Maths

Mathematics

At Scorton Primary School, we believe that mathematics is a fundamental part of everyday life for people all over the world and across a wide range of different cultures. It helps us understand many aspects of the world around us and live independently both as children and in our future lives.

National Curriculum Purpose of Study

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

A Whole School Curriculum ...

Early Years Foundation Stage (EYFS)

Mathematics in EYFS comes under two strands, each of which has an Early Learning Goal (ELG) below:

Number- Children at the expected level of development will: have an understanding of number to 10, linking names of numbers, numerals, their value, and their position in the counting order, subitise (recognise quantities without counting) up to 5, and automatically recall number bonds for numbers 0-5 and for 10, including corresponding partitioning facts.

Numerical Patterns- Children at the expected level of development will: automatically recall double facts up to 5+5, compare sets of objects up to 10 in different contexts, considering size and difference and explore patterns of numbers within numbers up to 10, including evens and odds.

Key Stage 1

The principal focus of mathematics teaching in KS1 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 KS1.

Lower Key Stage 2

The principal focus of mathematics teaching in lower KS2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including numbers 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 reading word knowledge and their knowledge of spelling.

Upper Key Stage 2

The principal focus of mathematics teaching in upper KS2 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 of 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.

Our Approach - Red Rose Maths 

A mastery curriculum rejects the idea that a large proportion of people ‘just can’t do maths’ (NCETM 2016) and instead focuses on the idea that all pupils can achieve depth in their learning which can be accomplished by using key principles including:

• representation and structure (effective pedagogies for modelling, concrete-pictorial-abstract approaches, effective use of manipulatives and transition between them)
• coherence (curriculum design, progression of objectives, sequencing learning, small steps, contextualising learning between different areas of mathematics)
• mathematical thinking (effective questioning, identifying patterns and relationships, deep understanding through reasoning and problem solving, supporting children to achieve deeper learning where appropriate)
• variation (progression through representations using conceptual variation, progression through questioning using procedural variation)
• fluency (efficiency, accuracy, flexibility, developing unconscious competence)

These elements of effective mathematics teaching are supported in both the National Curriculum and the Ofsted Inspection Framework.

The scheme provides teachers with comprehensive planning materials for each lesson including teaching resources, detailed planning guidance and children’s task sheets, including deeper learning tasks to challenge more able mathematicians.

What are manipulatives and concrete materials in maths?

Concrete resources, also known as manipulatives, are physical objects that children can pick up and manipulate to improve their maths knowledge. Used in maths education, a variety of concrete maths resources can help children to understand the relationship between numbers and the number system. Here are some we use in school.

Numicon

Numicon is an approach to teaching maths that helps children to see connections between numbers. It supports children as they learn early maths skills. It is a multi-sensory way of learning, which means your children learns by seeing and feeling. 

Physical resources like the colourful Numicon Shapes are an important part of Numicon. The holes in the Numicon Shapes represent the numbers 1 and 10. When they are arranged in order, as in the picture below, children can easily see connections between numbers such as ‘one’ more and ‘one less’. 

Later on, children will be able to see more complex mathematical ideas, like how two fours make eight, three twos make six and so on. This lays the foundation for their understanding of number all the way through school.

Base 10

Have you used numbers 0 - 9 to count? Then without even realising, you've used base-10! Base 10 is a method of assigning a place value to numbers. It's also known as the place value number system, or decimal system, as the numerical value of a number relies on where the decimal point sits.

Base Ten is widely recognised as a preferred teaching resource for place value, but also for demonstrating early addition, subtraction and algebra. The children are able to physically hold the tens and ones and see a representation of a large number which supports their understanding of what that number in terms of tens and ones.

For example, a common misconception is that the digit 4 in ‘45’ means 4 when in fact in represents ‘40’. By using Base 10 the children are able to clearly see the representation and have a clearer understanding of place value. 

Ten-Frame

A ten frame is a simple tool for teaching maths. They help children to develop number sense and early numeracy skills. The more young children encounter numbers and how they interact with each other, the more their number sense and skill grows.

You can use a ten frame to help children with addition and subtraction. Ten frames are two-by-five rectangular frames that form a base for which objects like counters can be placed. Using this device, children can practice with numbers from one to ten. By using ten frames, children can develop number sense in a visual and physical way, which is great news for their memory cognition as it activates all parts of the brain.  A ten frame reinforces fluency skills and ensures children a complete understanding of numbers to 10 and beyond.

Part Whole Model 
The part-whole model is the concept of how numbers can be split into parts. Children using this model will see the relationship between the whole number and the component parts. This helps learners make the connections between addition and subtraction