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.
Mathematics is a subject which constantly builds on previous knowledge in order to make further progress which makes the sequencing of topics imperative. Our process to produce the sequencing of topics has been extremely rigorous, which has led to detailed schemes of work where topics are ordered in a way that is logical to build on prior knowledge. The schemes contain learning stages which are detailed and constantly adjusted through regular reflection from all members of the department.
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.
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. |
Y10 Support
Number
Recapping of number content from Key Stage 3 is completed throughout this chapter. Pupils are also introduced to the laws of indices, rounding to significant figures and estimating calculations. If this knowledge is secured, pupils study the basics of error intervals.
Algebra
Recapping of algebra content from Key Stage 3 is completed throughout this chapter. Pupils simplify expressions which involve multiplication and division and expand and simplify two sets of brackets. Pupils also factorise more complex linear expressions and substitute negative values into expressions with and without and calculator.
Data Handling
Recapping of data content from Key Stage 3 is completed throughout this chapter. Pupils draw pie charts and interpret and draw line graphs. Scatter graphs are drawn and interpreted to identify trends and averages from grouped frequency tables are introduced.
Fractions, decimals and percentages
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils continue to calculate with fractions and are asked to complete mixed number calculations. Pupils also calculate percentage changes that have occurred, including percentage profit, and begin to use multipliers to percentage increases and decreases.
Equations
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils are introduced to equations with unknowns on both sides and start to rearrange basic formulae. Pupils are also asked to solve inequalities and represent their answers on a number line.
Angles
Recapping of content from Key Stage 3 is completed throughout this chapter. Angles in parallel lines are revisited and angles in polygons are introduced to pupils.
Sequences and straight-line graphs
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils learn to identify the nth term of a linear sequence and how to check whether a number is a term in a given sequence. Linear graphs are also revisited and with pupils asked to identify the equation of lines in the form y = mx + c.
Transformations
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils complete translations using column vector notation, enlarge a shape from a centre of enlargement, reflect a shape in a given line and rotate shapes clockwise and anti-clockwise. Pupils are also asked to describe transformations.
Perimeter, area and volume
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils develop their volume of 3D shapes knowledge to find the volume of other prisms.
Ratio and Proportion
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils write and simplify ratios and share quantities into a ratio. Pupils are write ratios in the form 1:n and n:1 and write ratios as fractions and vice versa. Pupils study direct proportion further to include converting between currencies.
Y11 Support
Probability
Recapping of content from Key Stage 3 is completed throughout this chapter. The concept of relative frequency is introduced to pupils and pupils use sample spaces to represent outcomes from an event. Pupils also complete frequency trees and calculate probabilities from them. Venn diagrams are introduced to pupils and, if this knowledge is secured, set notation may be introduced.
Right-angled triangles
Pythagoras’ Theorem is introduced to pupils and applied to find missing lengths on right-angled triangles. Depending on the class, pupils may then be introduced to trigonometry to find missing side lengths and angles.
Bearings and loci
Recapping of content from Key Stage 3 is completed throughout this chapter. Plans and elevations are revisited to draw more complex 3D shapes which may not be made from cm cubes. Bearings and scale drawings and covered and pupils are introduced to loci and constructing bisectors.
Multiplicative reasoning
Recapping of content from Key Stage 3 and Year 10 is completed before pupils are introduced to repeated percentage change such as compound interest. If learning is secure in using multipliers, reverse percentage problems may be investigated. Pupils then use the speed, density and pressure formulae to solve real life problems. Finally, pupils convert between units, including units for area.
Quadratics
Where pupils’ knowledge of previous algebra topics is secure, they are introduced to expanding double brackets and factorising quadratic expressions. Pupils also use a calculator to complete tables of values for quadratic graphs and plot them.
Circles
Pupils identify the parts of a circle and use this knowledge to calculate the circumference and area of a circle using the relevant formulae.
Standard Form
Pupils convert between standard form and ordinary numbers and, where this knowledge is secure, continue to multiply and divide calculations involving standard form.
Year 10 Core
Number
Recapping of number content from Key Stage 3 is completed throughout this chapter. Pupils will also be introduced to error intervals and the use of venn diagrams to find HCF and LCM. Pupils will also review fraction, decimal and percentages and apply their knowledge to GCSE problem solving style questions.
Algebra
Recapping of algebra content from Key Stage 3 is completed throughout this chapter. Pupils will understand how to solve linear inequalities and display the solution sets on a number line. Algebraic vocabulary will be developed further as well as solving more complex equations involving fractions as well as an introduction of how to change the subject of formulae.
Data handling
Recapping of data content from Key Stage 3 is completed throughout this chapter. Pupils draw pie charts and interpret and draw line graphs. Scatter graphs are drawn and interpreted to identify trends and averages from grouped frequency tables are introduced.
Angles and constructions
Recapping of content from Key Stage 3 is completed throughout this chapter. Angles in parallel lines are revisited and angles in polygons are introduced to pupils. Plans and elevations are also revisited to draw more complex 3D shapes which may not be made from cm cubes. Bearings and scale drawings are covered and pupils are introduced to loci and constructing bisectors.
Sequences and straight line graphs
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils revisit the nth term of a linear sequence and learn how to check whether a number is a term in a given sequence or how to calculate a number in a quadratic sequence. Linear graphs are also revisited and with pupils asked to identify the equation of lines in the form y = mx + c. Pupils will also revisit conversion graphs, distance-time graphs and other graphs of real life situations.
Right angled triangles
Pupils will recap their Pythagoras knowledge and apply this to solve problems and will then be introduced to trigonometry. Pupils will learn how to use trigonometry to find missing lengths and angles in right-angled triangles.
Ratio and proportion
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils write and simplify ratios and share quantities into a ratio. Pupils will write ratios in the form 1:n and n:1 and write ratios as fractions and vice versa. Pupils study direct proportion further to include converting between currencies. Pupils will also be introduced to direct and inverse proportion.
Transformations
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils complete translations using column vector notation, enlarge a shape from a centre of enlargement, reflect a shape in a given line and rotate shapes clockwise and anti-clockwise. Pupils are also asked to describe transformations.
Multiplicative Reasoning
Pupils will work with the speed, density and pressure formulae and use these to solve problems that also require converting units. Pupils will calculate compound interest and begin to work with growth and decay problems.
Perimeter, Area and Volume
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils will extend their knowledge of circumference and area of circles to find surface area and volume of cylinders. Pupils will also find the surface area and volume of spheres, pyramids, cones and composite solids
Y11 Core
Probability
Recapping of probability content from Key Stage 3 is completed throughout this chapter. Pupils are introduced to frequency trees and recap calculating probabilities from two-way tables. Pupils then study set notation and probabilities from Venn diagrams, including shading such diagrams to represent a given set. The chapter finished with pupils studying tree diagrams in great detail, including non-replacement examples.
Quadratics and non-linear graphs
Recapping of algebraic content from Key Stage 3 is completed throughout this chapter. Pupils start by recapping expanding and simplifying double brackets from the Y9 scheme of work using the FOIL method. Pupils then build on this to factorise quadratic expressions, which leads to solving quadratic equations by factorising. Pupils finish the chapter by recognising quadratic, cubic and reciprocal graphs, with a particular focus on drawing and interpreting quadratic graphs.
Fractions, indices and standard form
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils recap calculating with fractions, with the aim of being able to add, subtract, multiply and divide mixed numbers. Indices is then reviewed, recalling learning from Year 9, before pupils look at standard form in more detail, extending previous work to be able to answer calculations involving standard form.
Congruence, similarity and vectors
Recapping of content from Key Stage 3 is completed throughout this chapter. Pupils learn how to prove whether shapes are congruent, with a particular focus on triangles. Pupils then build on their previous knowledge of similar shapes to calculate missing lengths using scale factors. Vectors is then introduced to pupils, including column vector arithmetic and vector geometry using diagrams.
More algebra
Simultaneous equations are studied in greater detail than in Year 9 at this stage, with pupils expected to solve simultaneous questions where coefficients are different in each equation. Pupils then start to solve equations graphically, looking at linear equations initially, leading on to simultaneous equations.
Year 10 Extension
Number
Recapping of number content from Key Stage 3 is completed throughout this chapter. Pupils are also introduced to the product rule for counting, higher level fractional and negative indices, surd calculations and converting a recurring decimal to a fraction. Pupils will also review fraction, decimal, percentage and ratio knowledge and apply to GCSE problem solving style questions.
Equations
Recapping of algebra content from Key Stage 3 is completed throughout this chapter. Pupils will also factorise higher-level quadratic expressions and understand the difference of two squares. Changing the subject of more complex formulae is covered as well as finding the nth term of quadratic sequences. Pupils will also solve quadratic and simultaneous equations to a higher level.
Graphs
Recapping of graphs content from Key Stage 3 is completed throughout this chapter. Pupils will extend knowledge of linear graphs and will find equations of perpendicular lines and display inequalities as regions on graphs. A variety of non-linear graphs will be studied as well as how to use graphs to solve equations.
Area and volume
Recapping of area and volume content from KS3 is completed throughout this chapter. Pupils will solve problems involving more complex shapes such as spheres, hemispheres, pyramids and cones. Equations will be formed and solved relating to a variety of shapes and the concept of accuracy and bounds will be developed.
Probability
Recapping of probability content from KS3 is completed throughout this chapter. Pupils will problem solve with probability using frequency trees, tree diagrams and venn diagrams. Higher level conditional probability will also be studied as well as understanding how to express probability algebraically.
Ratio and multiplicative reasoning
Recapping of ratio and percentage content from KS3 is completed throughout this chapter. Pupils will extend their understanding of ratio relationships and be able to work with growth and decay problems. Pupils will work with compound measure formulae, in particular speed, density and pressure, to solve problems and combined measures will also be studied as part of this unit.
Angles and Trigonometry
Recapping of angles and trigonometry content from KS3 is completed throughout this chapter. Pupils will develop geometrical reasoning to higher level GCSE content and develop pythagoras and trigonometry to 3d shapes as well as further trigonometry of sine rule, cosine rule and the area of triangles. Pupils are also expected to know exact trigonometric functions.
Similarity and congruence
Recapping of transformations and loci content from KS3 is completed throughout this chapter. Pupils will learn about similar shapes and how similarity affects area and volume. Pupils will also study congruency conditions and proof.
Data
Recapping of data content from KS3 is completed throughout this chapter. Pupils will understand further sampling methods such as capture-recapture as well as constructing and interpreting cumulative frequency graphs, boxplots and histograms. Pupils will develop a further understanding of how to compare distributions and calculate interquartile ranges.
Year 11 Extension
Higher algebra
Pupils will further develop skills involving algebra. These include solving simultaneous equations where one is linear and one is non-linear, algebraic fractions, algebraic proof, functions, iteration and quadratic inequalities.
Proportion
Pupils will understand whether graphs show direct or inverse proportion and set up and use proportionality formulae.
Vectors
Pupils will understand and use vector notation as well as being able to work out the sum of vectors, the difference of vectors and scalar multiples of vectors. Pupils will use vectors to solve geometric problems and, where this is secure, pupils will also understand how to prove that points are collinear and vectors/lines are parallel.
Circles and circle geometry
Pupils will need to use circle theorem facts to develop geometrical reasoning further and, where this knowledge is secure, be able to prove the circle theorems. Where graph work is secure pupils will further study equations of circle graphs and equations of tangents to circles.
Higher graphs
Pupils will recognise, sketch and interpret trigonometric graphs and where graph work is secure, they will further study the transformations of functions. Pupils will study non-linear graphs further and investigate gradients of curves and area under graphs being able to interpret the meaning of these within the context of the question.
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.
There are basic numerical skills that are vital to access the mathematics curriculum at each key stage. We refer to these skills as the ‘building blocks’ of mathematics. We have used evidence from research to identify which skills are the most important for each year group at Key Stage 3 and have produced numeracy assessments to test all pupils in those year groups on where, if any, the weaknesses are for each pupil. Once their weaknesses are identified, pupils are given targeted intervention from a Lead Teacher of Mathematics on those topics to ensure the obstacles to their learning are removed. Pupils are then retested after the sessions to assess the impact of the intervention.
‘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.
For further information regarding our Mathematics curriculum please contact:
Mr L Hankin, email: lhan@ccc.lancs.sch.uk or telephone school reception: (01772) 716912.
