Mathematics
William Harding Maths Calculation Strategy KS1
William Harding Maths Calculation Strategy LKS2
William Harding Maths Calculation Strategy UKS2
William Harding School Mathematics Long-Term Plan
William Harding Magic Maths Long Term Plan
If you would like to find out more about our Maths curriculum, please email the office FAO Mrs Sharp.
If you would like to find out more about our EYFS curriculum, please click here
Our aims for our Mathematics curriculum are to provide a foundation for understanding the world, the ability to reason mathematically, develop an appreciation of the power of Mathematics and a sense of enjoyment and curiosity about the subject. At William Harding we believe that Mathematics is a fundamental life skill, enabling thought, learning and expression and ensuring that our pupils can play a full and active part as individuals within society.
Intent
We aim to ensure that the pupil’s needs as learners and mathematicians are effectively met across the curriculum and that practice within the school is consistent and clear.
We aim for our pupils to;
become numerically fluent so that they have quick recall of number facts and the ability to manipulate and apply number facts.
become fluent using methods to calculate so that the pupils know when and how to use a range of methods.
be able to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using concise mathematical language
solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication
be able to break down problems into a series of simpler steps and persevere in seeking solutions.
use discussion in order to learn; they should be able to elaborate and explain clearly their understanding and ideas, using concise mathematical vocabulary
develop a deep and sustained understanding of mathematical concepts, that are built on in subsequent lessons and units
build knowledge of concepts through small steps
develop, understand and use accurate mathematical vocabulary
apply their mathematical skills to a range of areas across the curriculum
Implementation
At William Harding, Mathematics is taught through a mastery approach. We use Power Maths, a DFE approved scheme, as the main structure of our curriculum. This means that lessons are carefully planned and taught progressively, developing pupils’ mathematical fluency, mathematical thinking and conceptual understanding. Lessons are planned using a small steps approach to ensure that pupils can build on learning to develop a deep understanding of concepts. Pupils’ ability to connect new ideas to concepts that have already been understood is at the heart of this approach.
Each lesson begins with an opportunity to develop fluency. The pupils then complete a discover task where pupils work together, using manipulatives, to solve a problem. Teaching uses the initial problem and enables pupils to develop and use a range of representations to understand concepts. Learning is carefully scaffolded to support children to complete independent tasks.
Arithmetic
In the Foundation Stage, pupils are taught to count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number.
In Key Stage 1, the principal focus of mathematics teaching 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. By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value.
In Key Stage 2, the principal focus of mathematics teaching is to ensure that pupils become increasingly fluent with whole numbers, fractions and the four operations, including number facts and the concept of place value. This will ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers, to include larger numbers as the pupils progress. By the end of year 4, we aim for pupils to have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.
Counting and Magic Maths
The National Curriculum states that 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.
In the Foundation Stage pupils are taught to count reliably from 1 to 20, placing them in order and saying which number is one more or one less than a given number. They solve problems that involve combining groups of 2, 5 or 10. The aim of Magic Maths is to embed these key skills.
In Key Stage 1, the knowledge and skills developed in Magic Maths within the Foundation Stage are built upon and daily counting takes place in Year 2.
In Key Stage 2, numerical fluency is developed through developing understanding and recall of number facts including multiplication facts and counting in specified steps beyond the 12 x 12 tables. Pupils also have the opportunity to count in decimals, fractions and whole numbers.
Reasoning and Problem Solving
In the Foundation Stage pupils are taught to use quantities and objects, pupils learn to add and subtract two single-digit numbers and count on or back to find the answer. They learn to solve problems, including doubling, halving and sharing.
In Key Stage 1 and 2 there are daily opportunities to solve a range of problems and develop a range of reasoning skills. Pupils are given the opportunity to orally rehearse their reasoning during lessons and create written reasoning responses. Each lesson starts with a discover section which gives pupils the chance to explore a problem, discuss a solution and justify the method.
In Key Stage 1, 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. They are able to discuss and solve problems in familiar practical contexts, including using quantities.
In Key Stage 2, pupils develop their ability to solve a range of problems, including those with simple fractions and decimal place value. Teaching ensures 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 ensures that pupils can use measuring instruments with accuracy and make connections between measure and number. By the end of year 6, we aim for pupils to be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
Vocabulary development
Pupils’ acquisition and command of vocabulary are key to their learning and progress across the whole curriculum and vocabulary must be explicitly taught these skills. Teachers therefore develop vocabulary actively, building systematically on pupils’ current knowledge. They will increase pupils’ store of words in general and make links between known and new vocabulary. In this way, pupils expand the vocabulary choices that are available to them. It is particularly important to introduce pupils to accurate mathematical language.
Manipulatives and Pictorial Representations
As we follow a mastery approach to teaching we give pupils the opportunity to use concrete materials initially to develop an understanding of concepts. Teachers model pictorial representations to support understanding and pupils are encouraged to represent ideas using a range of representations. When pupils have a sound understanding of a concept they move on to an abstract representation, for example a formal written method.
Impact
The aim of our approach to teaching maths is that pupils will;
have developed numerical and conceptual fluency
have developed reasoning and problem solving skills
have developed an understanding of how concepts in mathematics are interlinked
be passionate and enthusiastic about mathematics and see how important mathematics is in everyday life
have an understanding of a broad range of mathematical vocabulary