Curriculum Leaders: Meghan Tamsett, Sam Davison and Libby Searle

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.

Aims

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 an 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.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Maths in EYFS

Developing a strong grounding in number is essential so that all children develop the necessary building blocks to excel mathematically. By the end of YR, children should be able to count confidently and develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. By providing frequent and varied opportunities to build and apply this understanding - such as using manipulatives, including small pebbles and tens frames for organising counting - children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built. In addition, the curriculum must include rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics, including shape, space and measures. Children must develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

Our maths curriculum focuses on developing children's understanding of numbers, shapes, and spatial awareness through various practical and hands-on activities. Working this way ensures a strong foundation for future learning and develops children's confidence and enjoyment of maths.

During the autumn term, children begin by exploring the concepts of matching and sorting and creating sets and rules for sets.  They then move on to exploring numbers 1, 2, and 3. Each number is looked at in-depth and from various mathematical principles:  They learn to represent these numbers differently and compare them using language such as more than, less than, and equal to.  Subitising numbers, number formation and recognising each number’s place in the number system permeates all number lessons throughout the year.

In the spring term, children move on to numbers 4, 5, and 6. Again, time is spent looking at these in depth before beginning to develop an understanding of addition and subtraction through practical activities such as combining and taking away objects. They also explore length and height and develop their understanding of time.

In the summer term, children progress to numbers 7, 8, 9, and 10. They learn to compare and order numbers, as well as develop their understanding of place value and bonds to 10.

Throughout the year, children consolidate their learning by developing their number formation skills, subitising to 5, and recognising numbers on a number line.  In addition to this, they explore the concepts of shape, investigating 2-D and 3-D shapes: length, height, time and pattern.

Year 1 

In Year 1, the maths curriculum builds on the foundation laid in Reception and introduces new concepts to help children develop their understanding of number and calculation, shape, and measurement.

At the beginning of the year, children explore place value within 10, developing their understanding of how numbers are composed of tens and ones. They learn to count forwards and backwards, compare and order numbers, and use a range of representations, such as numicon and tens frames, to support their understanding.

The focus then moves to addition and subtraction within 10, where children learn to use various strategies to solve simple problems. They learn to use concrete resources such as counters and cubes to help them understand the concepts and develop their mental arithmetic skills.

As the year progresses, children develop their understanding of place value within 20, using their knowledge of tens and ones to represent and compare numbers. They also move on to addition and subtraction within 20, using more complex strategies such as counting on and using number bonds to 10 to solve problems.

In the spring term, children extend their understanding of place value within 50, exploring larger numbers and using various resources such as number lines to help them understand the concepts. They also learn about measurement, including length, height, mass, and volume.

In the summer term, children continue to develop their understanding of number, exploring fractions and place value within 100. They also learn about money, time, and geometry, including position and direction, left, right, forwards, and backward. From the beginning of the summer term, the children begin to explore multiplication and division, counting in 2s, 5s, and 10s, and using arrays and equal groups to solve problems.

Throughout the year, children have opportunities to develop their problem-solving skills, using a range of strategies and resources to solve problems and explore mathematical concepts. They also have opportunities to develop their mathematical language, using precise vocabulary to describe and explain their thinking.

Year 2

In Year 2, children continue to build on the mathematical skills and knowledge they developed in Year 1. They start the year by revising and consolidating their understanding of place value within 100, and begin to apply this knowledge to addition and subtraction problems involving two-digit numbers. They continue to develop their addition and subtraction skills, now focusing on problems that require them to exchange tens and ones

In the second half of the autumn term, children start to explore the properties of 2D and 3D shapes, and how to compare and classify them based on their attributes.

During the spring term, children learn about money including how to make different amounts using a range of coins and notes. They also begin to learn about multiplication and division, exploring these concepts through counting in 2s, 5s, and 10s.

In the second half of the spring term, children continue to develop their knowledge and understanding of measurement, focusing on length, mass, temperature and capacity.

In the summer term, children learn about fractions, including how to find half and quarters of shapes and quantities. They also explore time, learning to read and write times on analogue and digital clocks, and to solve problems involving time intervals and duration.

During the second half of the summer term, children learn about position and direction, including rotations and turns, and explore statistics through the use of pictograms, tally charts, block diagrams, and tables.

Throughout the year, children engage in a range of practical activities and problem-solving tasks to help them apply and develop their mathematical skills. They also have opportunities to develop their reasoning and communication skills through discussing and explaining their thinking.

Year 3 

In Year 3, students continue to build on their mathematical skills and knowledge, working towards a deeper understanding of key concepts and their application in problem-solving.

During the autumn term, students begin to explore place value up to 1,000, understanding the relationships between ones, tens, and hundreds. They also develop their skills in addition and subtraction, using mental and written methods to solve problems involving larger numbers. Students then move on to multiplication and division, focusing on the 3x, 6x, 4x, and 8x tables.

In the spring term, they deepen their understanding of multiplication and division, exploring larger numbers and developing strategies for solving problems. They then work with measures of length and find the perimeter of square and rectangular shapes using standard units and estimating measurements.

During the second part of the spring term, children look at fractions, working with both unit and non-unit fractions, equivalent fractions, and tenths. They continue their work with measures focusing on mass and capacity, developing their skills in using standard units and solving problems that require them to add, subtract, and compare measurements.

In the summer term, students deepen their understanding of fractions, working with decimals and solving problems that involve adding and subtracting fractions. They also deepen their understanding of money, adding and subtracting various quantities linking to their addition and subtraction skills. They also begin to tell time to the nearest minute and use am and pm to distinguish between morning and afternoon times.

During the second part of the summer term, students are introduced to statistics, using tables, bar graphs, pictograms, and tally charts to organize and interpret data. They continue their work with geometry, exploring the properties of shapes, types of lines, quadrilaterals, and angles.

Throughout the year, students engage in a range of activities to develop their mathematical fluency and reasoning skills. They work on mental arithmetic, developing strategies to solve problems quickly and efficiently. They engage in problem-solving activities that require them to apply their mathematical knowledge to real-world situations. They also work collaboratively, discussing and evaluating different approaches to solving problems and communicating their thinking clearly and effectively.

Year 4

In Year 4, students continue to build on their foundational math skills while also delving deeper into new concepts. At the start of the year, the focus is on place value, with students learning to recognize and round numbers up to 10,000. They also work on addition and subtraction up to 10,000, using mental and written methods to solve problems.

During the second part of the autumn term, children focus on using multiplication to find the area of square and rectangular shapes as part of their measurement unit. They then go on to further their understanding of multiplication and division methods and learn to multiply and divide by 1, 0, and 10, and use these skills to solve problems involving money, decimals, and fractions.

In the spring term, children continue with multiplication and division as their main focus, learning the 9x, 7x, 11x, and 12x tables. From here, they delve deeper into length and perimeter using different units of measure.

During the second part of the spring term, the children move on to fractions, which become more complex in Year 4, with students working with mixed numbers and improper fractions. They learn to add and subtract fractions with the same denominator and to convert tenths and hundredths to decimals. This then links to their decimal unit where they explore tenths and hundredths in more detail.

During the summer term, children continue to explore decimals and then relate this to money. They recap on the previous year’s learning of time, telling the time to the nearest minute.

At the end of the year, geometry takes centre stage, with students learning about the properties of triangles and quadrilaterals, as well as symmetry. They also learn to describe movement on a grid and find the perimeter of shapes.

Throughout the year, students also work on statistics, creating and interpreting line graphs, and using comparison, sum, and difference to solve problems.

As the year progresses, the math concepts become more challenging, but the students continue to build on their knowledge and skills, gaining confidence in their ability to solve increasingly complex problems. By the end of Year 4, they are well-equipped to take on the challenges that lie ahead in their math education.

Year 5 

In Year 5, students continue to build on the mathematical knowledge and skills they acquired in previous years. They are introduced to more complex concepts and are expected to develop a deeper understanding of mathematical principles.

The first topic in Year 5 maths is place value. Students learn to identify the place value of each digit in numbers up to one million, including decimals up to two decimal places. They also learn to round numbers to the nearest ten, hundred, thousand, or decimal place.

Next, they move on to addition and subtraction. They are expected to estimate the answer to a calculation and to use efficient methods, such as column addition and subtraction, to calculate accurately.

In multiplication and division, students learn to identify common multiples and factors, as well as prime, square, and cubed numbers. They are also taught to multiply and divide by 10, 100, and 1,000. Students learn formal methods of multiplication and division and are expected to solve more complex problems.

In fractions, students learn to work with mixed numbers and improper fractions. They also learn to multiply fractions by integers and to add and subtract mixed and improper fractions with the same denominator.

Decimals and percentages are also introduced in Year 5. Students learn to convert hundredths and thousandths to decimals, round decimals to the nearest whole number or one decimal place, and find equivalent fractions, decimals, and percentages.

Measurement topics include calculating the perimeter of rectilinear shapes and the area of compound shapes. Students also learn to convert units of measure, such as millilitres to litres or kilometres to meters.

Statistics is another key topic in Year 5 maths. Students learn to read and interpret line graphs and use these to compare different data sets. They also learn to find the sum and difference of data sets.

In geometry, students learn about regular and irregular polygons, how to calculate angles, and how to use a protractor. They also learn to draw angles and lines accurately. They are introduced to the concept of lines of symmetry and learn how to translate and reflect shapes.

Year 6 

In Year 6 maths, the focus is on consolidating and deepening the knowledge and skills acquired in previous years. The curriculum covers various mathematical concepts and skills, including place value, four operations, fractions, decimals, ratio, algebra, geometry, and statistics.

At the beginning of the year, students continue to work on place value, extending their knowledge to numbers up to 10 million. They then move on to addition and subtraction of numbers, including decimals. Children learn to solve multiplication and division problems using the short and long methods, focusing on using efficient methods and solving multi-step problems. They also learn about square and cube numbers, and the rules of divisibility.

Fractions are a major focus in Year 6, and students learn to identify equivalent fractions and simplify them. They also learn about converting between fractions, decimals, and percentages and solve problems using these concepts.

Ratio and proportion are introduced, with a focus on scale factors and solving ratio problems. Algebra is also introduced, and students learn to find rules, form expressions, and use formulae.

In geometry, students learn to use protractors to calculate angles in shapes and on a straight line. They also learn about four quadrants, translations, and reflections. In statistics, they learn to read, interpret, and create line graphs and pie charts with percentages.

Problem-solving and application are emphasized throughout the year, and students are given opportunities to apply their mathematical knowledge and skills to real-life situations.

By the end of Year 6, students are expected to have achieved a level of mathematical fluency and proficiency that prepares them for secondary school mathematics. Themed projects are designed to support the children in making links between a wide range of concepts and putting their learning from the year into practice ready for secondary school mathematics.