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Being a Mathematician at Cayton 

At Cayton 

 

We are following the National Curriculum for Mathematics, which aims to ensure that all pupils:

  • Become fluent in the fundamentals of mathematics, including through varied and frequent practice, so that pupils develop conceptual understanding and recall and apply knowledge

  • Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and using mathematical language

  • Can solve problems by applying their mathematics to a variety of routine and non-routine problems

This is supported mainly by White Rose Maths that we use to structure our curriculum. The scheme provides rich resources to structure high-quality lessons through the use of representations and skills of fluency, reasoning and problem solving. However, this is not exclusive as teachers are able to use a wider range of sources to deliver first-class lessons and teaching including NCETM, Maths Hub material, Oak Academy and other providers, who specialise in the delivery of Maths.

By using the CPA (Concrete, Pictorial, Abstract) approach, which is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils, we enable pupils to achieve the best possible outcomes and become successful mathematicians for the future.

The Learning Journey

Early Year

In Early Years, children start by looking at single digit numbers in different ways and representations. This provides a clear understanding of value and children learn varied ways of recognising, using and applying these numbers. This is then extended to numbers beyond 10. 

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Maths is delivered in small groups within the classroom and children then have sessions beyond the classroom in carefully constructed activities in both the indoor and outdoor areas. Children learn skills in subitising, composite numbers, exploring patterns, comparing and recognising mathematical concepts through the delivery of Maths in around the classroom. Vocabulary is a fundamental principle during the early acquisition of number and children are immersed in rich vocabulary throughout the year. 

Key Stage One

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Through Key Stage 1, children further develop the concept of value and build on their representation knowledge by using a wider range of manipulatives and diagrams to show understanding. 

Children start to record, read and write their ideas, calculations and understanding. Using the acquired skills in Early Years, they develop a deeper understanding of patterns within number and count on and backwards in different intervals. They develop a greater understanding of mathematical symbols and use these to compare numbers. They develop methods of addition and subtraction using the CPA approach and link this to the inverse operation. Pupils are taught simple fractions of shapes and describe position and properties of shapes through sorting and comparing. They begin to measure in various ways and learn the basic measures of time. 

Lower Key Stage Two

Throughout Lower Key Stage 2, children extend on their knowledge of place value and extend  to numbers up to 10 000. They develop a deeper understanding of comparing numbers and begin to order numbers beyond 1000. Pupils build on their prior knowledge of estimation and apply this knowledge when problem-solving in context. They are introduced to Roman Numerals in various structures, including real-life situations - Time and architecture. They also are introduced to decimal notation and this is taught holistically across the units.  

        

Building on the previously taught content of the curriculum, children further their understanding of the four operations and extend on the formal methods for calculation. Again, this is applied through a range of reasoning and problem-solving to have a rich and substantial knowledge of concepts and methods. In Lower Key Stage 2, pupils start to convert different units of measurements and use these to calculate and measure in varied ways. They learn the associated vocabulary and key knowledge such as seconds in a minute, hours in a day, etc. 

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Pupils develop more understanding of the position and geometry of shapes they have been taught at Key Stage one including symmetry, properties of shapes, and they are introduced to angles within shapes. They look at more complex concepts such as parallel and perpendicular lines within shapes. They begin to plot co-ordinates in the first two quadrants on a grid.

       

They start to develop a greater understanding of data and how it can be presented in graphs and charts, which builds on the data collection taught in previous years. In Lower Key Stage 2, pupils work extensively on their multiplication knowledge and facts of all facts up to multiples of 12 ready for the multiplication check at the end of the year.

Upper Key Stage Two

During Upper Key Stage 2, children develop a full range of knowledge based around place value and work with numbers up to 10 000 000. 

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Pupils develop an understanding of negative numbers and calculate across intervals. They work in detail with numbers in steps of power of 10. They round numbers to different degrees and build on key number facts such as square and cube numbers. 

Pupils develop an understanding of negative numbers and calculate across intervals. They work in detail with numbers in steps of power of 10. They round numbers to different degrees and build on key number facts such as square and cube numbers. Pupils build on knowledge of Roman Numbers by applying the knowledge to years and dates. The majority of lessons will include reasoning and multi-step problem-solving to allow pupils to investigate and explore concepts, ideas and methods in detail. 

In Upper Key Stage 2, pupils refine formal methods and use efficient methods by choosing specific methods dependent on the context of the question. They use estimation and approximation to check the validity of an answer and use mental methods to check jottings. 

They use their prior knowledge of multiplication facts to develop their understanding of factors and multiples including prime and non-composite numbers. They use short and long methods for both multiplication and division and interpret remainders in context.

Building on their knowledge from Lower Key Stage 2, they work with fractions in varied ways and scale up and down to find equivalence, which in turn helps them to develop methods of addition and subtraction of fractions. They are introduced to multiplying and dividing fractions and through the use of representations, children can apply knowledge to new concepts. Pupils extend on their work with decimals and make links between their respective equivalence of percentages and fractions. They use their prior knowledge of formal methods of multiplying and apply it to multiplying decimal. 

Pupils develop an extensive knowledge of measures and look at a full range of conversions including imperial measures. They extend their shapes knowledge to look at volume of shapes and use formulae for specific shapes. They learn and build on the specific properties of shapes and look at the associated vocabulary for circle properties - radius, diameter and circumference. Children plot co-ordinates in all four quadrants on a grid and describe translations using STEM sentences .  

Pupils study extra units of statistics, algebra and ratio and proportion to consolidate all the skills and knowledge visited through the year and apply their acquired skills in various contexts.

Maths Progression Map - What we learn

Adaptive Teaching in Maths for SEND support

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Gallery - Maths at Cayton

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