At The Blue School, we consider mathematics to be an international language. Through the development of a mastery curriculum, we aim to enable all children to achieve mastery in maths through reasoning, generalising and solving problems. We aim for our children to become fluent mathematicians, allowing them to function ably in a range of situations.
Our approach to teaching maths is underpinned by the dimensions of depth – which together enable pupils to develop deep understanding of the subject. We use the content of the national curriculum as the starting point for our curriculum but this is expanded upon by making explicit the foundational knowledge that learners need to understand in order to access this. We encourage pupils to be systematic, to generalise and to seek out patterns through a sequenced curriculum.
The three principles of the dimensions of depth are:
Mathematics tasks are about constructing meaning and making sense of relationships. The children at The Blue School deepen their understanding by representing concepts using objects, pictures, symbols and words. Tasks and topics are sequenced to help all learners build a narrative through different strands of the curriculum. These topics are then sequenced in a logical progression that allows learners to establish connections and draw comparisons. Multiple representations are carefully selected so that they are extendable within and between different areas of mathematics.
The use of mathematical language is of paramount importance at The Blue School to enable all children to reason and explain. Talk is an essential element of every lesson and time is dedicated to developing confidence with specific vocabulary as well as verbal reasoning through talk tasks.
This means our children acquire and achieve a deep, long-term, secure and adaptable understanding of the subject. Our emphasis in lessons is on understanding the mathematical concepts. Here follows some detailed examples of the key skills and learning each child will experience through each key phase within the primary curriculum.
At the end of the early years foundation stage, the children will be able to verbally count beyond 20, recognising the pattern of the counting system. They will be able to compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or equal to the other quantity. They will also explore and represent patterns within numbers up to 10, including evens and odds, doubles, and how quantities can be distributed equally.
During key stage one, children will develop their learning in a variety of different units within the curriculum. They will be able to use place value and number facts to solve problems, as well as read and write numbers to at least 100 in numerals and words. They will also be able to solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplicative facts, including problems in contexts. They will develop skills to calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs. They will explore calculation strategies such as how to add and subtract numbers mentally, including: a two-digit number and ones; a two-digit number and tens; adding three one-digit numbers.
During lower key stage two, the children will further deepen their understanding of mathematical concepts, operations and fluency. They will be able to add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate; estimate and use inverse operations to check answers to a calculation; solve addition and subtraction two-step problems in context, deciding which operations and methods to use and why. They will explore fractions and be able to add and subtract fractions with the same denominator; recognise mixed numbers and improper fractions; and convert from one form to the other and write mathematical statements. In measurement they will learn to use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places. In geometry, the children will recognise that shapes with the same areas can have different perimeters and vice versa; recognise when it is possible to use formulae for area and volume of shapes. For position and direction, they will be able to describe positions on a 2-D grid as coordinates in the first quadrant.
In key stage two, the children secure and develop their understanding of mathematical concepts across all units. In the unit of integers and decimals, they will be able to round numbers, make estimates and use this to solve problems in context, as well as solve multi-step problems involving addition and subtraction. They will develop the operational skills to divide integers by 1-digit and 2-digit numbers representing remainders appropriately, whilst being able to illustrate and explain formal multiplication and division strategies. They will be introduced to the use of brackets and use knowledge of the order of operations to carry out calculations. In geometry they will be able to draw a range of shapes using given dimensions and angles, and describe, translate and reflect shapes on a coordinate plane. Furthering their understanding of fractions, they will be able to multiply two proper fractions and divide a fraction by an integer. Statistically, they will learn to connect percentages with fractions; explore the equivalence of fractions, decimals and percentages; calculate the mean; and construct and interpret line graphs and pie charts.