITIONS
Every second counts in maths
lessons. So between tasks the
children sing songs or do call
and response with the teacher.
It helps keep them focussed
and keeps the lesson flowing.
5 MINS
“I would bring in a task from a previous lesson.A game
where they have to work out which number out of
100 is missing would work well to remind them of
previous learning.”
Jasbir Mahey, Gilbert Colvin
“I might ask them to make the numbers that we need
for the next task on place value charts. It makes sure
they’re all on track for the new learning coming next.”
Stephanie Lester,ARK Atwood
1 DO NOW
A warm up task to get the
brain working quickly
and effectively

8. All the children sit in rows on the carpet. I’m using the interactive white
board.We’re learning that to compare two numbers you can look first at
the tens column and then at the ones column. I’m using two big place value
charts which they’re all really familiar with.
I start off using CONCRETE manipulatives - dienes blocks. I put 6 ten rods
in the tens column and 9 ones in the ones column.We all count them out
together – “there are 6 tens and 9 ones, we’ve got 69!”. I then put 7 ten
rods in the other chart. I ask one of the children to tell me what number I’ve
made.“70!”.And please tell me how you know? “Because I count each rod 10,
20, 30, 40, 50, 60, 70!”.
I ask them to talk to their partners about which number is biggest. I
walk around the classroom listening in, reminding them to talk in FULL
SENTENCES and checking their understanding.
I then say that when you compare numbers you always have to look at the
tens column first.We look at the tens column in 69 and count that there
are 6 tens.And we do the same for 70 and count that there are 7 tens. I
emphasise that 7 is bigger than 6 and so we know that 70 is bigger than 69
just by looking at the tens column.
Then we make two different numbers on the charts: 57 and 59.We count the
tens in each and find out that they’re the same. So I say that we don’t know
which is bigger just by looking at the tens column – we need to look at the
ones column too.We count the ones and we say together than 9 ones is
bigger than 7 ones. And so we’ve worked out that 59 is the biggest number.
I then do two more examples and I get the children to come up and make
the numbers themselves, so that they are participating in the New Learning.
We’re now 15 minutes into the lesson and it’s time to transition – this time
we sing their Secret Number song – back to their maths tables.
2 NEW LEARNING
To introduce the main maths
concepts for the day’s lesson
SPOTLIGHT ON
CONCRETE, PICTORIAL
AND ABSTRACT
Dienes are concrete objects.
Pictures of objects are pictorial.
Written numbers are abstract.
Mathematics Mastery uses all
three throughout each topic.
FULL SENTENCES
Pupils learn to express and
explain concepts by always
talking about maths in full
sentences.This improves their
understanding and helps them
become more articulate.
“I also ask them questions like “Is it better to have 69 or
70 sweets?” to make sure they’re also understanding why
comparing is important in real life.”
Jasbir Mahey, Gilbert Colvin
“I would also put 69 and 70 up on
flashcards as written numbers so
they’ve got the abstract representation
as well as the dienes blocks.”
Stephanie Lester,ARK Atwood
10-15 MINS

9. The pupils are back at their tables ready for the talk task, which they’ll do in
pairs.This part of the lesson is really valuable as it helps me check progress
and assess understanding.
The main focus here is on the children working together and talking in full
sentences about maths.They’re all on mixed ability tables here and the task
is essentially the same as the New Learning but in the format of a game. I’ve
ADAPTED the suggested task slightly to fit it to my class – I want them to
keep using dienes blocks and not introduce dice just yet.
Each child picks a number card and then makes it on their place value chart
using dienes blocks.Then one of them tells the other one which number is
bigger and how they know.The person with the biggest card wins and keep
the card.Then they pick some new cards and the other person explains
which is the biggest.They love playing games – introducing the competitive
edge keeps them all engaged.
As they play I walk around and check how they’re doing. If I notice that
anyone is behind I flag to my teaching assistant that they need to be given
some small group attention for the next part of the lesson.After about 10
minutes I ask the children to transition back to the carpet, counting in tens.
3TALKTASK
To practise the new learning
and talk about maths
SPOTLIGHT ON
ADAPTING
Maths Mastery has core
principles and they work best
when teachers are creative and
adapt the suggested tasks so
that they work for their pupils.
“I love the emphasis on language.
I’ll give stars out when I hear
pupils using the star words
correctly.”
Stephanie Lester,ARK Atwood
“I’ll vary the task so that the win-
ner is sometimes the person who
gets the lowest number.”
Jasbir Mahey, Gilbert Colvin
10 MINS

10. The Develop Learning segment mirrors the New Learning segment earlier in
the class but aims to take their learning on a bit further. In this lesson we’re
doing this first by introducing another resource – a number line.And then by
introducing a problem solving element.
Children sit in pairs and I give each pair a number line with 100 beads on it.
We’re about to play a Mystery Number game – my pupils love this game – so
I introduce them all as detectives with a puzzle to solve.We go through a
list of mystery number clues, after each one eliminating numbers that can’t
be the mystery number.The clues focus on “greater than” and “less than”
so they’re using the new learning from earlier on. As we go through I keep
asking them QUESTIONS about how they know which numbers to eliminate
and whether they know the mystery number yet.
I’m so pleased that my pupils can follow this activity. It’s pretty demanding for
Year 1. But because the FOUNDATIONS were so well laid during the Autumn
term, the pupils are really starting to show that they can use what they’ve
learnt to tackle quite complex concepts.
4 DEVELOP LEARNING
To build on the new learning
and develop a deeper understanding
SPOTLIGHT ON
QUESTIONING
Smart questioning is key.The
right questions get pupils to
explain themselves in different
ways and encourage a deeper
understanding of concept.
Pupils are encouraged to ask
questions themselves.
FOUNDATIONS
Maths Mastery focuses on
depth of understanding. If
children have a good foundation
they’ll remember what they’ve
learnt and be able to apply it to
more complex concepts.
“I would give each child a laminated 100 square and
marker pen so that they can eliminate the numbers
themselves as we go along.”
Jasbir Mahey, Gilbert Colvin
“I would give them a small
selection of different apparatus
so they start learning to use the
one that suits them.”
Stephanie Lester,ARK Atwood
10 MINS

11. The pupils now transition back to their desks singing the Secret Number
Song again.This next task is a chance for them to practise their Develop
Learning independently.They are given their own mystery number clues along
with a number line.
The suggested task is a great basis and it needs to be adapted to make sure
that it’s challenging everyone in the class. I’ve adapted the exercise suggested
by Maths Mastery so that it is DIFFERENTIATED for high, middle and lower
attaining pupils. My lower attaining pupils are given only 3 mystery numbers
with 2 clues to work out each number. My middle attaining pupils are given
5 mystery numbers with 3 or 4 clues for each number. My higher attaining
pupils are given 4 examples with all 6 clues. I’ve added in some unhelpful clues
to see if they can spot them.
I go round the room at the same time as the teaching assistant and mark
over their shoulders as I go round. I give individual assistance if I hear children
that need it.And I remind them to always use their number line and record
the answers they get.
I expect my higher attaining pupils to finish their mystery numbers. So for
those that finish I’ve put an extra task in the middle of the table with a
challenge to create their own mystery number and clues to go with it.
5 INDEPENDENTTASK
To practise their learning
independently by solving problems
SPOTLIGHT ON
DIFFERENTIATION
Differentiation is not about
accelerating pupils through the
curriculum or holding them
back. For higher attaining pupils
it’s about pushing for increased
depth and exploration. For
lower attaining pupils it’s about
scaffolding tasks but not putting
a ‘cap’ on their learning.
“I’d give my lower attaining pupils
some extra scaffolding and ask
the TA to read out the clues for
them.”
Stephanie Lester,ARK Atwood
“I’d link this to another class topic—for example, if we
were also learning about the beach that week, I’d say that
one of my 100 beach balls had gone missing and ask
them to find which one.”
Jasbir Mahey, Gilbert Colvin
10 MINS

12. Our ONE HOUR lesson is nearly over and it’s time for the final part—the
plenary. I’m using this segment to sum up what the children have learnt and
to assess their understanding.
I ask the children who created their own mystery numbers to come up to
the front and present their number to the class.They take the whole class
through the clues and we check the answers as we go along still using our
number lines.
We’ve also got a maths wall at the back of the classroom which shows all
the maths learning objectives for this week.At the end of the lesson I ask the
children to say what they’ve learnt and then it gets written up on the wall.
6 PLENARY
To recap on the lesson,
check understanding and
celebrate success
SPOTLIGHT ON
TIMING
The suggested timings are all
based on a recommended one
hour lesson. But if a school
needs to have shorter maths
lessons then timings, like all
other aspects, can be adapted
to fit.
“Sometimes I use the plenary
to introduce a topic for the next
maths lesson. So here I could
introduce ordering numbers”
Stephanie Lester,ARK Atwood
“I would play a game with my TA at the front of the class,
where we’d both pick a number and say which one we
thought was bigger/smaller. Only one of us would be right
and I’d ask the class to decide who.”
Jasbir Mahey, Gilbert Colvin
5-10 MINS

14. 1A
MASTERY
M AT H E M AT I C S
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WOULDYOUR SCHOOL LIKE TO
BECOME A PARTNER? APPLY NOW TO
JOIN THE PROGRAMME
To find out more please contact us on:
http://www.mathematicsmastery.org/
+44 (0)203 116 0793
info@mathematicsmastery.org