Mathematics
The vision for the Mathematics Department at Corpus Christi is to provide an education which inspires pupils to be ambitious and reach their God given potential. To achieve this, we have developed a curriculum which supports and challenges all pupils, regardless of their ability, and ensures pupils are meeting the expected outcomes set out in the National Curriculum, and in some cases exceeding them. Teachers are highly skilled in adapting their teaching in response to feedback from pupils, allowing them to provide extra support or to stretch pupils further where appropriate. We believe it is our duty to make mathematics a subject which all pupils can access and enjoy, ensuring they are equipped to use mathematics after they leave school, whether that is using the basic numeracy skills required in adult life or studying mathematics at A level and beyond.
Teaching and Learning
Due to the interconnected relationship between topics in mathematics, it is vital that pupils have mastered any prior learning in order to compound their knowledge throughout their time at Corpus Christi. The sequencing of topics is imperative, referred to in the key stage 3 overview section of this page, but once this is in place, there are several fundamental aspects of teaching which allow our pupils to experience success in mathematics.
Firstly, the environment created in mathematics classrooms is highly conducive to learning, with exceptional behaviour displayed from pupils in all year groups and strong relationships between teachers and pupils clearly evident. When introducing a new concept to pupils, teachers systematically check the security of the prior skills required to access the next step in learning. This is achieved through various forms of formative assessment such as use of mini-whiteboards, diagnostic questioning and purposeful paired discussion. Alongside this, all key stage 3 pupils are tested on the fundamental numeracy skills required for the scheme they are following, with immediate intervention provided for pupils with gaps in learning (more detail available in the numeracy intervention section of this page). Once the security of prior learning is established, highly effective modelling is used to explain the methods required for each topic, with the most effective methods agreed on by all staff members and put into the schemes of work, ensuring consistency and quality of explanations in all classrooms. Throughout the learning process, pupils are given regular opportunities to model methods to their partner to consolidate learning, improve oracy and to increase their confidence in the subject.
To maintain skills in mathematics, regular and purposeful recapping is imperative. To achieve this, teachers have highly impactful and regular recapping routines which incorporate paired discussion, addressing misconceptions and written practice.
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 programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects.
Decisions about progression should 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 in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on.
For pupils to achieve success in mathematics, they must accumulate knowledge and skills over time in order to access future topics. The spiralling nature of our schemes of work allow pupils to develop their skills gradually and securely, revisiting topics in future years to retain and enhance their knowledge throughout their time in our school. This approach ensures that pupils are secure in the fundamental skills required for new learning, providing the necessary space in their working memory to absorb new and more complex content.
All pupils study the skills detailed in the national curriculum, with teachers adapting their teaching where necessary to provide extra support or to stretch pupils beyond the national curriculum where appropriate.
Year 7
| UNIT 1 STATISTICS | UNIT 4 FRACTIONS & PERCENTAGES | UNIT 7 RATIO & PROPORTION |
| Calculating averages and range. Constructing and interpreting; Pictograms Bar charts Line graphs Two-way tables Frequency tables Grouping data. Misleading graphs. | Comparing fractions. Simplifying fractions. Fractions, decimals & percentages. Fractions of amounts. Percentages of amounts. Expressing as a percentage. | Writing and simplifying ratio. Using ratio. Fractions and proportions. Direct proportion. Proportional reasoning. |
| UNIT 2 NUMBER SKILLS | UNIT 5 ANGLES & SHAPE | UNIT 8 SEQUENCES & GRAPHS |
| Place value. Mental arithmetic. Written methods; Addition & subtraction Multiplication & division Negative numbers. Factors, multiples and primes. Square numbers and roots. BIDMAS. | Measuring and drawing angles. Drawing triangles. Angle facts. Triangles. Quadrilaterals. | Plotting and reading coordinates. Finding midpoints. Sequences. Extending sequences. Recognising graphs parallel to x-axis and y-axis. Drawing straight line graphs. |
| UNIT 3 ALGEBRAIC EXPRESSIONS | UNIT 6 DECIMALS & MEASURE | UNIT 9 PROBABILITY |
| Simplifying expressions. Writing expressions. Formulae. Substitution. | Rounding. Converting measures. Time. Calculating with decimals. Perimeter. Area. | Language of probability. Probability scale. Calculating probability. Experimental probability. Expected outcomes. |
Year 8
| UNIT 1 SHAPES & SOLIDS | UNIT 4 STRAIGHT LINE GRAPHS | UNIT 8 CALCULATING WITH FRACTIONS |
| Area of 2D shapes and compound shapes. Volume of prisms. Properties of 3D shapes. Surface area. | Plotting straight line graphs. Exploring y = mx + c. Calculating the gradient. Identifying the equation of a line. Identifying parallel and perpendicular lines. Introduction to quadratic graphs. | Use the four operations with fractions. Finding one amount as a fraction of another. Finding the reciprocal of a number. Apply the four operations to mixed numbers. |
| UNIT 2 NUMBER | UNIT 5 FRACTIONS, DECIMALS & PERCENTAGES | UNIT 9 LINES & ANGLES |
| Calculating with decimals. Estimation. Powers and roots. Calculating with combinations of powers, roots and brackets. Writing a number as a product of prime factors. Finding the HCF and LCM by listing and prime factors. | Recalling equivalent fractions, decimals and percentages. Ordering fractions. Calculating percentages of amounts. Calculating one number as a percentage of another. Calculating percentage change. Increasing and decreasing by a percentage. Reverse percentages. Repeated percentage change. | Properties of quadrilaterals and triangles. Angles in parallel lines. Finding missing angles by forming and solving equations. |
| UNIT 3 EXPRESSIONS & EQUATIONS | UNIT 6 TRANSFORMATIONS | UNIT 10 REAL-LIFE GRAPHS |
| Simplify expressions involving powers. Expand brackets. Factorising expressions. Solving equations | Identifying congruent shapes. Perform and describe enlargements. Perform and describe reflections. Perform and describe rotations. Perform and describe translations. Combine transformations. Finding the perimeter or volume after an enlargement. | Conversion graphs. Distance-time graphs. Line graphs. |
| UNIT 7 STATISTICS | ||
| Pie charts. Averages from a frequency table. Stem and leaf diagrams. Identifying appropriate averages. Scatter graphs and correlation. Misleading graphs. |
Year 9
| UNIT 1 INDICES & STANDARD FORM | UNIT 5 MULTIPLICATIVE REASONING | UNIT 8 RATIO & REASONING |
| Laws of indices. Calculating with indices. Standard form. Negative and fractional indices. Surds. | Percentage increase/decrease. Percentage change. Compound measure – speed, density and pressure. Inverse proportion. Proportion problem solving. | Writing and simplifying ratio. Solving ratio problems. Combining ratios. Applying ratio. |
| UNIT 2 ALGEBRA | UNIT 6 SHAPE & RIGHT-ANGLED TRIANGLES | UNIT 9 CONSTRUCTION |
| Writing expressions and formulae. Substitution. Expanding single and double brackets. Factorising expressions. | Converting units of area and volume. Circumference of circles. Area of circles. Pythagoras’ Theorem. Volume of prisms. Surface Area of prisms. Trigonometry. | Using scales and maps. Constructing triangles. Constructions with compasses. Constructing accurate nets. Loci. |
| UNIT 3 STATISTICS | UNIT 7 SEQUENCES & GRAPHS | UNIT 10 PROBABILITY |
| Planning a survey. Collecting data. Calculating averages from grouped frequency tables. Displaying and analysing data. | Understand geometric, arithmetic, quadratic and Fibonacci sequences. Generate sequences. Find nth term rules. Plot linear graphs. Identify gradients and y-intercepts. Write equations of graphs. Non-linear graphs. | Calculating probabilities. Relative frequency. Probability diagrams – sample spaces and Venn diagrams. Independent events. Tree diagrams. |
| UNIT 4 ALGEBRA EQUATIONS & INEQUALITIES | ||
| Forming and solving equations. Changing the subject of a formula. Inequalities. Solving inequalities. Simultaneous equations. |
All pupils at Key Stage 4 study the Edexcel GCSE (9 – 1) Mathematics course. This course has two tiers of entry, the Foundation Tier and the Higher Tier. We have ordered our sequence of learning in a manner which allows the two tiers to mirror each other as much as possible. This allows teachers to delay the decision on tier of entry for certain pupils, meaning more pupils have the possibility of sitting the Higher Tier in Year 11. If pupils were to study topics in an entirely different order, it would be difficult for them to switch to the Higher Tier at a later point due to the amount of content they would have missed in comparison with their peers. The simultaneous nature of the two schemes also allows us to teach the 101B class as a ‘crossover’ class, meaning they are studying content in Year 10 which allows them to sit the Higher Tier, but also consolidates learning on the Foundation Tier if the decision is made to change tiers at a later stage.
For more information about the Edexcel GCSE (9 – 1) Mathematics course, please use the following link, Specification: Level 1/2 GCSE (9-1) in Mathematics (pearson.com)
Year 10
| TERM 1 | TERM 2 | TERM 3 |
|---|---|---|
| UNIT 1 NUMBER | UNIT 5 PYTHAGORAS & TRIGONOMETRY | UNIT 8 MULTIPLICATIVE REASONING |
| UNIT 2 ALGEBRA | UNIT 6 SEQUENCES & STRAIGHT-LINE GRAPHS | UNIT 9 TRANSFORMATIONS |
| UNIT 3 DATA HANDLING | UNIT 7 RATIO & PROPORTION | UNIT 10 PERIMETER, AREA & VOLUME |
| UNIT 4 ANGLES & CONSTRUCTION | ||
| CHRISTMAS | EASTER | SUMMER |
Year 11
| TERM 1 | TERM 2 | TERM 3 |
|---|---|---|
| UNIT 1 PROBABILITY | UNIT 4 CONGRUENCY, SIMILARITY & VECTORS | |
| UNIT 2 QUADRATICS & NON-LINEAR GRAPHS | UNIT 5 MORE ALGEBRA | |
| UNIT 3 INDICES & STANDARD FORM | ||
| CHRISTMAS | EASTER | SUMMER |
Year 10
| TERM 1 | TERM 2 | TERM 3 |
|---|---|---|
| UNIT 1 NUMBER | UNIT 4 ANGLES & CONSTRUCTION | UNIT 7 MULTIPLICATIVE REASONING |
| UNIT 2 ALGEBRA | UNIT 5 PYTHAGORAS & TRIGONOMETRY | UNIT 8 TRANSFORMATION & SIMILARITY |
| UNIT 3 STATISTICS | UNIT 6 SEQUENCES AND GRAPHS | UNIT 9 AREA & VOLUME |
| CHRISTMAS | EASTER | SUMMER |
Year 11
| TERM 1 | TERM 2 | TERM 3 |
|---|---|---|
| UNIT 1 PROBABILITY | UNIT 4 PROPORTION | UNIT 7 HIGHER GRAPHS |
| UNIT 2 HIGHER ALGEBRA | UNIT 5 VECTORS | |
| UNIT 3 SURDS | UNIT 6 CIRCLE THEOREMS & CIRCLE GEOMETRY | |
| CHRISTMAS | EASTER | SUMMER |
At Corpus Christi we believe that all pupils should be equipped with and supported in developing a high level of reading and literacy capability, as is required by each subject discipline. In mathematics, there are standards of mathematical oracy which each pupil must adhere to. In topics where poor oracy is a common issue, there are statements in the schemes which explains what pupils’ verbal answers should consist of. This is modelled by teachers and explained to pupils to continually reinforce the expected standard.
In mathematics, reading is differentiated to meet the needs of different ability groups, not only to support access to the curriculum but to also develop fluency and deepen understanding. Command words are a key issue in mathematics. Teachers therefore expose pupils to a variety of command words and ensure pupils understand what the instruction requires them to do. For example, you can ‘expand’ a bracket in algebra, but ‘multiplying out’ means the same thing. Such issues are best addressed by exposing pupils to a variety of instructions regularly.
Where there are examination questions that require a lot of reading, the emphasis is still on the command words involved. The reading age of pupils in each class will decide whether they are asked to read the question or have the question read to them. Either way, any key words or instructions in the question must be defined beforehand to provide context for the pupils. When doing this in mathematics, staff provide a definition which includes a mathematical calculation as an example. For instance, when discussing the word deposit, stating the definition ‘the amount paid to secure goods or services’ may not help pupils to understand what calculation is required. Instead, this definition would be followed by an example such as, ‘If you pay a deposit of £200 for an item which costs £1000, you will have £800 left to pay’. This way, as pupils read the question, they are already processing which calculations are needed at each stage to gain the final answer.
Strategy
Due to the interconnected relationship between topics in mathematics, it is vital that pupils have mastered key numeracy skills in order to remove barriers to learning throughout their time at Corpus Christi. To support with this, key numeracy skills such as multiplication, division, fractions and percentages are paramount for pupils’ to be confident in using numbers, which is an essential life skill, and will underpin their success in GCSEs. At Corpus Christi, we monitor numeracy skills alongside the mathematics curriculum and provide intervention and support where necessary.
Intervention
In Year 7, all pupils engage with the numeracy ninjas programme in class as a means of early intervention. This regularly reviews key skills by working with their class teacher to address any gaps in knowledge. As a result of this, some pupils may be identified for further times tables intervention.
Following the successful completion of the numeracy ninjas programme, intervention becomes more focused in Year 8 and Year 9. All pupils complete numeracy testing in mathematics lessons and, from this, small groups of pupils are identified for numeracy intervention targeted towards a particular skill where there is a gap in a pupil’s knowledge. Intervention with specialist mathematics teachers provides targeted focus on correcting and clarifying their understanding of a particular skill. Focusing on one key numeracy skill at a time, ensures teachers identify misconceptions and give confidence to pupils through repeated practise of the fundamental elements of each skill. Following a series of intervention lessons, pupils are tested in the short-term to ensure pupils have improved, and in the long-term to ensure this improvement has been sustained in the following months. Pupils in Year 10 and Year 11 may also be put forward for numeracy intervention where class teachers identify gaps in knowledge that are fundamental to accessing the GCSE syllabus.
Numeracy is also supported across the curriculum. Each subject and Head of Department is linked to a member of the Mathematics Department in order to support the precise planning and delivery of agreed numeracy skills. Heads of Department ensure that they, and teachers in their department, utilise their subject link colleague regularly in the planning and delivery to ensure consistency and familiarity for pupils to support their progress.
‘The support that pupils receive to improve their numeracy skills has been particularly effective.’
Ofsted, 2019.
At Corpus Christi, we believe that high quality summative assessment must primarily enable pupils to demonstrate their knowledge and understanding acquired throughout the implementation of the planned curriculum. Subsequently, this will allow teachers to measure the progress made by pupils through the curriculum, in relation to learning outcomes set out in schemes of work. In measuring the extent to which pupils have acquired knowledge and a secure understanding, teachers will be able identify gaps in learning, to inform future teaching and planned interventions.
In mathematics, there are three key assessments in Years 7 – 10, one in each term of the academic year. At each of the three assessment stages, pupils are tested on what they have been taught since the start of that academic year to ensure knowledge is accumulated and retained throughout the curriculum. All assessments provide the correct amount of challenge for pupils, whilst ensuring their needs are met. This in turn leads to meaningful feedback for teachers to effectively address gaps in knowledge and consider the intervention required.
Following assessments, there is a clear and shared rationale for the awarding of progress grades in mathematics. In addition to summative assessment results, the awarding of progress grades will incorporate the use of formative assessment, enabling teachers to use their daily feedback through questioning and marking, to inform decisions related to progress grades.
In 2022, Corpus Christi achieved their best ever GCSE mathematics results, placing in the top 20 schools in Lancashire for the progress made by the 2022 cohort.
In 2023, Corpus Christi, again, achieved their best ever GCSE mathematics results, with 70% of pupils achieving a grade 4 or above in the subject.
% of pupils achieving a grade 4 or more in mathematics
| 2017 | 2018 | 2019 | 2022 | 2023 |
| 50% | 52% | 55% | 65% | 70% |
Our consistently strong teaching, high levels of engagement and improved outcomes in mathematics has led to us offering the AQA Level 2 Further Mathematics course to Higher Tier GCSE pupils in addition to their Edexcel GCSE Mathematics course. This offers pupils the opportunity to familiarise themselves with work that is completed during A Level Mathematics and strengthens their understanding of key concepts which can help to secure a grade 9 in their GCSE examinations. Furthermore, pupils receive UCAS points for this course, making it an extremely useful qualification when applying to university.
All of our highest achieving pupils in Years 7 to 10 are entered into the UKMT Mathematics Challenge each year with many pupils receiving certificates and being asked to enter further competitions by the organisation. This gives pupils the opportunity to compete against the best mathematicians in the country within their age group.
The Mathematics department also offer a weekly club to all pupils called ‘Mathletics’. This is consistently well-attended and gives pupils the opportunity to experience mathematics they may not encounter whilst studying the National Curriculum during lessons.
For further information regarding our Mathematics curriculum please contact:
Mr L Hankin, email: lhan@ccc.lancs.sch.uk or telephone school reception: (01772) 716912.
