Mathematics
At Shaw Wood Academy we want children to see themselves as mathematicians who: are curious learners; can learn from mistakes; can make mathematical links with the real world; can rapidly recall mathematical facts and skills mentally; have built up confidence and an ambition to succeed; and achieve their full potential through determination and resilience.
Intent
- We believe that every child can achieve
- Small steps build a solid foundation of deep mathematical understanding
- Pupils’ mathematical fluency should be built without the need for rote learning
- New concepts will be introduced using the Concrete-Pictorial- Abstract (CPA) approach
- Pupils learn to think mathematically to find patterns, connections and relationships between different concepts
Implementation
Our maths curriculum is aligned to the National Curriculum and White Rose Maths Small Steps, which is used as a whole class mastery resource.
- White Rose Maths - the research-based schemes of learning are designed to support a mastery approach to teaching and learning and are consistent with the aims and objectives of the National Curriculum
- Depth before breadth - easy-to-follow schemes support teachers to stay within the required key stage so that children acquire depth of knowledge in each topic. Opportunities to revisit previously learned skills are built into later blocks
- Working together - Children can progress through the schemes as a whole group, encouraging students of all abilities to support each other in their learning
- Fluency, reasoning and problem solving – the schemes develop all three key areas of the National Curriculum, giving children the knowledge and skills they need to become confident mathematicians
Concrete, Pictorial and Abstract (C-P-A)
Research shows that all children, when introduced to a new concept, should have the opportunity to build competency by following the CPA approach. This features throughout our schemes of learning.
- Concrete - Children should have the opportunity to work with physical objects/concrete resources, in order to bring the maths to life and to build understanding of what they are doing
- Pictorial - Alongside concrete resources, children should work with pictorial representations, making links to the concrete. Visualising a problem in this way can help children to reason and to solve problems
- Abstract - With the support of both the concrete and pictorial representations, children can develop their understanding of abstract methods
Primary Long Term Sequence
|
Year |
Autumn Term |
Spring Term |
Summer Term |
|
Year 1 |
Place value (within 10) – Number Addition and subtraction (within 10) - Number Geometry - Shape |
Place value (within 20) - Number Addition and subtraction (within 20) - Number Place value (within 50) - Number Length and height - Measurement Mass and volume - Measurement |
Multiplication and division - Number Fractions - Number Position and direction - Geometry Place value (within 100) - Number Money - Measurement Time - Measurement |
|
Year 2 |
Place Value – Number Addition and subtraction - Number Shape - Geometry |
Money - Measurement Multiplication and division - Number Length and height - Measurement Mass, capacity and temperature - Measurement |
Fractions – Number Statistics Position and direction - Geometry |
|
Year 3 |
Place value – Number Addition and subtraction - Number Multiplication and division A - Number |
Multiplication and division B – Number Length and perimeter - Measurement Fractions A - Number Mass and capacity - Measurement |
Fractions B - Number Money - Measurement Time - Measurement Shape - Geometry Statistics |
|
Year 4 |
Place value – Number Addition and subtraction - Number Area - Measurement Multiplication and division A - Number |
Multiplication and division B - Number Length and perimeter - Measurement Fractions - Number Decimals A - Number |
Decimals B - Number Money - Measurement Time - Measurement Shape - Geometry Statistics Position and direction - Geometry |
|
Year 5 |
Place value – Number Addition and subtraction – Number Multiplication and division A – Number Fractions A - Number |
Multiplication and division B – Number Fractions B – Number Decimals and percentages – Number Perimeter and area – Measurement Statistics |
Shape – Geometry Position and direction – Geometry Decimals – Number Negative numbers – Number Converting units – Measurement Volume - Measurement |
|
Year 6 |
Place value – Number Addition, subtraction, multiplication and division - Number Fractions A – Number Fractions B – Number Converting units - Measurement |
Ratio Algebra Decimals – Number Fractions, decimals and percentages – Number Area, perimeter and volume – Measurement Statistics |
Shape – Geometry Position and direction – Geometry Projects, consolidation and problem solving |
Learning Sequence
Every block in our schemes of learning is broken down into manageable small steps.
Reasoning and problem-solving activities and questions are used in class to provide further challenge and to encourage deeper understanding of each topic.
Flexibility is built into White Rose Maths so additional time can be spent on ‘lessons’ and concepts meaning teachers can pace their teaching according to their class. This may include pre-teach and consolidation of concepts. While some children will need to spend longer on a particular concept (through interventions or additional lessons) others will reach deeper levels of understanding. The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace.
Progression Overview
Reception
The first few years of a child’s life are especially important for mathematics development. Research shows that early mathematical knowledge predicts later reading ability and general education and social progress. Conversely, children who start behind in mathematics tend to stay behind throughout their whole educational journey. In Reception, our objective is to ensure that all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age. We organise our curriculum into key concepts, which underpin our early mathematics curriculum. The typical progression highlights the range of experiences (some of which may be appropriate for younger children) but the activities and opportunities can be developed across our Reception provision. There are six key areas of early mathematics learning, which collectively provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond:
CARDINALITY AND COUNTING - Understanding that the cardinal value of a number refers to the quantity, or ‘how many’ of things it represents
COMPARISON - Understanding that comparing numbers involves knowing which numbers are worth more or less than each other
COMPOSITION - Understanding that one number can be made up from (composed from) two or more smaller numbers
PATTERN - Looking for and finding patterns helps children notice and understand mathematical relationships
SHAPE AND SPACE - Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
MEASURES - Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later Additionally, our curriculum in the Reception provides the foundations for understanding calculations
|
Addition |
Subtraction |
Multiplication and Division |
|
Children start to explore addition by sorting groups. They then use sorting to develop their understanding of parts and wholes.
Children combine groups to find the whole, using a part-whole model to support their thinking. They also use the part-whole model to find number bonds within and to 10.
Using a five frame and ten frame, children add by counting on. They start by finding one more before adding larger numbers using counters or cubes on the frames.
Children use a number track to add by counting on. Linking this learning to playing board games is an effective way to support children’s addition.
|
Children start to explore subtraction by sorting groups. They use sorting to develop their understanding of parts and wholes.
When comparing groups, children use the language more than and fewer than. This will lead to finding the difference when they move into KS1.
Children then connect subtraction with the idea of counting back and finding one less using a five frame to support their thinking.
They explore subtraction by breaking apart a whole to find a missing part. This links to their developing recall of number bonds.
Children count back within 20 using number tracks and ten frames to see the effect of taking away. |
Children first start to look at the idea of equal groups through their exploration of doubles. They use five frames and objects to check that groups are equal.
Children then explore halving numbers by making two equal groups. They highlight patterns between doubling and halving seeing that double 2 is 4 and half of 4 is 2.
As well as halving, children also explore sharing into more than two equal groups. They share objects one by one, ensuring that each group has an equal share.
|
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 involves working with numerals, words and the four operations, including with practical resources [for example, concrete objects and measuring tools]. At this stage, pupils develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching also involves 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 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 read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
Children develop the core ideas that underpin all calculation. They begin by connecting calculation with counting on and counting back, but they should learn that understanding wholes and parts will enable them to calculate efficiently and accurately, and with greater flexibility. They learn how to use an understanding of 10s and 1s to develop their calculation strategies, especially in addition and subtraction.
| Addition and Subtraction | Multiplication and division | Fractions |
|
Children first learn to connect addition and subtraction with counting, but they soon develop two very important skills: an understanding of parts and wholes, and an understanding of unitising 10s, to develop efficient and effective calculation strategies based on known number bonds and an increasing awareness of place value. Addition and subtraction are taught in a way that is interlinked to highlight the link between the two operations. A key idea is that children will select methods and approaches based on their number sense. For example, in Year 1, when faced with 15 − 3 and 15 − 13, they will adapt their ways of approaching the calculation appropriately. The teaching should always emphasise the importance of mathematical thinking to ensure accuracy and flexibility of approach, and the importance of using known number facts to harness their recall of bonds within 20 to support both addition and subtraction methods. In Year 2, they will start to see calculations presented in a column format, although this is not expected to be formalised until KS2. We show the column method in Year 2 as an option; teachers may not wish to include it until Year 3. |
Children develop an awareness of equal groups and link this with counting in equal steps, starting with 2s, 5s and 10s. In Year 2, they learn to connect the language of equal groups with the mathematical symbols for multiplication and division. They learn how multiplication and division can be related to repeated addition and repeated subtraction to find the answer to the calculation. In this key stage, it is vital that children explore and experience a variety of strong images and manipulative representations of equal groups, including concrete experiences as well as abstract calculations. Children begin to recall some key multiplication facts, including doubles, and an understanding of the 2, 5 and 10 times- tables and how they are related to counting. | In Year 1, children encounter halves and quarters, and link this with their understanding of sharing. They experience key spatial representations of these fractions, and learn to recognise examples and non-examples, based on their awareness of equal parts of a whole. In Year 2, they develop an awareness of unit fractions and experience non-unit fractions, and they learn to write them and read them in the common format of numerator and denominator. |
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. In Years 3 and 4, children develop the basis of written methods by building their skills alongside a deep understanding of place value. They should use known addition/subtraction and multiplication/division facts to calculate efficiently and accurately, rather than relying on counting. Children use place value equipment to support their understanding, but not as a substitute for thinking.
| Addition and Subtraction | Multiplication and division | Addition and Subtraction |
|
In Year 3 especially, the column methods are built up gradually. Children will develop their understanding of how each stage of the calculation, including any exchanges, relates to place value. The example calculations chosen to introduce the stages of each method may often be more suited to a mental method. However, the examples and the progression of the steps have been chosen to help children develop their fluency in the process, alongside a deep understanding of the concepts and the numbers involved, so that they can apply these skills accurately and efficiently to later calculations. The class should be encouraged to compare mental and written methods for specific calculations, and children should be encouraged at every stage to make choices about which methods to apply. In Year 4, the steps are shown without such fine detail, although children should continue to build their understanding with a secure basis in place value. In subtraction, children will need to develop their understanding of exchange as they may need to exchange across one or two columns. By the end of Year 4, children should have developed fluency in column methods alongside a deep understanding, which will allow them to progress confidently in upper Key Stage 2. |
Children build a solid grounding in times-tables, understanding the multiplication and division facts in tandem. As such, they should be as confident knowing that 35 divided by 7 is 5 as knowing that 5 times 7 is 35. Children develop key skills to support multiplication methods: unitising, commutativity, and how to use partitioning effectively. Unitising allows children to use known facts to multiply and divide multiples of 10 and 100 efficiently. Commutativity gives children flexibility in applying known facts to calculations and problem solving. An understanding of partitioning allows children to extend their skills to multiplying and dividing 2- and 3-digit numbers by a single digit. Children develop column methods to support multiplications in these cases. For successful division, children will need to make choices about how to partition. For example, to divide 423 by 3, it is effective to partition 423 into 300, 120 and 3, as these can be divided by 3 using known facts. Children will also need to understand the concept of remainder, in terms of a given calculation and in terms of the context of the problem. |
Children develop the key concept of equivalent fractions, and link this with multiplying and dividing the numerators and denominators, as well as exploring the visual concept through fractions of shapes. Children learn how to find a fraction of an amount, and develop this with the aid of a bar model and other representations alongside. in Year 3, children develop an understanding of how to add and subtract fractions with the same denominator and find complements to the whole. This is developed alongside an understanding of fractions as numbers, including fractions greater than 1. In Year 4, children begin to work with fractions greater than 1. Decimals are introduced, as tenths in Year 3 and then as hundredths in Year 4. Children develop an understanding of decimals in terms of the relationship with fractions, with dividing by 10 and 100, and also with place value. |
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.
In upper Key Stage 2, children build on secure foundations in calculation, and develop fluency, accuracy and flexibility in their approach to the four operations. They work with whole numbers and adapt their skills to work with decimals, and they continue to develop their ability to select appropriate, accurate and efficient operations.|
Addition and subtraction |
Multiplication and division |
Fractions |
| Children build on their column methods to add and subtract numbers with up to seven digits, and they adapt the methods to calculate efficiently and effectively with decimals, ensuring understanding of place value at every stage. Children compare and contrast methods, and they select mental methods or jottings where appropriate and where these are more likely to be efficient or accurate when compared with formal column methods. Bar models are used to represent the calculations required to solve problems and may indicate where efficient methods can be chosen. | Building on their understanding, children develop methods to multiply up to 4-digit numbers by single-digit and 2-digit numbers. Children develop column methods with an understanding of place value, and they continue to use the key skill of unitising to multiply and divide by 10, 100 and 1,000. Written division methods are introduced and adapted for division by single-digit and 2-digit numbers and are understood alongside the area model and place value. In Year 6, children develop a secure understanding of how division is related to fractions. Multiplication and division of decimals are also introduced and refined in Year 6. |
Children find fractions of amounts, multiply a fraction by a whole number and by another fraction, divide a fraction by a whole number, and add and subtract fractions with different denominators. Children become more confident working with improper fractions and mixed numbers and can calculate with them. Understanding of decimals with up to 3 decimal places is built through place value and as fractions, and children calculate with decimals in the context of measure as well as in pure arithmetic. Children develop an understanding of percentages in relation to hundredths, and they understand how to work with common percentages: 50%, 25%, 10% and 1%. |
Please see the link to White Rose Maths where you can access home learning resources. Please select the relevant year group from the drop down box.
https://whiteroseeducation.com/parent-pupil-resources/maths/home-learning?year=early-years