Mathematics

Head of Department: Mr Munday

Our vision is to ensure that every child at Ark Greenwich Free School enjoys Mathematics, and is able to succeed, regardless of their background. The department has a team of teachers who love collaborative planning and are always keen to develop their approach to teaching different topics. All teachers are passionate about supporting the development of our students, both inside and outside of the classroom.

 

Key Stage 3 curriculum

At Key Stage 3, we follow the Mathematics Mastery programme which has been inspired by internationally recognised practice, particularly drawing on evidence from Singapore and Shanghai. Currently, around 475 schools are subscribed nationally.

The Mathematics Mastery approach has three key principles: deep understanding, mathematical thinking and mathematical language, with problem solving at the heart of our curriculum.

 

What is Mathematics Mastery?

  • Understanding concepts in depth; Use of multiple representations and problem solving to deepen understanding.
  • Cumulative learning; Topics studied are revisited and integrated into content throughout the programme.
  • Challenge through depth, not acceleration; Extension tasks delve further into the problem, as opposed to accelerating to Year 8 or 9 content.
  • Number sense and place value come first; Studied during the first half term as these skills underpin the remainder of the programme.

 

What Mathematics Mastery is not?

  • Learning ‘rules’ or ‘tricks’; Students are able to explain why the maths ‘works’.
  • Practising 50 times; More focus on exploring the maths and problem solving in a wide variety of situations.

Students are assessed regularly throughout the year in the form of Pre and Post-Assessments which help us to measure the progress made and identify areas of strength and those which may need developing further.

 

Year 7:

  Content covered What is being assessed in the end of term exam
Term 1
  • Understand place value to compare and order numbers including decimals
  • Use approximation and rounding in problem solving
  • Understand and solve problems involving addition and subtraction including perimeter
  • Multiply and divide multi-digit numbers including decimals
  • Find and understand factors and multiples, including LCMs and HCFs
  • Understand and apply the formulae for area of a rectangle, triangle and parallelogram
All content covered so far to be assessed.
Term 2
  • Accurately draw, measure, and identify types of angles
  • Use facts to solve problems involving unknown angles on a line and at a point
  • Understand and use properties of triangles and quadrilaterals
  • Understand and use fraction notation in a variety of contexts
  • Compare and order fractions, decimals and mixed numbers
  • Multiply and divide with fractions
All content covered so far to be assessed.
Term 3
  • Carry out combined calculations using all four operations with brackets
  • Represent unknowns with letters forming and manipulating algebraic expressions
  • Evaluate algebraic expressions through substitution
  • Understand and use percentage including percentage increase and decrease
  • Draw, read and interpret statistical diagrams, including pie charts
All content covered so far to be assessed.

 

Year 8:

  Content covered What is being assessed in the end of term exam
Term 1
  • Understand and use prime factor decomposition
  • Add and subtract fractions
  • Compare and calculate with negative numbers
  • Find and use both term-to-term and position-to-term rules to describe sequences
  • Form and solve linear equations in one unknown
All content covered so far to be assessed.
Term 2
  • Construction of triangles and quadrilaterals
  • Understand and use properties of angles in parallel lines
  • Understand and convert between metric units of area for all rectilinear shapes
  • Use percentage change including reverse percentages
  • Understand and use ratio
  • Understand and use multiplicative relationships in contexts including speed
All content covered so far to be assessed.
Term 3
  • Understand and use the formulae for area and circumference of circles
  • Represent and use the properties of three-dimensional shapes
  • Find the volumes and surface areas of prisms and composite solids
  • Understand and use appropriate strategies to collect, tabulate and classify data
  • Understand and use summary measures of data
All content covered so far to be assessed.

 

Year 9:

  Content covered What is being assessed in the end of term exam
Term 1
  • Understand linear graphs and their equations
  • Use direct and inverse proportion in context
  • Understand and compare numbers in standard form
  • Recognise, interpret and investigate non-linear sequences
  • Find the product of binomials
  • Rearrange formulae from familiar contexts
All content covered so far to be assessed.
Term 2
  • Use standard constructions with a pair of compasses and a straight edge
  • Know and apply the criteria for congruence of triangles
  • Understand and use Pythagoras’ Theorem
  • Derive and use rules for interior and exterior angle sums of polygons
  • Form and solve linear equations and inequalities, including with unknowns on both sides
  • Find graphical solutions to linear and quadratic equations, including simultaneous linear equations.
  • Find graphical solutions in a variety of non-linear contexts, including reciprocal, exponential and piecewise linear relationships
All content covered so far to be assessed.
Term 3
  • Understand the relationship between relative frequency and theoretical probability, calculating probability for independent events
  • Use appropriate measures of central tendency and spread for grouped data
  • Plot scatter graphs and understand correlation
  • Draw and describe enlargements, reflections, rotations and translations
  • Understand similarity and solve problems involving similar triangles
  • Use sine ratio to solve problems involving missing sides and angles in right angle triangles
All content covered so far to be assessed.

 

KS3 Revision

At Key Stage 3, we believe the best revision tool is that students simply use their exercise books to prepare for assessments. All content will have been covered prior to exams and we always encourage note-taking in class. Online tools such as Hegarty Maths and MathsWatch can also be used.

 

Key Stage 4 curriculum

At Ark Greenwich Free School we follow the Edexcel GCSE (9-1) scheme of work.

The aims and objectives of the GCSE (9–1) in Mathematics are to enable students to:

  • develop fluent knowledge, skills and understanding of mathematical methods and concepts
  • acquire, select and apply mathematical techniques to solve problems
  • reason mathematically, make deductions and inferences, and draw conclusions
  • comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

Students will sit their Mathematics GCSE at either Foundation or Higher tier. The course is assessed at the end of Year 11 in the form of three exam papers (1 non-calculator and 2 calculator exams), all lasting 1 hour and 30 minutes.

 

Year 10 Foundation:

  Topics What is being assessed in the end of term exam
Term 1 Integers and place value

Decimals

Indices, powers and roots

Factors, multiples and primes

Algebra: the basics

Expressions and substitution into formulae

Tables, charts and graphs

Pie charts

Scatter graphs

Fractions, decimals and percentages

Percentages

All content covered so far to be assessed.

One full exam paper to also be sat.

Term 2 Equations and inequalities

Sequences

Properties of shapes, parallel lines and angle facts

Interior and exterior angles of polygons

Statistics, sampling and the averages

Perimeter, area and volume

All content covered so far to be assessed.
Term 3 Real-life graphs

Straight-line graphs

Transformations

Ratio

Proportion

Right-angled triangles: Pythagoras and trigonometry

Full suite of 3 GCSE mock exam papers.

 

Year 10 Higher:

  Topics What is being assessed in the end of term exam
Term 1 Calculations, checking and rounding

Indices, roots, reciprocals and hierarchy of operations

Factors, multiples, primes, standard form and surds

Algebra: the basics, setting up, rearranging and solving equations

Sequences

Averages and range

Representing and interpreting data and scatter graphs

Fractions and percentages

Ratio and proportion

All content covered so far to be assessed.

One full exam paper to also be sat.

Term 2 Polygons, angles and parallel lines

Pythagoras’ Theorem and trigonometry

Graphs: the basics and real-life graphs

Linear graphs and coordinate geometry

Quadratic, cubic and other graphs

Perimeter, area and circles

3D forms and volume, cylinders, cones and spheres

Accuracy and bounds

Transformations

Constructions, loci and bearings

All content covered so far to be assessed.
Term 3 Solving quadratic and simultaneous equations

Inequalities

Probability

Multiplicative reasoning

Similarity and congruence in 2D and 3D

Full suite of 3 GCSE mock exam papers.

 

Year 11 Foundation:

  Topics What is being assessed in the end of term exam
Term 1 Probability

Multiplicative reasoning

Plans and elevations

Constructions, loci and bearings

Quadratic equations: expanding and factorising

Quadratic equations: graphs

Full suite of 3 GCSE mock exam papers.
Term 2 Circles, cylinders, cones and spheres

Fractions and reciprocals

Indices and standard form

Similarity and congruence in 2D

Vectors

Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations

Full suite of 3 GCSE mock exam papers.
Term 3 Revision and Exam Preparation Final GCSE exams.

 

Year 11 Higher:

  Topics What is being assessed in the end of term exam
Term 1 Graphs of trigonometric functions

Further trigonometry

Collecting data

Cumulative frequency, box plots and histograms

Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics

Circle theorems

Circle geometry

Full suite of 3 GCSE mock exam papers.
Term 2 Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof

Vectors and geometric proof

Reciprocal and exponential graphs; Gradient and area under graphs

Direct and inverse proportion

Full suite of 3 GCSE mock exam papers.
Term 3 Revision and Exam Preparation Final GCSE exams.

 

KS4 Revision

After termly assessments, all students will receive Personalised Learning Checklists, detailing their areas of strength and weakness. It is important that students use the document to address any misconceptions. This can be done online using Hegarty Maths, MathsWatch and the PiXL Maths App or using a revision guide. As a department, we recommend the CGP Edexcel Mathematics revision guides.

There will be interventions for pupils who are not making expected progress and also support available for those pupils who would like to develop their maths skills further by looking at more challenging problems.

Furthermore, there will also be the chance in Year 11 for some students to complete an additional qualification in Maths, which is a useful bridging course for AS level Maths.

 

Feedback

Pupils will receive individual and group verbal feedback every single lesson. Pupils will typically receive personalised written feedback typically once every 5-6 lessons.  This feedback may be written by the teacher but could also be written by the pupils from an activity planned by the teacher. Teachers will use feedback sheets with questions designed to consolidate and/or extend pupil understanding.

In both Key Stages, students will be formally assessed at the end of every half term. These grades will be recorded so that classroom teachers can report progress data to parents on a termly basis via the whole school reporting system. Personalised Learning Checklists will be provided to all students on a termly basis.

 

Ambition and careers

In 2017 Sir Adrian Smith published a review of post-16 mathematics education for the government. Some key quotes from the report can be found below:

  • ‘Adults with basic numeracy skills earn higher wages and are more likely to be in employment than those who fail to master these skills.’
  • ‘Individuals who achieve five or more good GCSEs (including English and mathematics) as their highest qualification have a lifetime productivity gain worth around £100,000 compared to those with below level 2 or no qualifications.’
  • ‘Around half of individuals in jobs where mathematical sciences qualifications are essential were found to have salaries of £29,000 or more, compared with only 19 per cent of the UK workforce overall.’
  • ‘In the UK, around seven in ten employees report that quantitative skills are essential or important to carry out their work. … In 2012, around 20 per cent of young people in the UK did not have basic skills.’

 

Enrichment and Drop Down Days

At Key Stage 4, students will have normal lessons during enrichment time.

The Mathematics department are heavily involved in Drop Down Days throughout the year, with most years having at least one day focused to mathematics. At Key Stage 3, this could be a day in school completing fun mathematics based activities or for Key Stage 4, a day focused to exam preparation and revision.

Year 8 students will be given the opportunity to visit Bletchley Park, the home of British codebreaking and a birthplace of modern information technology. It played a major role in World War Two, producing secret intelligence which had a direct and profound influence on the outcome of the conflict.