Maths

Intent

The National Curriculum for mathematics aims to ensure that all pupils:

Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing and argument, justification or proof using mathematical language.
Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

At Holy Trinity, we intend to provide a spiral across the terms of the White Rose curriculum. The spiral curriculum is a curriculum model in which a sequence of topics or themes are revisited in turn with the complexity of the content increasing each time learners encounter the topic or theme, with foundational concepts being taught to begin with and then added to, or built upon, as the spiral loops and prior knowledge is revisited. This curriculum model allows for previous learning to be reinforced as well as allowing for related new content to be taught and learned in the context of what has already been learned. We create a MTP to incorporate the CPA approach.

Key principles of a spiral curriculum

Harden and Stamper identify 4 key features of Bruner’s spiral curriculum. Over time:

Topics are revisited

Levels of difficulty increase

New learning is related to previous learning

And that as a result:

The competence of students increases and knowledge is retained

We intend for this to set all pupils up with the skills and knowledge to be successful in their future lives, and to help them understand and contribute to the world around them.

We implement our approach through high quality teaching delivering appropriately challenging work for all individuals. To support us, we have a range of mathematical resources in classrooms including Numicon, base10 and counters (concrete equipment). When children have grasped a concept using concrete equipment, images and diagrams are used (pictorial) prior to moving to abstract questions. Abstract maths relies on the children understanding a concept thoroughly and being able to use their knowledge and understanding to answer and solve maths without equipment and images. Concrete, Pictorial, Abstract, where children use resources to enable them to access questions whether to answer fluency questions or reasoning by proving it and explaining.

We incorporate sustained levels of challenge through varies and high quality activities where children can develop determination, perseverance and resilience. Challenge is provided by going deeper rather than accelerating into new mathematical content. Teaching is focused, rigorous and thorough, to ensure that learning is sufficiently embedded and sustainable over time.

Implementation

A typical Maths sequence will spiral between the White Rose units to offer retaintionand build upon skills. We provide the opportunity for all children, regardless of their ability, to work through Fluency, Reasoning and Problem Solving activities. We follow the White Rose schemes of learning to ensure that the coverage for the year is completed and we recognise that in order for pupils to progress to deeper and more complex problems, children need to be confident and fluent across each yearly objective. Lessons may be personalised to address the individual needs and requirements for a class but coverage is maintained. We also use a range of planning resources including those provided by the NCETM and NRICH to enrich our children’s maths diet. Through mathematical talk, children will develop the ability to articulate, discuss and explain their thinking. Children are provided with the necessary resources to allow all children to access the curriculum and encourage them to use this where appropriate to explain their logic and reasoning. Teachers use the learning challenges to teach for mastery – and approach to extend and deepen the understanding of pupils within each year group.

Flashback and recall

In each class children are set a maths task to ensure general maths knowledge and fluency are maintained and developed, these may take many forms, for example: arithmetic, specific times tables or several questions about a mixture of maths topics. While the class are solving the questions, the staff are able to support children with consolidation or pre teaching ensuring they are confident with the skills required for the upcoming session.

Online Maths tools are used in order to advance individual children’s maths skills in school and at home, we utilise Times Tables Rock Stars for multiplication practise, application and consideration. We also use Numbots to support in fluency.

Impact

Pupil Voice

Through discussion and feedback, children talk enthusiastically about their maths lessons and speak about how they love learning about Maths. They can articulate the context in which maths is being taught and relate to this in real life purposes.

Evidence in Knowledge Pupils know how and why maths is used in the outside world and in the workplace. They know about different ways that maths can be used to support their future potential. Mathematical concepts or skills are mastered when a child can show it in multiple ways using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations. Children demonstrate a quick recall of facts and procedures. This includes the recollection of the times table.

Evidence in Skills Pupils use acquired vocabulary in Maths lessons. They have the skills to use methods independently and show resilience when tackling problems. The flexibility and fluidity to move between different contexts and representatives of Maths. Children show a high level of pride in the presentation and understanding of the work. The chance to develop the ability to recognise relationships and make connections in maths lessons. Teachers plan a range of opportunities to use maths inside and outside school.

Outcomes At the end of each year we expect the children to have achieved Age Related Expectations (ARE) for their year group. Some children will have progressed further and achieved greater depth (GD). Children who have gaps in their knowledge receive appropriate support and intervention. Mastery, All children secure long-term, deep and adaptable understanding of maths which they can apply in different contexts.

EYFS

In Early Years, we follow the Mastering Number and White Rose Scheme. Mathematics involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measure.

Pupils are taught to:

Number

count reliably with numbers from 1 to 20
place them in order and say which number is one more or one less than a given number
add and subtract two single-digit numbers and count on or back to find the answer using quantities and objects
solve problems, including doubling, halving and sharing
Shape, space and measure
use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems
recognise, create and describe patterns
explore characteristics of everyday objects and shapes
use mathematical language to describe them.

Key Stage 1

The National Curriculum (2014) states that:

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.

Lower Key Stage 2

The National Curriculum (2014) states that:

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.

Upper Key Stage 2

The National Curriculum (2014) states that:

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.