Mathematics

‘Good mathematics is not about how many answers you know… It’s about how you behave when you don’t know.’

What attributes, skills and knowledge do we want children to have when they leave Willow Tree?

Number sense:

The ability to explain their mathematical thinking orally and in writing (including using pictures and mathematical symbols);
To develop problem solving and reasoning skills that will benefit them in future learning;
A belief that anyone can achieve in maths;
To know key number facts by heart;
To choose efficient calculation methods;
To appreciate how maths is used and useful outside of school/education.

Willow Tree is currently working towards developing ‘Teaching for mastery’ in our maths curriculum. Teaching maths for mastery is a transformational approach which stems from research into high performing Asian nations such as Singapore.

An important feature of teaching for mastery is that the whole class works on the same topics at broadly the same pace, with lots of time and practice in each topic before moving on. An idea is carefully introduced and formed, then reinforced by lots of practice over a series of lessons. This enables children to develop a deep and long-lasting understanding of the concepts being taught.

Why did we choose the ‘Maths – No Problem!’ scheme?

The scheme is based on research and evidence and endorsed by the Department for Education, Ofsted and the NCETM (National Centre for Excellence in Teaching Mathematics).
It builds students’ mathematical fluency, reasoning and develops their ability to solve problems - the key aims of the maths curriculum.
The scheme teaches pupils to understand maths in stages, often beginning with concrete objects (such as counters, Base 10 and number disks), then moving to pictorial representations (representing problems using pictures), and finally working in the abstract (where children represent problems using mathematical notation, such as 12 ÷ 4 = 3). Through this process, children learn numerous strategies to work with numbers and build understanding and confidence in maths.
The scheme encourages pupils learn to think mathematically, as opposed to reciting formulas/’tricks’ they don’t understand.

What would you see in a ‘Maths – No Problem!’ lesson?

Each lesson is divided into distinct parts: an explore task, guided practice and independent practice. During the explore task, children work in groups on a problem from the textbook. During guided practice, children work through further questions from the textbook with a partner but under the guidance of the teacher, to practise an idea that has been developed in the explore task. The final section of the lesson is independent practice, where the children work in their own workbook to apply the ideas taught that lesson.

Within a mastery curriculum, the differing abilities of the children within our school will be catered for through the questioning and scaffolding individual pupils receive in class as they work through problems. Children who grasp ideas quickly and confidently will be challenged through more demanding problems which deepen their knowledge of the content. Where children are struggling, they will receive intervention to support them to keep pace with their peers.

For more information, please feel free to talk to the staff in school or visit the ‘Maths - No Problem!’ website, which includes a range of information and videos about the ideas behind the scheme’s approach.

Mastering Number Programme

The Mastering Number Programme was developed by the NCETM (National Centre for Excellence in Teaching Mathematics) and Maths Hubs. The project aims to secure firm foundations in the development of good number sense for all children from Reception through to Year 1 and Year 2. The aim over time is that children will leave Key Stage 1 with fluency in calculation and a confidence and flexibility with number.

The programme involves a daily 10-15 minute teaching session for all pupils in the class. In Reception, the Mastering Number sessions are the basis of the main mathematics lesson each day. In Year 1 and Year 2, the Mastering Number sessions are taught in addition to the main ‘Maths – No Problem!’ lesson.

Pupil interviews show that the children have a positive attitude towards their maths lessons and their learning.

Improvements to the curriculum and teaching of mathematics were noted in the school’s last Ofsted inspection, in 2019, and identified as contributing to our pupils’ positive experiences of school.

Standards in Maths have improved over time. In 2019, prior to the pandemic, the end of Key Stage 2 Mathematics results were above national expectations.

End of Key Stage 2 Mathematics 2019

	National	Willow Tree
Expected	79%	85%
Higher Standard	27%	29%

"We are not teaching math. We are teaching thinking through the medium of math."

Dr Yeap Ban Har

Maths Subject Content - EYFS

In EYFS the children at Willow Tree develop mathematical understanding through continuous provision and taught sessions.

Children will begin to develop a sense of number by partitioning and combining numbers within 10 and making numbers different ways. Children will develop a sense of the number system by verbally counting forward to and beyond 20, pausing at each multiple of 10, as well as playing games that involve moving along a numbered track, and understand that larger numbers are further along the track. We investigate doubles and odd/even numbers as well as distributing equally.

Children will see, explore and discuss models of common 2D and 3D shapes with varied dimensions and presented in different orientations and describe their properties. This is achieved through continuous provision by selecting, rotating and manipulating shapes for a particular purpose, for example:

• rotating a cylinder so it can be used to build a tower

• rotating a puzzle piece to fit in its place

At Willow Tree we provide experiences that develop understanding of sorting, pattern, time, position, sharing fairly, more/less and measures e.g. height. We encourage correct mathematical vocabulary through the use of stem sentences, shared talk, questioning, reasoning and explaining.

Children move on to Y1 with a deep understanding of the number system and curiosity for the World and how maths is embedded in everyday life.

Maths Subject Content - Key Stage 1

The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources [for example, concrete objects and measuring tools].

At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.

Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.

Maths Subject Content - Lower Key Stage 2

The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number.

By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.

Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

Maths Subject Content - Upper Key Stage 2

The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.

By the end of year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Pupils should read, spell and pronounce mathematical vocabulary correctly.

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