Curriculum Intent and Implementation
Maths Curriculum Statement of Intent
At Westwood, we believe that maths is essential to everyday life and provides a foundation for understanding the world. We want to ignite a sense of curiosity of maths in our children and ensure that they enjoy the subject. Our aim in maths is to ensure that the children become fluent in the fundamentals, can reason mathematically and can solve problems by applying their learning to varied situations with confidence.
We want the children to see that maths is an interconnected subject, to make connections across the different areas to develop their fluency. This is why we have adopted the mastery approach to teaching and learning maths. The idea is introduced in the Foundation Stage, developed through the Maths No Problem scheme of work in Years 1-5 and embedded in Year 6. At the same time, we unlock a passion for the subject, motivating the children to learn; encourage the children to believe that they can and will achieve in maths; and produce lifelong learners of the subject.
Below outlines the progression through the 6 distinct domains in maths at Westwood. Progression in the four operations can be seen in our Calculation Policy.
Number and place value:
During the Early Years, children become familiar with the idea of numbers through songs, counting small numbers of objects, beginning to use marks to represent numbers and starting to recognise numbers in the environment. By the end of this phase, children are able to count to 20, use number bonds to 10 and recognise odd and even numbers. This number knowledge is then developed in Keys Stage 1 when children become familiar with numbers up to 100, understanding the place value of the digits in these numbers and being able to count forwards and backwards in jumps of 2, 10, 3 and 5. Throughout Lower Key Stage 2, children’s number knowledge is extended to 10,000. Again, they use place value to recognise the worth of each digit and use patterns to help them count forward and backwards in jumps of varying size. Rounding numbers is also introduced with children learning how to round to the nearest 10, 100 or 1000. Roman numerals to 100 are also introduced. In Upper Key Stage 2, children are able to compare, order, read and write numbers up 10,000, 000 and are able to round to the nearest ten, hundred, thousand, ten thousand, hundred thousand and million. Their ability to write Roman numerals is extended to 1000 and negative numbers are also introduced. By the end of this key stage, children are also able to use simple algebraic equations to find variables.
In the Early Years, children are introduced to the language of sharing and describing amounts and are able to solve problems that involve halving and doubling. In Key Stage 1, children’s knowledge of fractions is extended beyond halves to quarters and thirds. They are able to find parts of quantities as well as sets of objects and can name different fractions. Children also begin to compare and order unit fractions and fractions with the same denominator. During their time in Lower Key Stage 2, children build on their knowledge of fractions by finding equivalents and simplifying fractions. They move on to comparing and ordering non-unit fractions as well as those with different denominators. Children are able to add fractions with the same denominator and the idea of mixed numbers and improper fractions are introduced. Decimals are also introduced at the end of this Key Stage, with children able to write and order decimals up to hundredths and round numbers with one decimal place to the nearest whole number. They use their understanding of decimals to divide whole numbers by 10 and 100. In Upper Key Stage 2, children apply their knowledge of finding equivalent fractions learnt previously to be able to add and subtract fractions with different denominators. They use their simplifying skills to write fractions in their simplest form or as mixed numbers when adding or subtracting results in an improper fraction. Children also learn how to multiply and divide fractions. Their knowledge of decimal numbers is developed to 3 places: they can round decimal numbers; multiply decimals; divide whole numbers that gives an answer with up to 2 decimal places; and divide and multiply by 10, 100 and 1000. Percentages are introduced as another way of representing fractions and children learn equivalent decimals, fractions and percentages.
Whilst in the Early Years, children at Westwood start to make comparisons of things in their environment and begin to collect simple data such as eye or hair colour. This data collection is then developed in Key Stage 1, when children start to present the information they have collected using picture graphs with a 1:1 scale or where the picture represents 2, 5 or 10. In Lower Key Stage 2, children are also introduced to bar charts as a way of presenting data and they are able to construct their own as well as interpret existing ones. Line graphs are also introduced. During Upper Key Stage 2, children begin to read tables and line graphs where more than one piece of data may be included (2 lines, various columns etc). They learn how to transfer data from a table into a graph and describe the relationship between the sets of data. By the end of Upper Key Stage 2, children are able to construct and interpret a full range of charts and graphs (including pie charts) and are able to find the mean as the average of a set of data.
Geometry-Property of Shapes:
During the Early Years, children are encouraged to show an interest in shapes in the environment and to talk about the shapes of everyday objects. They are able to describe 2D and 3D shapes using the correct language and begin making and recognising repetitive patterns. When in Key Stage 1, children build on their base knowledge of 2D and 3D shapes to sort them according to the properties and to talk about 3D shapes in terms of faces, edges and vertices. In Lower Key Stage 2, children are introduced to angles and learn that there are different types of angles within the 2D shapes they have learnt about previously. They learn about different types of lines and begin to describe 2D shapes in terms of their angles and lines. Children learn about broad shape names (triangles and quadrilaterals) and use their properties to recognise them. Symmetry is also introduced as a way of describing the properties of shapes. Children’s knowledge of angles is further developed in Upper Key Stage 2 where they learn about the properties of angles on a line and around a point. They use their existing knowledge of triangles and quadrilaterals to find missing angles and can classify geometric shapes. Finally, they learn about circles: the names of the different parts and the relationship between the radius and diameter.
Geometry-Position and Direction
Children in the Early Years use positional language, prepositions and ordinal numbers. In Key Stage 1, the children are then introduced to the idea of objects and shapes moving left or right, clockwise or anti-clockwise, up or down etc. Turns are also introduced in terms of a quarter, half or three-quarter to describe how a 2D shape has moved. This language is then applied to positions of shapes on a grid in Lower Key Stage 2. Children also plot coordinate points (in the first quadrant) and translate shapes using language of up/down and left/right. When in Upper Key Stage 2, children move on to reflecting and enlarging shapes as well as moving them on a grid. They also begin to use coordinates in four quadrants on a full grid.
In the Early Years, children begin using the language of time (before, later, soon) and begin anticipating time-specific events such as lunch time and home time. This understanding of time is developed in Key Stage 1 when children learn to tell the time to 5 minutes, including o’clock, half past, quarter to and quarter past. They are able to draw hands on clocks, sequence events and find start and finishing times. In Lower Key Stage 2, children build on their ability to tell the time by writing them to the nearest minute, using am and pm and using both analogue and digital clocks. They learn how to tell the time using a 24 hour clock and can convert between minutes and seconds, and hours and minutes. By the time they are in Upper Key Stage 2, children can convert between all units of time, including days, weeks and months and continue to solve problems involving time.
Temperature is introduced in Key Stage 1, where children learn how to read and estimate temperature. This knowledge is then used and embedded throughout the rest of the school when teaching other areas such as statistics and negative numbers.
Children in the Early Years are introduced to some of the language associated with money. When in Key Stage 1, children learn how to recognise notes and coins, find total amounts and give money in coins, notes and a mixture of both as well as how to show equivalent amounts of money in different ways. After learning about money notations previously, children in Lower Key Stage 2 are able to add and subtract amounts of money and calculate change. The also begin to use other skills such as estimating to work out how much something will cost as well as rounding to work out an approximate total. In Upper Key Stage 2, children’s money knowledge is embedded through problem solving and by using money in the context of other areas such as statistics.
Length, Mass and Capacity
During the Early Years, children begin to use language of size and start comparing and ordering objects in terms of their height, weight or length. They are introduced to capacity by talking about objects being full, half-full or empty. In Key Stage 1, children measure the length or weight of objects using non-standard measures (e.g. body parts, other objects) before being introduced to centimetres and metres; grams and kilograms; and litres and millilitres. Throughout this, children compare the length/weight/height/volume of objects. When in Lower Key Stage 2, children use the units they learned about previously to measure objects in a mixture of units (e.g. the length of a line in centimetres and millimetres). They begin reading scales to measure objects. It is in this phase that children are also introduced to perimeter and area of rectangles and squares. In Upper Key Stage 2, children learn to convert between all the units of measurement they have used before (using their multiplying/dividing by 10, 100, 1000 knowledge). This also includes converting between imperial and metric units. Volume is also introduced and children use their knowledge of perimeter and area to explore the relationship between the two (for example, can a shape have the same perimeter but different areas). They use their knowledge of finding the area of rectangles to be able to find the area of triangles and parallelograms. Ratio and proportion is also introduced.
In the Early Years, maths is strongly linked to the adventure being taught giving real purpose to the subject. Due to the nature of Maths No Problem, this isn’t always possible in other year groups, although teachers are encouraged to use the context of their adventure where appropriate. Maths lessons should incorporate active learning and use the outdoors to strengthen and deepen children’s understanding. Children are also provided with practical opportunities to apply what they have learnt as well as when they are learning new concepts. In all classrooms, a selection of practical resources are available for children to select from to enable them to move through the concrete, pictorial and abstract model of learning in maths. The profile of maths is kept high through our weekly celebrations of children’s achievements in the Times Table Mountain. We also hold special days, such as Number Day, for children to experience maths in a new, exciting and memorable way. At all times, children are encouraged to make connections across the different areas of maths and to apply their knowledge to different contexts.