# Mathematics

**Extra-Curricular Activities**

- UKMT Maths Challenge
- KS3 and KS4 Homework Support
- Belgium Euro Space Center trip
- Maths in Action conferences
- Sixth Form Problem Solving day

**Key Stage 3**

**What are the knowledge and skills that students will gain over Key Stage 3?**

The Key Stage 3 curriculum in mathematics aims to develop students’ mathematical knowledge; enhance numeracy skills and stretch and challenge students' understanding of mathematics through the areas of: number, algebra, ratio, proportion and rates of change, geometry and measures, probability and statistics. Students will be able to use a calculator confidently in all of their maths lessons.

Students are able to recall facts, terminology and definitions and apply it to a range of mathematical contexts. An emphasis on using the key mathematical vocabulary when communicating ideas both verbally and in written form is extremely important for all our students.

In Key Stage 3, students are given the opportunity and encouraged to make connections between the different content areas. For example, how geometric shapes can form sequences that can be represented numerically or how algebra can be used to represent unknown lengths and area.

We aim to equip students with the skills to be able to reason, interpret and communicate mathematically. Students will be able to select the appropriate values from a question and eliminate any irrelevant content. Furthermore, students will begin to make deductions, inferences and draw conclusions from mathematical information. Students will be regularly exposed to mathematical misconceptions through activities developed by the classroom teacher to be aware of them and critical of their own work.

In Key Stage 3, students will strengthen their problem solving skills: students will begin to translate mathematical and non-mathematical contexts into a series of mathematical processes; students will be given opportunities to work collaboratively to solve mathematical problems and communicate their ideas to the class.

**Why is it delivered in this way?**

The most important focus of our teaching at Key Stage 3 is for our students to develop a deeper understanding of mathematical concepts. For example, when learning that the formula for area of a triangle, we want our students to understand how it links to a rectangle and to visualise it using a practical approach.

It is essential that students can begin to make links between different mathematical areas to demonstrate the interconnectedness of mathematics. Mathematics in the real world will require them to draw on a number of different areas of their subject knowledge and often their analytical skills to solve a problem.

It is our hope that, by the end of Key Stage 3, our students are prepared for the rigors of Key Stage 4. As the content increases in challenge, many of the essential numeracy skills are already embedded and students can tackle these mathematical problems with an element of fluency.

**Key Stage 4**

Edexcel GCSE Mathematics (1MA1) GCSE-Mathematics-Specification.pdf

**What are the knowledge and skills that students will gain over Key Stage 4?**

The Key Stage 4 curriculum continues to develop the knowledge and understanding; mathematical reasoning and problem solving techniques developed in Key Stage 3. The content of the GCSE is challenging and demanding but is taught in a way that builds on prior knowledge and skills to make it accessible and engaging. For example, Grade 8/9 content such as functions will build on their understanding of graphs; making x the subject and function machines from Key Stage 3.

Problem solving at Key Stage 4 will involve students to tackle multi-step problems requiring students to draw knowledge from multiple content areas and use a variety of mathematical skills, presenting their work in a clear and organised manner.

Students will develop more fluent knowledge, skills and understanding of mathematical methods in the areas of: number, algebra, ratio, proportion and rates of change, geometry and measures, probability and statistics. These concepts will be taught through a range of differentiated activities and practical approaches. The use of technology and exam style questions is used to ensure that students are fully equipped for the GCSE examinations. Students will be able to comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context because they will be regularly exposed to challenging tasks in their mathematics lessons.

Students will develop interpersonal skills from their mathematics lessons such as decision making, analysing and synthesising information, communication skills and teamwork, adaptability and self development.

Why is it delivered in this way?

We must continue to instill a deeper understanding of topics because this will develop students’ fluency throughout the whole course and eliminate any misconceptions. Students will be more likely to recall information if they understand where it has been derived from.

It is also essential that students develop exam techniques to ensure that they are prepared for the requirements of the GCSE examinations. By regularly exposing students to exam style questions using scaffolded approaches and analysis of the mark scheme, students will ultimately improve their attainment in mathematics.

Students are given the confidence that the mathematical skills, knowledge and understanding that they acquired throughout the GCSE course will equip them for the wider world and their chosen career by regularly making links to the real life application of these processes.

For some students in KS4, the mathematics GCSE will provide a stepping stone for more advanced studies in mathematics and further mathematics at A Level. In turn, this then leads to a natural progression to study the subject at university level and preparing them for a wide range of STEM careers. For others, it will be their last formal study of the subject that will provide the basis of their mathematical fluency in the working world.

**Sixth Form**

Course title: AQA GCE A Level Mathematics, AQA-7357-SP-2017.PDF

**What are the knowledge and skills that students will gain over Key Stage 5?**

The study of AQA Mathematics develops: the skills of using and applying complex mathematical knowledge built on from GCSE; the ability to reason, interpret and communicate mathematically; as well as solve problems within mathematics and in other contexts. At John Colet School, we aim to provide a stepping stone for future study as well as to foster a passion for the subject.

The key mathematical skills that will be developed throughout Year 12 and Year 13 are:

Students will be able to select and correctly carry out routine procedures, accurately recall facts, terminology and definitions.

Students will be able to construct rigorous mathematical arguments (including proofs); make deductions and inferences; assess the validity of mathematical arguments; explain their reasoning and use mathematical language and notation correctly.

Students will be able to translate problems in mathematical and non-mathematical contexts into mathematical processes; interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations; translate situations in context into mathematical models; use mathematical models; evaluate the outcomes of modelling in context, recognise the limitations of models and - where appropriate - explain how to refine them.

Students will become familiar with a number of specific large data sets in advance of the final assessment. The use of real data will enable the concepts and skills of data presentation and interpretation in the specification to be explored. Students will use technology such as spreadsheets or specialist statistical packages to explore the data sets. Students will interpret real data presented in summary or graphical form as well as using the data to investigate questions arising in real contexts.

Use of technology is an intrinsic part of the course. Scientific calculators are used to promote efficiency and place an emphasis on interpretation rather than computation. Students will be fully aware of the functionality of the calculator and we will insist that all students purchase a Casio Classwiz. Online graphical calculators such as Desmos will offer students a graphical representation of a number of otherwise algebraic problems.

The study of mathematics at A Level is consistent across all examination bodies and the mathematical skills are taught through the following content:

Pure:

Proof

Algebra and functions

Coordinate geometry

Sequences and Series

Trigonometry

Exponentials and Logarithms

Differentiation

Integration

Numerical methods

Mechanics

Vectors

Quantities and units in mechanics

Kinematics

Forces and Newton’s laws

Moments

Statistics

Statistical sampling

Data presentation and interpretation

Probability

Statistical distributions

Statistical hypothesis testing

**Why is it delivered in this way?**

The AQA A Level in mathematics was selected at John Colet School due to the interesting large data set involving cars. We felt that the content would engage our students and offer a wide range of opportunities to compare different aspects of the data set using technology.

We feel that it is important that proof is taught in a scaffolded and interesting way at A Level to deepen our students' understanding of key mathematical concepts. We do not want them to appear complicated to the students but logical and satisfying. It forms an essential part of each topic area with students occasionally having to know specific mathematical proofs by recall.

The content is taught in a way that builds upon mathematical skills and content at GCSE as well as linking to previous content taught throughout the A Level course. For example, the equation of a circle is taught at GCSE, extended upon in Year 12 and then linked to parametric equations in Y13. The scheme of work provides opportunities for links between pure and mechanics as well as pure and statistics.

Problem solving and reasoning forms such an essential part of the A Level mathematician: the ability to tackle content in a range of contexts as well using their embedded mathematical skills not only will result in success in the examination but will provide them with the important attributes beyond A Level and improve their confidence.

It is also essential that students develop exam techniques to ensure that they are prepared for the requirements of the A Level exam. By regularly exposing students to exam style questions using scaffolded approaches and analysis of the mark scheme, students will ultimately improve their attainment in Mathematics.

**A Level Further Maths**

Course title: AQA GCE A Level Further Mathematics, AQA-7367-SP-2017.PDF

Proof

Complex numbers

Matrices

Further Algebra and Functions

Further Calculus

Further Vectors

Polar coordinates

H: Hyperbolic functions

I: Differential equations

J: Trigonometry

K: Numerical Methods

Choice: Students must study two of these options.

Optional application 1 – mechanics

Optional application 2 – statistics

Optional application 3 – discrete