Mathematics
“Neglect of Mathematics works injury to all knowledge, 
since he who is ignorant of it cannot know the other sciences or the things of the world.”-Roger Bacon
We believe that, with the right scaffolding and support, every child can be successful in Maths.
The mathematics curriculum at Newman Catholic College intends to instil in students an appreciation for the beauty and power of mathematics and an understanding of how it permeates every aspect of our day to day lives. By adopting a mastery style approach to our teaching and curriculum design, we provide the knowledge and skills that will enable our students to reason mathematically and problem solve in a range of contexts.
We recognise and celebrate the highly inter-connected nature of mathematics. Students are given the opportunity to build upon their prior knowledge and make connections between topics within the subject itself and across different fields of education and employment. Mathematics is essential to everyday life, critical to science, technology and engineering, and necessary for most forms of employment. In particular, financial literacy is an essential tool for overcoming social inequality. Given the challenges our students face growing up in Brent, we feel we have a moral duty to raise aspirations and provide our students with the education necessary to fully engage with society and become active citizens of the world.
Key Stage 3
Curriculum
Students in Key Stage 3 follow a carefully sequenced scheme of work that exceeds the requirements of the National Curriculum. The curriculum design builds on research in cognitive science to maximise opportunities to make connections, deepen understanding and improve memory. The programme ensures that the students have ample time to explore each topic and how it connects with others. Regular opportunities to revisit topics are built in to increase students’ confidence and retention. For example, once students have completed the unit on sequences in Year 7, this is revisited and developed throughout the course. In Year 8 students find and use the nth term rule for linear sequences and in Year 9, extend this idea to linear graphs and later non-linear graphs. This design also ensures students can access the learning at their own level, providing appropriate support and challenge as necessary. Consequently, this allows us to teach students in mixed attainment groups rather than in sets over Years 7 and 8 and in streams for Year 9. We believe this is beneficial for students because they experience a diverse range of perspectives, all students are exposed to higher level thinking and it supports confidence in mathematics.
Cross Curricular Links
Mathematics has many connections with other subjects at school as well as the wider world and it is important that students understand this to have a deeper appreciation of the world around them. Cross-curricular links are embedded into the curriculum. Some examples;
· Art: tessellation, the golden ratio, the work of Escher
· History: early development of maths including number systems from around the world
· Modern mathematicians: Yitang Zhang, Katherine Johnson, Alan Turing, Maryam Mirzakhani
· Science: compound measures, Fibonacci numbers
· Data Science: misleading graphs and statistics, choosing appropriate averages
· Careers: everything from plumbing to AI specialist or health economist
Of particular importance to us is teaching students to be financially literate. We have worked with Young Money, a charity sponsored by Martin Lewis (of “MoneySavingExpert”), to engage students with a variety of money matters including debt, borrowing, savings, fraud, taxation, etc. Local banks and charities have been generous enough to support us by running whole-school assemblies and workshops.
Homework
All students in Key Stage 3 are set homework on a weekly basis which provides practice and consolidation for concepts covered during lessons as well as previous topics. We are fortunate to have worked with Sparxmaths and Colin Hegarty as one of their launch schools. This homework platform provides homework tasks tailored to each student, allocating them questions with the optimum amount of challenge to make students think hard but still be achievable. We expect a 100% completion rate for all homework tasks. Students are supported with homework by:
· Support videos on sparxmaths.com
· All classroom lessons are accessible on Google Classroom.
· Weekly homework club
· Class teachers can be contacted in person, via email or through Google Classroom.
Assessment and Feedback
The Mathematics department aims to use assessment and feedback in an effective and timely manner to ensure that all students can make good progress in their learning of mathematics. During lessons teachers regularly assess students understanding. The feedback that teachers give encourages students to think and to understand the next steps for improvement. Teachers create a supportive environment that encourages students to welcome feedback and provide opportunities for them to act on it.
We aim to support students with written assessments by using short, low stakes assessments on a regular basis. Each topic assessment tests the most recent topic looking at basic skills, deeper understanding and connecting it with another topic as well as testing the topic before and a topic from the previous term. The purpose of this is to improve students’ retention, provide connections between topics and prepare students for the style of questioning in more formal written assessments. These topic assessments also provide students with immediate feedback and allow the teacher to address any areas for improvement promptly. Termly assessments cover the topics from the year cumulatively and are also used to identify any areas that need further attention and inform future planning. This approach allows students to build their stamina and resilience to put them in the best position when they reach the GCSE examinations and further study.
Key Stage 4
Curriculum
The scheme of work for Key Stage 4 (Years 10 and 11) follows the same design principles as Key Stage 3, allowing students to build on their previous learning, continue to make connections, develop a deep understanding of concepts and problem solve in different contexts. Students are taught in sets for Key Stage 4.
The exam board for GCSE mathematics is Edexcel. Broadly, the content covers the following areas:
Foundation
- Number (22 - 28%)
- Algebra (17 - 23%)
- Ratio, proportion, rates of change (22 - 28%)
- Geometry and measures (12 - 18%)
- Probability & Statistics (12 - 18%)
Higher
- Number (12 - 18%)
- Algebra (27 - 33%)
- Ratio, proportion, rates of change (17 - 23%)
- Geometry and measures (17 - 23%)
- Probability & Statistics (12 - 18%)
Homework
All students in Key Stage 4 are set homework on a weekly basis. Year 10 continue to use Sparxmaths and we expect a 100% completion rate for all homework tasks. Year 11 continue to have access to Sparxmaths but homework will be a written task and will focus on exam skills and exam style questions to support preparation for the final assessment. Students are supported with homework by:
· Support videos on sparxmaths.com
· All classroom lessons are accessible on Google Classroom.
· Weekly homework club
· Class teachers can be contacted in person, via email or through Google Classroom.
Assessment and Feedback
As in Key Stage 3, during lessons teachers regularly assess students understanding. The feedback that teachers give encourages students to think and to understand the next steps for improvement. Teachers create a supportive environment that encourages students to welcome feedback and provide opportunities for them to act on it.
In Year 10 students continue to complete short topic assessments at the end of each unit and in Year 11, students complete short assessments every fortnight. These regular assessments allow students to practice answering exam style questions and encourage regular revision of learning. Teachers are also able to give feedback, promptly address any gaps in learning and inform future planning to ensure lessons are meeting the needs of the class. Termly assessments allow students to experience answering a full GCSE paper, building from 1 paper at the start of Year 10 to all 3 papers at the end of Year 11.
Further Support
Throughout Key Stage 4, students also benefit from:
- Access to sparxmaths.com which has an independent learning section supported by videos
- Access to PiXL maths app (in year 11) which is directly linked to performance in mock assessments
- Small group booster classes
- Revision sessions before school, lunchtimes or after school
- Drop in sessions at lunchtimes
- Holiday revision sessions
- Printed resources including past papers, model practice pairs and aiming for grade assessments
External Assessment
GCSE mathematics is a linear course and will be assessed at the end of the two years. There are three 90-minute papers. Each is worth 80 marks and counts as one third of the overall grade. Students can take the Foundation tier which covers grades 1-5 or the Higher tier which covers grades 4-9.
Paper 1: Non-Calculator
Paper 2: Calculator
Paper 3: Calculator
Any topic from any part of the specification can be tested on any of the papers and topics can be repeated. The examination papers will assess the following assessment objectives in the context of the content and skills set out in the specification.
- AO1 Use and apply standard techniques
- AO2 Reason, interpret and communicate mathematically
- AO3 Solve problems within mathematics and in other contexts
Level 2 Further Mathematics and GCSE Statistics Option
The Mathematics Department offers both Level 2 Further Mathematics and GCSE Statistics as a single option in Key Stage 4. These qualifications are for those students who plan to study A Level mathematics or science. Both qualifications provide the opportunity to strengthen knowledge and skills of high-level GCSE mathematics content and an introduction to some A Level mathematics concepts. This places students in a very strong position for making the transition to sixth form study.
Curriculum
The exam board for Level 2 Further Mathematics is AQA. The course covers the areas of algebra and geometry in greater depth and breadth than GCSE mathematics. The emphasis is on higher order technical proficiency, rigorous argument and problem-solving skills. It also introduces calculus and matrices and develops further skills in trigonometry, functions and graphs.
The exam board for GCSE Statistics is Edexcel. The course gives students the opportunity to apply statistical techniques within the framework of the statistical enquiry cycle using real data from authentic contexts. This will involve the critical analysis of data and application of statistical techniques across the curriculum in subjects such as science, computer science, geography and economics. Students will also understand the role technology plays in the use of large quantities of data to inform decision making processes in public, commercial and academic sectors.
Homework
Students in year 10 use Sparxmaths and we expect a 100% completion rate for all homework tasks. Year 11 continue to have access to Sparxmaths but homework will be a written task and will focus on exam skills and exam style questions to support preparation for the final assessment. Students are supported with homework by:
· Support videos on sparxmaths.com
· All classroom lessons are accessible on Google Classroom.
· Weekly homework club
· Class teachers can be contacted in person, via email or through Google Classroom.
Assessment and Feedback
Similarly to maths, teachers regularly assess students understanding during lessons. The feedback that teachers give encourages students to think and to understand the next steps for improvement. Teachers create a supportive environment that encourages students to welcome feedback and provide opportunities for them to act on it.
Students will receive short assessments at least once per half term. These assessments allow students to practice answering exam style questions and encourage regular revision of learning. Teachers are also able to give feedback, promptly address any gaps in learning and inform future planning to ensure lessons are meeting the needs of the class. Termly assessments allow students to experience answering full papers.
External Assessment
Level 2 mathematics is a linear course and will be assessed at the end of the two years. There are two 105-minute papers. Each is worth 80 marks and counts as 50% of the overall grade.
Paper 1: Non-Calculator
Paper 2: Calculator
Any topic from any part of the specification can be tested on any of the papers and topics can be repeated. The examination papers will assess the following assessment objectives in the context of the content and skills set out in the specification.
• AO1: Recall and use knowledge of the prescribed content for routine and multistep procedures
• AO2: Apply mathematical reasoning, skills and knowledge to solve mathematical problems including rigorous justification and formal proof.
GCSE statistics is also a linear course and will be assessed at the end of the two years. There are two 90-minute papers. Each is worth 80 marks and counts as 50% of the overall grade. Both papers allow calculators to be used. Whilst this GCSE is offered at Foundation and Higher tiers, students choosing this option will be expected to be entered at Higher. Any topic from any part of the specification can be tested on any of the papers and topics can be repeated. The examination papers will assess the following assessment objectives in the context of the content and skills set out in the specification.
• AO1 Demonstrate knowledge and understanding, using appropriate terminology and notation, of standard statistical techniques used to: collect and represent information, calculate summary statistics and probabilities
• AO2 Interpret statistical information and results in context and reason statistically to draw conclusions
• AO3 Assess the appropriateness of statistical methodologies and the conclusions drawn through the application of the statistical enquiry cycle
Key Stage 5 overview
The Mathematics department offer Level 3 Mathematical Studies (Core Maths) and A Level Mathematics to students in Key Stage 5.
The entry requirement for Level 3 Mathematical Studies is a grade 4 in GCSE Mathematics.
The entry requirement for A Level Mathematics is a grade 7 in GCSE Mathematics.
Why study Maths at Level 3?
- Level 3 Mathematical Studies and A level Mathematics compliment several other level 3 courses with mathematical content including geography, economics, biology, business, psychology, PE and sociology.
- Students who study A level Mathematics are well placed to pursue a wide range of subjects at university. For most STEM courses A level Mathematics is a prerequisite.
- A level mathematics is a requirement for several degree level apprenticeships.
- Level 3 Mathematical Studies and A level Mathematics will provide the skills that future employers are looking for. For example, “The majority of private sector organisations believe the use of data analytics will be the most important factor in increasing growth in UK businesses” (Professor Sir Adrian Smith)
- There is a wide range of career opportunities that involve Mathematics.
− Mathematics in technology. For example: medical, game design, internet security, financial cryptography, computing, communications, artificial intelligence
− Engineering. For example: aircraft modelling, fluid flows, acoustic, software development, electronics, civil engineering
− New scientific processes. For example: modelling populations, modelling diseases, quantum physics, astronomy, forensics, DNA sequencing
− Applications relating to human behaviours. For example, data science, psychology, law, economics, climate change, environmental modelling, political science, international development
- Students who study A level Mathematics could attract earnings 11 per cent higher on average.
- University applications that include Level 3 Mathematical Studies can attract more favourable offers.
A Level Curriculum
A level mathematics is a two year linear course. We follow the Edexcel specification. There are three overarching themes that permeate the curriculum.
1. Mathematical argument, language and proof.
2. Mathematical problem solving
3. Mathematical modelling
Students study pure mathematics, mechanics and statistics. Pure mathematics is the concepts, methods and techniques that underpin all other mathematics. Mechanics looks at how to model the world around us using mathematics. Statistics uses data to make inferences
A Level External Assessment
A level mathematics is a linear course and will be assessed at the end of the two years. There are three two hour papers. Each paper counts for one third of the overall grade.
Paper 1: Pure Paper 2: Pure Paper 3: Statistics and Mechanics
Students will be assessed on their ability to:
• use and apply standard techniques
• reason, interpret and communicate mathematically
• solve problems within mathematics and wider contexts.
Level 3 Mathematical Studies (Core Maths) Curriculum
Mathematical studies is a two year linear course equivalent to an AS level. We follow the AQA specification. The main topics of study are:
· Analysis of Data
· Maths for Personal Finance
· Estimation
· Critical Analysis of Data and Models
For the optional content students at Newman Catholic College study:
· Critical Path and Risk Analysis
· Expectation
· Cost Benefit Analysis
Level 3 Mathematical Studies (Core Maths) External Assessment
Mathematical Studies is a linear course and will be assessed at the end of the two years. There are two 90 minute papers worth 60 marks each. Each paper counts for half of the overall grade.
Paper 1 covers the compulsory content.
Paper 2B assesses the optional content and students are expected to draw on the mathematical content of paper 1. Students are also expected to develop and demonstrate confidence and competence in the understanding and application of mathematical modelling in the solution of problems related to decision making and the planning of projects.
Extended offer – Challenge for All
Extra-Curricular Opportunities
The Mathematics Department recognise the importance of experiencing mathematics in a variety of ways and are fortunate enough to have worked with a range of organisations to provide numerous extra-curricular opportunities for our students.
Maths Circles are run for students in Year 7 and Year 8. In Maths Circles, students grapple with intriguing questions, discover and explore exciting ideas and learn to think like mathematicians. Maths Circles aim to develop students’ mathematical thinking and expand their mathematical curiosity. Sessions include a mixture of group and independent work and follow a carefully sequenced and structured curriculum that was developed by MESME in conjunction with King’s College Mathematics School.
Students in Years 7, 8, 9, 10 compete in the UKMT mathematics challenges yearly. This is a national competition with around 250 000 entries and the top 50% receive certificates. We also run a team challenge for students in Year 7 and Year 8.
We work with a number of institutions providing additional sessions for keen mathematicians including Royal Institute, Axiom Maths, Parallel Academy and King’s College Mathematics School. These sessions expose students to mathematical concepts beyond the National Curriculum and some explore ideas that are university level.
We have also benefited from additional support from The Promise Foundation and MyTutor, organisations that provide one-to-one and small group tuition.
We run trips on a regular basis and have taken students to a number of venues including Bank of England Museum, Kew Gardens, Bletchley Park, the Science Museum and the Royal Observatory, Greenwich.
Celebrating various mathematics days throughout the year is another way we involve students with mathematics. This includes NSPCC Number Day, Pi Day and National Numeracy Day.
