Mathematics and Statistics

Intent

The Mathematics curriculum at Beauchamps has been designed to allow students to develop a mastery of the broad range of topics covered throughout Key Stages 3, 4 and 5. As well as a depth of understanding, we intend to promote a curiosity and enjoyment of the subject, and ensure that all students are able to reach their potential within the subject. Relevance of Maths is a key focus throughout the curriculum, ensuring students are engaged by seeing how they so frequently use Maths, often without realising it, and how their Maths understanding feeds so well into other areas, as too does their grasp of skills such as literacy into Maths. The knowledge and skills developed throughout their studies, as well as the qualifications students achieve in the subject, should equip them either to pursue a future studying and working within Maths, or to use in a wide range of careers and scenarios.

Image

Implementation

All students at Beauchamps are taught in differentiated, engaging lessons, where depths of understanding are explored, and tricks and shortcuts are discouraged. At every possible opportunity references to relevance in everyday life, future careers and cross-curricular links are explicitly made to students. The emphasis of fundamental skills such as the correct use of language is visible through all Key Stages.


Year 7

Students in Year 7 are taught in tutor groups and have a curriculum centred the approach of Teaching for Mastery. This means all students have the opportunity to learn new skills with a deep understanding of why they work, and where the connections between various mathematical areas are, as well as expanding on and mastering skills developed throughout the Key Stage 2 curriculum. Where necessary the curriculum is differentiated, in terms of the content covered, depending on the tutor group it is being used with. The content of lessons is pitched at the higher attainers in lessons, with suitable differentiation for those with lower prior attainment.

There are several topics focused on in Year 7. Firstly, number skills, including the use of the four operations, rounding, time and money, factors and multiples, order of operations, and square and cube numbers. Later in the year these number skills are developed further to include fractions, decimals and percentages in various contexts. The second topic, which is focused on as a skill as well as a new topic, is algebra, including simplifying, substitution, and solving equations. Again this is something which is developed throughout the year, in this case onto sequences and graphs. The penultimate overarching topic for the year is statistics and data, including probability, analysing data, and displaying data. The final topic covered is geometry, consisting in Year 7 of 2D and 3D shapes, perimeter and area, and angle rules. Where these topics have been introduced in Key Stage Two, the focus is on deepening understanding and stretching and challenging to higher level questions.

Students identified as not ‘secondary ready’ are included in our Year 7 catch-up programme, led by a teacher with experience in Key Stage 2. Through rigorous assessment, it is measured as to when students are then considered to be ‘secondary ready’, and this allows students to complete the programme, whilst their progress is still monitored by the class teacher, Key Stage Leader and Subject Leader.

Higher attaining students are offered the chance to take part in the UKMT Junior Maths Challenge, allowing them to develop their understanding of problem solving whilst putting their skills against students of similar attainment nationally. Elsewhere intervention is overseen by our Year 7 & 8 Intervention Coordinator, who targets various students based on a particular focus, including key groups such as PPG and SEN.

 

Image
Year 8

Students in Year 8 are put into three sets within three mixed ability bands. The curriculum path these students follow will be determined by which set they are in within their respective bands. This differentiated approach to the curriculum allows higher attaining students to be stretched and challenged throughout their studies in all sets, deepening their understanding of a range of high-level topics, whilst those with lower prior attainment are given more time to develop their understanding and fully master the necessary skills to progress onto the more challenging areas.

In Year 8 the focus is on introducing new topics from the Key Stage 3 curriculum whilst also developing on those that were introduced in Year 7. As with Year 7, the initial focus is on number skills, only this time looking at prime factors, standard form, indices and significant figures. This also links to the ratio and proportion content covered later in the year. Fractions, decimals and percentages are developed further later in Year 8 as well. Algebra understanding and use is extended into Year 8, with more of a focus on equations and linking to problem solving, as well as using algebra graphically. Statistics is taken further with the introduction of other forms of analysing and displaying data, as well as taking probability to a more challenging context. Finally the geometrical elements of Maths are developed into Year 8, looking at area, perimeter and volume in more challenging contexts.

As with Year 7, the Year 7 & 8 Intervention Coordinator oversees the provision of intervention for this year group, again with a particular focus of key groups, attainment, etc.

Higher attaining students in Year 8 are offered the opportunity to study for an additional qualification in Maths, namely the Level 2 Edexcel Award in Algebra. This promotes a passion for the subject through exposing them to the areas of Maths they will not encounter in Key Stage 3 and encouraging students to consider pursuing studies and a career in Maths in the long-term. Students are also given the chance to again take part in the UKMT Junior Maths Challenge.

 

Image
Year 9

Year 9 is when students are first put into two ability-based bands, with four sets in the higher band and five in the lower band. This follows on from the curriculum path the students followed in Year 8, and has a longer-term view of the two-tiered GCSE exam students will take at the end of Year 11, whilst ensuring Year 9 sees the completion of the mastery of the Key Stage 3 curriculum. For those students with prior attainment low enough that accessing the Key Stage 3 curriculum has been highly challenging, the alternative Level 1 Entry Level Course is offered to ensure they are equipped with the key skills that it covers in areas such as finance and time, whilst also giving them a credible qualification in Mathematics.

Despite there being differences in the curriculum content between sets at this stage, there remains overarching similarities in the topics. As with Year 7 and 8 there are clear focuses on the big concepts in Maths; number skills, algebra, statistics and data, and geometry, but the extent to which they are developed is greater in this Year, albeit to different depths depending on the branch of the curriculum being covered based on which set it is relevant to.

The Year 9 & 10 Intervention Coordinator oversees the intervention provision in this year group, in a very similar manor to that of Year 7 & 8. Higher attaining students in Year 9 progress to the Intermediate UKMT Maths Challenge, developing on the skills they have used in the Junior Challenge into a more challenging context.

 

Image
Year 10

The setting and banding from Year 9 is maintained into Year 10, on the whole, and as a result students maintain their path towards the most appropriate GCSE exam at the end of the Key Stage 4 curriculum. Delving more into the Key Stage 4 topics begins to expose our higher attaining students to the topics from the higher end of the curriculum, whilst the small steps mastery approach allows this to be done with ease, explicitly connecting to prior learning. If not already completed, students with the lowest prior attainment have the opportunity to complete the Level 1 Entry Level Qualification.

Year 10 being the first Key Stage 4 year means the topics covered begin to encompass the more challenging areas of Maths. Students will be exposed to concepts such as Trigonometry, albeit to differing depths, as well as other challenging geometrical concepts such as developing understanding of Pythagoras’ theorem, transformations and constructions and in some cases looking at circle theorems. Elsewhere the development of algebra continues with a focus on quadratics, rearranging difficult formulae, algebraic fractions and non-linear graphs. Alongside these key topics for the GCSE at the end of Year 11, students still develop their mastery of understanding of fundamental mathematical skills seen at Key Stage Three.

The Year 9 & 10 Intervention Coordinator oversees the provision of Year 10 in very much the same way as Year 9.

The Higher attainer provision is also similar in Year 10 with the UKMT Maths Challenge being offered to those higher students.

Year 11

Year 11 again sees the setting and banding system introduced in Year 9 maintained, and thus the curriculum from then follows through into the final year of Key Stage 4 study. The exam exposure is raised in Year 11 with revisiting earlier material being the primary focus beyond the Easter break. The immanency of the GCSE examinations require a consistent reference to how their understanding will be applied throughout their three exam papers, in addition to the real-life modelling and references present throughout both Key Stages 3 and 4.

In Year 11 the content covered is determined by the tier of entry that is most appropriate to each student. Where the higher paper is being taken, students will be exposed to the highest level of Key Stage Four topics, including extending understanding of topics such as circle theorems and trigonometry, whilst looking into some new ideas such as recurring decimals and trigonometric graphs. Where the foundation paper is more appropriate, the curriculum will be tailored to stretching and challenging students at the relevant content for this paper. Of course there is a lot of crossover in the overarching themes of the course, and students’ understanding of Maths in the wider world is not hindered by the lack of exposure to content beyond the foundation paper.

The Key Stage 4 data and intervention leader takes charge of the programme for intervention for this year group, with a heavy focus on the progress of students towards their potential achievements at the end of the academic year, but with an underlying importance placed on the key groups of SEN, PPG, Higher Attainers, etc.

Higher attainers in Year 11 are encouraged to think about their options beyond Year 11, namely into studying Maths into Key Stage 5. There are currently three courses offered at Beauchamps in Year 12 for Maths; A Level Mathematics, A Level Further Mathematics, and AQA Level 3 Certificate in Mathematical Studies. Having the different styles of qualifications like this means we are able to maintain the broadest possible interest in Maths beyond the age of 16.

 

Image
Year 12 & 13

Throughout Year 12 and 13 students are taught in mixed classes based on the options they chose.

In A Level Maths and Further Maths, there is a slightly heavier exam focus than previously in order to give students the best chance of achieving well in the qualification in order to allow them to pursue Maths into the next stage of their studies or to take their experience into a career. This is not to say that the intended mastery, outside-relevance and cross-curricular emphases are undermined by this, as in the case of A Level Maths and Further Maths these different approaches tend to go together well, and given the potentially abstract nature of the content of the course this can prove hugely beneficial in Key Stage 5.

In A Level Maths the course is split into two thirds Pure Mathematics with the remaining third being split equally between Mechanics and Statistics. The overarching themes of Pure Mathematics; algebra, calculus, polynomials, trigonometry, graphs, vectors, circles, and some areas of number such as surds, all lend themselves in some way to helping students’ understanding of the applied areas of the course. Within these applied areas students focus on; constant and variable acceleration, kinematics, moments and pulleys within Mechanics, whilst the Statistics focus is on analysing and displaying data, which is an extension from Key Stages Three and Four, distributions including binomial and normal, probability, and hypothesis testing.

In Further Maths there is an equal split between the Pure Mathematics, known as Core Pure Mathematics, and the applied content. The applied content has an element of choice to it in that the department chooses which particular modules will be studied. At Beauchamps we choose to study Further Statistics, developing on the statistical knowledge from A Level Mathematics, and Decision Mathematics, a new concept to students focusing on algorithms.

As well as the challenging nature of the course, higher attaining students are given the opportunity to again take part in the UKMT Senior Maths Challenge, as well as where possible taking part in external student events ran by organisations such as the Advanced Maths Support Programme (AMSP).

The AQA Level 3 Certificate in Mathematical Studies is an alternative Maths course at Level 3 aimed at students who wish to study Maths beyond GCSE but not the full A Level course. It is of great benefit to other subjects, most notably Science, Geography and Business/Economics, due to its statistical and financial content, but also sets students up well for real-life mathematical scenarios that they will face, such as tax, national insurance, interest rates, student loans, and mortgages. The statistical content is directly relevant to several other subjects at both Level 3 and degree level, again meaning these lessons will directly prepare students for further studying in various disciplines.

The Key Stage 5 Leader oversees intervention for Year 12 & 13, and the focus is a mixture of two criteria. Firstly it is done through identifying which topics require more practice for a significant number of student, and secondly targeting those students who may be struggling to access the challenging content or not quite making the progress they could be making.

 

Image
GCSE Statistics

In Year 9 students are offered the chance to take a taster into a GCSE Statistics qualification. The GCSE Statistics course covers a wide range of topics such as representing and processing data, correlation, sampling, probability and distribution, all of which develop students’ mathematical understanding into an applied statistical context. For those students who wish to continue studying Maths beyond Key Stage 4, particularly into A Level Maths, this course gives them a great insight as to what will be studied and indeed why Statistics is such an important area of the subject.

The GCSE Statistics students from Year 9 continue their studies in Year 10 with a view to completing the course at the end of the academic year. The high level analysis completed in this course benefits not only into A Level as previously mentioned, but also in developing their skills and understanding to complete their GCSE in Mathematics in Year 11.

The intervention provision in this area is overseen by the Statistics Coordinator, focusing on ensuring students are making appropriate progress in the subject.

Home Learning and extra-curricular

Homework tasks are set weekly from Year 7-13 and vary in nature between online tasks to assessed work. All students across all key stages are offered support with these tasks from their class teacher, or at the weekly Maths club, which also offers support for in-class activities or provides additional material for students looking to stretch and challenge themselves. The purpose of homework may in most cases be fluency of a topic studied in class, but it can also be used as a source of re-visiting prior learning, or pre-research of a new topic that will be covered.

Impact

Students leave Beauchamps equipped with the skills and knowledge to apply to a wide range of situations and careers. This is demonstrated in a number of ways, whether that be through strong examination results, or also the fact that Maths is frequently the most popular A Level in the Beauchamps Sixth Form, particularly showing the success of the Key Stage 3 and 4 provision. Many of these students embark on careers or university courses in Maths or a Maths-related discipline.

Ryan H, ex-A Level Maths and Further Maths student: “My maths education at Beauchamps is one of the main reasons why I have become a successful mathematician. The teaching was always of a high standard and I was always given all the support I needed to be successful. This has resulted in me being able to easily apply what I have learnt to my university course and has led to me attending the LMS summer school as a top undergraduate. This wouldn't have been possible without the solid mathematical foundations provided to me by Beauchamps. I may have left Beauchamps as a student now, but support is still shown to me despite this, and this has provided a path for me to go into a teaching career once I graduate”.

Annie B, ex-A Level Maths and Further Maths student: “I studied Maths at Beauchamps from Year 8 up until year 13, and the support of the teachers helped me pass my GCSE’s and Maths and Further Maths A-Level. All the teachers support their students in many ways, either one-on-one help, or after school intervention. Their help inspired me to do a Maths degree and aim to become a Maths teacher. With their help I was able to get onto the Future Teaching Scholarship.”

Emily H, Level 3 Certificate in Mathematical Studies student: “Maths at Beauchamps has been a really valuable experience. It has taught me real-life skills and prepared me well for life after school. The skills I learned also helped me in other subject such as Biology.”

Millie T, Entry Level student: “I have found Maths at Beauchamps really helpful, as I find myself using it in everything I do. When studying Maths I didn’t feel under pressure from my teacher as she was supportive.”

Alfie H, Level 2 Award in Algebra student: “The extra help I got in my Algebra Level 2 course was really helpful as it helped me in my Maths lessons as well. I find the lessons accessible and get extended to stretch when I find something easy.”