Programme of Study 2024-2025
Mathematics - Our Vision
Mathematics is essential for everyday life and understanding the world around us. It is not just about equations, numbers and calculations it is about deepening our understanding. At The Crypt we aim to empower our students by looking beyond the curriculum, to link mathematical concepts to practical and real-world examples.
As a department we create a generation of problem solvers and logical thinkers that can think creatively to tackle problems. In Key Stage 3 we follow a scheme of work which focuses on a strong mastery approach, and we aim to develop both the mental and written mathematical skills.
We aim to give a strong basis to move onto GCSE with topics on number, algebra, ratio and proportion, geometry and statistics. During year 11, some students have the opportunity to study AQA Certificate level 2 Further Maths GCSE and enhance their knowledge even further. Advanced mathematics is growing in popularity and is relevant to many careers. This is reflected by our popularity at KS5 with students taking Mathematics and Further Mathematics with students studying pure maths, statistics and mechanics.
INTENT: In Year 7 we give students the opportunity to become more fluent and confident in the basic concepts studied at Key Stage 2, while developing their depth of understanding and their reasoning skills. Students apply fundamental concepts to new and challenging contexts such as algebraic manipulation, prime factorisation, Pythagoras, and probability. Students also start to learn basic calculator skills, practicing these skills in units on averages, area, and angles.
Probability,
Baseline Assessment
Numbers & Calculation
Fractions
Factors, Multiples & primes
Decimals & Estimation
Non-Calculator assessment
Probability
Venn Diagrams
Simplifying expressions
Single Brackets
Factorising
Construction & Loci
Calculator assessment
Year 7 End Points
Ratio and Proportion
Area & Perimeter
Circles
Cuboids
Solving Equations
Sequences
Coordinates
Plotting graphs
Pythagoras
Solving Inequalities
percentage
increase & decrease
Value for Money
Angles and Parallel Lines
Congruent
End of Year
Non-Calculator assessment
Calculator assessment
Statistics & Transformations
Averages
Statistical Diagrams
Transformations
Alien Invasion Investigation
Note these topics will be assessed in year 8
✓ Use the four operations with decimals, fractions and mixed numbers
✓ Round a number to a significant figure or decimal place and use it to estimate
✓ Use a sample space diagram
✓ Draw a Venn diagram and know what is meant by union and intersect
✓ Use non-calculator methods to find percentage of a number and increase and decrease by a percentage
✓ Use angle rules for around a point, straight line, in a triangle, in a quadrilateral, corresponding, alternate, co-interior and vertically opposite angles
✓ Find areas and perimeters of rectangles, triangles, parallelograms, and trapeziums. Find the circumference and area of a circle
✓ Find the nth term of a linear sequence
✓ Understand and use lines parallel to the axes, y=x and y=-x
✓ Simplify expressions by collecting like terms and expanding a single bracket
✓ Solve linear equation with unknowns on both sides
✓ Use Pythagoras to find a long or short side of a triangle
✓ Know and calculate mean, median, mode and range
INTENT: In Year 8 students will continue to deepen their understanding of topics taught in Year 7 and at primary school. For example, their work on algebraic expressions will be extended to include index laws, expanding double brackets and further their understanding of percentages by learning methods involving decimal multipliers and continue to work with the fundamental concepts of ratio and proportion that were first introduced at primary school. They will be introduced to new and exciting mathematical concepts which draw on previously taught skills and knowledge. For example, trigonometry, bounds, solving equations involving fractions and negative enlargement. These topics give students the opportunity to develop their critical thinking skills and their ability to answer more complex problem-solving questions. Students will also extend their knowledge of number systems and effective calculator use will feature heavily throughout the year.
Prime factors, HCF & LCM
Estimation and errors
Recurring decimals
Rules of indices
Standard form
Literacy Investigation
Non-Calculator
assessment
(will contain year 7 content)
Expanding single and double brackets
Identities
Solving equations with unknowns on both sides
Sample space diagrams
Venn Diagrams and Tree Diagrams
Pythagoras
Solving inequalities
Changing the subject
Calculator assessment
Non-Calc reverse percentages
Compound Interest
Nth Term rule
Geometric Sequences
Parallel Lines
Angles in Polygons
Congruency
Rotation
Reflection
Negative Enlargement
Describing
Transformations
Ratio
Year
8 End Points
✓ Find the HCF and LCM using product of primes and a Venn diagram
✓ Use the laws of indices for multiplication, division, and power to a power
✓ Understand and convert standard form
✓ Expand two brackets using FOIL
✓ Create a solve equations and inequalities which includes division
✓ Change the subject of a formula when two steps are required
✓ Draw and use a simple probability tree diagram
✓ Find a probability from a Venn diagram
✓ Describe and draw the four transformations
✓ Use Pythagoras with multistep problems
✓ Use SOHCAHTOA to find a length or angle
✓ Calculate mean from a frequency table
✓ Draw and use a line of best fit on a scatter graph and describe correlation
✓ Use and understand y=mx+c
Introduction to Trigonometry (SOHCAHTOA) Collecting Data
Averages from frequency tables
Pie Charts
Scatter Graphs
Cumulative Frequency
Percentage Multipliers
Compound interest
Understanding bank accounts
Area and perimeter Circles
Volume & Surface Area of Prisms
INTENT: In year 9 we start the GCSE course, in addition to revisiting knowledge learnt throughout Years 7 and 8. We can further deepen understanding and give students the opportunity to develop their reasoning and problem-solving skills. We continue to develop trigonometry, probability and number skills we also introduce quadratics, bearings and surds. These topics will challenge students and develop resilience and confidence before moving into Year 10. In the units on angles and bearings, quadratics, volume and surface area students start to develop chains of reasoning, preparing them for the complex geometrical proofs they will construct at Key Stage 4 and beyond. Students will also be formally introduced to GCSE exam style questions and have the opportunity to develop exam technique.
Product of prime
Factors, HCF & LCM
Estimation
Error Intervals
Bounds
Rules of Indices inc.
fractional and negative
Standard form
Surds
Non-Calc Exam
(contains year 8 content)
Year 9 End Points
Single and double bracket factorising
Simplifying algebraic fractions
Simultaneous equations
Arithmetic Nth term rule
Quadratic nth term rule
Calc Exam
Famous Mathematicians investigation
✓ Understand and simplify surds
Circles, arcs and sectors
Cones and Spheres
Compound Units
Bearings
Percentages
Ratio
Direct proportion
equations
Pythagoras and SOHCAHTOA
Compound interest
Frequency tables
Cumulative Frequency
Quartiles
Box Plots
EOY Exams
Non Calc and Calc
Exams
Probability
Scatter Graphs
Sample space diagrams
Two-way tables
Set notation
Venn diagrams
Tree diagrams
✓ Write and error interval and calculate with upper and lower bounds
✓ Calculate in standard form
✓ Factorise a quadratic with a=1 including a difference of two squares
✓ Solve a simultaneous equation algebraically
✓ Problem solve with volume and surface areas.
✓ Understand bearings and use it to calculate a return journey
✓ Use Pythagoras and SOHCAHTOA in multistep problems and real-life circumstances
✓ Draw, use and interpret cumulative frequency diagrams and box plots
✓ Find conditional probabilities and use set notation with Venn diagrams
✓ Use and interpret tree diagrams with multiple routes
INTENT: In year 10, students will get the opportunity to really see the interconnected nature of Maths and they will learn to apply the subject knowledge they have already acquired in more complex and sophisticated ways. Students will experience questions that go beyond routine and repetition so they will be required to think about what skills or concepts need to be applied in different contexts. Our aim in year 10 is to help students become more confident and resilient problem solvers by encouraging them to try out different methods to see what works and what does not. We aim for students to start to appreciate the actual process behind reaching an answer.
Students will be exposed to more GCSE exam style questions and will have the opportunity to develop their exam techniques including common errors and misconceptions, layout, and workings, checking answers, mastering using a calculator, command words and how to tackle wordy questions.
Some students will be aiming to study AQA Level 2 Further Maths, those students will be following a revised programme of study.
Number and Equations
Indices
Surds
Recurring decimals
Bounds
Solving linear equations
Solving inequalities
Simultaneous equations
Solving quadratics by factorising and quadratic formula
Non calculator assessment
Year 10 GCSE End Points
Equations and Graphs
Creating and solving equations
Y=mx+c
Parallel lines
Perpendicular lines
Recognising graphs
Real life graphs
Velocity time graphs
Calculator Assessment
✓ Rationalise a denominator
✓ Negative and fractional indices
Statistics and Trigonometry
Gradient of curves
Areas under graphs
Averages
Cumulative Frequency
Box Plots
Histograms
SOHCAHTOA
Pythagoras
Exact trigonometric values
3D Trigonometry
✓ Algebraically prove any recurring decimal is a fraction
✓ Solve quadratics through factorising and quadratic formula
✓ Linear graphs, y=mx+c, parallel and perpendicular lines
✓ Draw and interpret histograms
✓ Gradients and areas underneath velocity time graphs
Proportion & Transformations
Sine Rule
Cosine Rule
Transformations
Rotation
Reflection
Translation
Enlargement including negative scale factors
Construction & Loci
Mock exams
Angles & Shapes
Direct and inverse proportion
Angles in polygons
Function notation
Graph Transformations
Probability
Product rule for counting
Set notation
Venn diagrams
Tree diagrams
Conditional probability
Vectors
Drawing and understanding vectors
Adding, subtracting & scalar multiples
Vector Geometry
Parallel vectors
Co-linear
✓ Sine and cosine rule to find a missing angle and length, use 1/2absinC for area of a triangle
✓ Appy graph transformations using function notation
✓ Prove two triangles are congruent and apply similarity to length, area and volume
✓ Use product rule for counting
✓ “And” and “Or” rules for probability
✓ Understand vectors and use them for geometric proof
Number and Equations Equations and Graphs
Indices
Surds
Recurring decimals
Bounds
Solving linear equations
Solving inequalities
Simultaneous equations
Solving quadratics by factorising and quadratic formula
Creating and solving equations
Y=mx+c
Parallel lines
Perpendicular lines
Recognising graphs
Real life graphs
Velocity time graphs
Gradient of curves
Areas under graphs
Averages
Cumulative Frequency
Box Plots
Histograms
Calculator Assessment
Statistics and Trigonometry
Pythagoras
Exact trigonometric values
3D Trigonometry
Sine Rule
Cosine Rule
Direct and inverse proportion
Proportion & Transformations
Construction & Loci
Transformations
Rotation
Reflection
Translation
Enlargement including negative scale factors
Function notation
Graph Transformations
Angles in polygons
Mock exams
Non calculator assessment
Year 10 GCSE End Points
✓ Rationalise a denominator
✓ Negative and fractional indices
✓ Algebraically prove any recurring decimal is a fraction
✓ Solve quadratics through factorising and quadratic formula
✓ Linear graphs, y=mx+c, parallel and perpendicular lines
✓ Draw and interpret histograms
✓ Gradients and areas underneath velocity time graphs
✓ Sine and cosine rule to find a missing angle and length, use 1/2absinC for area of a triangle
✓ Appy graph transformations using function notation
✓ Know and use circle theorems
✓ Prove two triangles are congruent and apply similarity to length, area and volume
✓ Use product rule for counting
✓ “And” and “Or” rules for probability
✓ Understand vectors and use them for geometric proof
Angles & Shapes
Congruency and similarity
Circle Theorems and Proofs
Probability
Product rule for counting
Set notation
Venn diagrams
Tree diagrams
Conditional probability
Vectors
Drawing and understanding vectors
Adding, subtracting & scalar multiples
Vector Geometry
Parallel vectors
Co-linear
INTENT: Year 11, students will learn the remaining content required to be successful in GCSE Mathematics as well have the opportunity to fully consolidate their learning throughout key stage 3 and year 10. Students will become confident in interpreting and communicating mathematical information in a variety of forms appropriate to the information and context. They will also concentrate on acquiring the mathematical skills equired to select and apply techniques to solve problems. There will be an emphasis on revision and retrieval of content as well as exam question practice to further develop their exam techniques.
From the student’s year 10 exams some students will also be studying the enrichment qualification Level 2 Further Mathematics
Further Algebra Circles and Proof Fractions, Graphs, Sequences and Surds
Expanding 3 brackets
Identities
Consolidating quadratics
Circle theorems and proof
Completing the Square Sketching Graphs
Iteration
Functions
Year 11 GCSE End Points
Quadratic Inequalities
Simultaneous Equations
Algebraic proof
Algebraic fractions
Exams
Equation of a circle
of a circle
sequences Cones and spheres
✓ Use identities and comparing coefficients to find missing values
✓ Completing the square
✓ Quadratics
✓ Functions
✓ Know and use circle theorems
✓ Simplify and calculate with algebraic fractions
✓ Algebraic proof
✓ Understand and use iteration
Expanding 3 brackets
Completing the Square
Sketching Graphs
Quadratic Inequalities
Quadratic & Linear
Simultaneous
Functions
Proof
Algebraic fractions
Equation of a circle
Tangent of a circle
Iteration
Differentiation
Tangents/Normals
Stationary Points
Binomial Expansion
Factor theorem
Factorising cubics
Mock Exams
Completing the square
Simultaneous equations w/3 unknowns
Functions
Matrices
Sine & Cosine rule
Trigonometry graphs
Trigonometric identities
CAST diagrams
Sequences
Equations of circles
Expanding 3 brackets
Completing the Square
Sketching Graphs
Quadratic Inequalities
Quadratic & Linear
Simultaneous
Functions
Proof
Algebraic fractions
Year 11 GCSE & Level 2 Further Mathematics End Points
✓ Use identities and comparing coefficients to find missing values
✓ Completing the square
✓ Quadratics
✓ Functions
✓ Know and use circle theorems
✓ Simplify and calculate with algebraic fractions
✓ Algebraic proof
✓ Understand and use iteration
Equation of a circle
Tangent of a circle
Iteration
✓ Find the equation of a tangent to a circle
✓ Differentiate and find stationary points
✓ Use a CAST diagram and solve trigonometric equations
✓ Use the identities ������2��+������2�� =1 and �������� = �������� ��������
✓ Use the factor theorem and algebraic long division to factorise cubics
✓ Binomial expand (����+��)��
✓ Solve simultaneous equations with 3 variables
✓ Calculate with matrices