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MathKS4

Intent

Our mission is to cultivate high level mathematical skills in all our students whilst inspiring a love of mathematics and of learning.  We aim to stimulate an appreciation of the intrinsic value of the application of logic and problem-solving and to evoke an understanding of the importance of mathematics in the world around us. 

Introduction 

Mathematics is an amazing subject that encompasses more than just numbers; it involves pattern and structure and is about logical analysis, deduction and calculation within these patterns and structures.

Learning mathematics is more than just following a method or process, it is key within everyday life, from journey planning, to many decisions made in the world of business and in the creation of the remarkable structures and buildings we view today.  Mathematics underpins the world around us, and in the workplace using maths is unavoidable.  It is both fundamental and functional!

Mathematics at Prince William School aims to develop a growing confidence and overall enjoyment of each student’s pathway.  Running parallel to this we aim to ensure students reach their full potential and to be successful in their careers.

The staff in the Mathematics Department are a dedicated and hardworking team, who really enjoy mathematics and really enjoy teaching. Our fundamental beliefs are that with hard work, resilience and a healthy sense of humour, everyone can succeed!

Examples of cross-curricular links

English: 

Non-fiction reading  -  problem-solving scenarios.

Vocabulary strategy - explicit teaching of technical vocabulary

Purpose and audience writingexplaining and justifying reasoning 

Science: Graphs, rearranging formulae,
Humanities: Interpreting data
Technology:  Measuring, scale, ratio.

 

Examples of Cultural Capital entitlement from NC

  • Fundamental numeracy and key mathematical skills
  • Problem-solving and application of logical processes
  • Understanding of applications of mathematics in the world around us.

Key Stage 3

In Years 7 and 8, students are taught the mathematics Key Stage 3 curriculum which is designed to provide all students with a firm foundation for their success and future mathematical studies throughout Key Stage 4. Key areas of mathematics include: number, algebra, geometry and measures, ratio and proportion as well as statistics and probability. Students are taught in sets according to their ability (using prior attainment and internal data / information).  They develop their understanding of fundamental mathematical concepts and are given the opportunity to apply their skills to a range of problems designed to improve fluency, problem-solving and reasoning skills.  In Year 9, they start applying their learning to the GCSE syllabus.

Year 7

Term 1

Term 2 

Term 3

Number - types of number, arithmetic.

Skills - use of arithmetic, knowing prime, square, cube numbers

Number - calculation problems. Geometry - exploring 3D shapes

Skills - being able to  use four operations

Content - area and perimeter of 2D shapes, using percentages, fractions and percentages - being able to convert between.

Skills - being able to find percentages. converting between fractions and %

Term 4 Term 5 Term 6

Content - reasoning and theoretical probability. Solving linear equations. Investigating statistics.

Skill - using four operations with fractions, bar charts, pie charts, pictograms, vertical line charts. Averages and range.

Content - shape work including identifying circles and graphs.

Skill - using coordinates. Using and understanding lines parallel o the axes. y=x y=-x

Content - Ratio, shape work including rotation, reflection and translation. Units of mass, length and capacity.

Skill - using ratio, converting between standard units.

 

Year 8 

Term 1

Term 2 

Term 3

Content - sequences, HCF, LCM, Prime factorisation, positive integer powers 

Skill - Using number and revising previous number skills

Content - using four operations with decimals, be able to write expressions and inequalities. Laws of indices


 Skill - developing use of algebraic skills, use of number

Content - circumference of circles, volume of prisms and cylinders. Percentage change and interest. Four operations with fractions 


Skill - using Venn diagrams, area and volume formulae, working with percentages

Term 4 Term 5 Term 6

Content - Linear equations with unknowns on both sides. Discrete and continuous data, compare using averages. 


Skill - scatter graphs and correlation. Interpreting and analysing. Being able to compare data

Content - Angles and scale drawings, maps, bearings and constructions. Linear and quadratic graphs. 


Skill - using angles and bearings. Be able to construct using ruler and compasses. Plot straight line graphs.

Content - Enlargement, compound units. Simple kinematic problems. 


Skill - be able to convert units.

 

Year 9

Term 1

Term 2 

Term 3

Content - Number work revision, factors, multiples and primes. Rules of indices. Shape work including angles

Support - Using four operations with numbers. Knowing shape properties.

Core - Shape properties and angle facts including angles in polygons

Higher - Standard form and estimation. Loci and construction.

Skill - Be able to revise previous skills. Use estimation to solve problems and check work.

Content - use and interpret algebraic notation, simplify and manipulate algebraic expressions. Order integers, decimals and fractions, apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers.

Higher - understand and use the concepts and vocabulary of identities, translate simple situations or procedures into algebraic expressions or formulae. Be able to use direct and inverse proportion. use compound units such as density and pressure; change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts.

Skill - being able to understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms. Be able to change freely between fractions, decimals and percentages, and factors.

Content - generate terms of a sequence either from a term-to-term rule or a position-to-term rule, recognise and use sequences of triangular, square and cube numbers as well as simple arithmetic progressions. Deduce expressions to calculate the nth term of linear sequences. solve linear equations in one unknown algebraically (including those with the unknown on both sides of the
equation)  

Higher - recognise and use Fibonacci type sequences, quadratic sequences and simple geometric progressions. understand and use standard mathematical formulae, rearrange formulae to change the subject  

Skill - Becoming more confident with algebra.

Term 4 Term 5 Term 6

Content - know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders), know the formulae, area of a circle, calculate: perimeters of 2D shapes including circles, areas of circles and composite shapes. Be able to use ratio and proportion in different contexts.

Higher - introduction to pythagoras. Being able to find congruent and similar triangles and use known results to obtain simple proofs.

Skills - Being able to use formulae to apply knowledge to questions.

Content - coordinates and linear graph properties, be able to interpret maps and scale drawings and use of bearings. Identify, describe and construct congruent shapes, including on coordinate axes. describe translations as 2D vectors.

Higher - find the equation of the line through two given points, or through one point with a given gradient. find approximate solutions to linear equations using a graph, solve two linear simultaneous equations in two variables algebraically.

Skills - be confident in graph work and able to construct different graphs.

Content -be able to use frequency of outcomes of probability experiments using tables and frequency trees. Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1
probability scale. Be able to use venn diagrams. interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and
pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use. Be able to use scatter graphs and describe correlation.

Higher - be able to use tree diagrams

Skills - using charts and graphs to build on previous knowledge

Example of skill progression

Simplifying expressions and solving linear equations in year 7 is developed so that in year 8 students write their own expressions and manipulate them using factorising and solve more complex equations, and in year 9 they can rearrange expressions and formulae and solve linear equations which involve the expansion of single or double brackets.

 

Key Stage 4

At KS4 students work towards the AQA Specification 8300.  All assessment is by terminal exams at end of Year 11 and there is no coursework.

Three exams of 90 minutes (80 marks) each.

All students are expected to have the correct equipment, namely; a pen, pencil, ruler, protractor, eraser and scientific calculator. (Two of the three final assessments will require a scientific calculator).

Revision

  • Watch online video clips and use the follow-on questions to check understanding
  • Practice exam style questions regularly, checking your answers against a mark scheme
  • Do little bits often to help you retain skills and knowledge
  • Take advantage of revision sessions on offer

www.corbettmaths.com/

www.mrbartonmaths.com/students/

Year 10

Term 1

Term 2 

Term 3

Content - use inequality notation to specify simple error intervals due to truncation or rounding, apply and interpret limits of accuracy. Calculate with roots, and with integer indices.
Calculate with and interpret standard form. Identify and apply circle definitions and properties, construct and interpret plans of 3D shapes.

Higher -  Fractional indices and surds. Equations of circles, Simultaneous equations

Skills - Being able to use prior knowledge about coordinates. Using metric and imperial units

Content - simplify and manipulate algebraic expressions including quadratic expressions.
know the difference between an equation and an identity; argue mathematically to show algebraic
expressions are equivalent, and use algebra to support and construct arguments. Solve problems involving percentage change including in financial mathematics. Solve problems involving direct and inverse proportion.

Higher - Be able to solve questions using algebraic fractions. change recurring decimals into their corresponding fractions and vice versa

Skill - Be able to use previous algebraic manipulation skills.

Content - Recognise and use Fibonacci type sequences, quadratic sequences and simple geometric progressions. Derive an equation, solve the equation and interpret the solution. Understand and use standard mathematical formulae, rearrange formulae to change the subject.

Higher - deduce expressions to calculate the nth term of quadratic sequences. Solve simultaneous equations where one is linear, one quadratic.

Skill - be able to spot the rule of sequences and whether they are arithmetic or geometric.

Term 4 Term 5 Term 6

Content - Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS).

Higher - calculate surface area and volume of spheres, pyramids, cones and composite solids. recognise and use the equation of a circle with centre at the origin.

Skill - Be able to use given facts to prove.

Content - Use the form y = mx + c to identify parallel lines. Be able to find the equation of the line. Identify and interpret roots, intercepts, turning points of quadratic functions graphically. Solve two linear simultaneous equations in two variables algebraically.

Higher - describe the changes and invariance achieved by combinations of rotations, reflections and translations. understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y ; construct and interpret equations that describe direct and inverse proportion.

Skill - be able to use graph knowledge to solve different problems.

Content - Apply property that the probabilities of an exhaustive set of outcomes sum to one; enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams. Introduction to cumulative frequency graphs, interpret, analyse and compare the distributions of data sets including box plots. Construct and interpret histograms.

Higher - calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams. Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling.

Skills - to be able to analyse data.

 

Year 11

Term 1

Term 2 

Term 3

Students are on an individualised pathway and following assessment at beginning of year areas are highlighted and worked on in class. Independent revision encouraged and identifying of areas needed.

Revision - using gaps identified from mocks to teach

Revision - using gaps identified from mocks to teach

Term 4 Term 5 Term 6

Revision - using gaps identified from mocks to teach

Revision - using gaps identified from mocks to teach

Revision - using gaps identified from mocks to teach

 

Example of skill progression

Learning the basic rules of trigonometry is followed by solving simple problems with triangles, which is developed to using those laws in various real-life contexts, and then learning how to use sine and cosine in non-right-angled triangles.

Key Stage 5

At Key Stage 5 students work towards the AQA A level specification 7357, and Further Maths A level specification 7367 is also offered. All assessment is by terminal exams at end of Year 13 and there is no coursework.

The A level maths exam consists of 3 papers: paper 1 is pure maths, paper 2 pure and mechanics and paper 3 pure and statistics. All are 2 hours long.

A level further maths consists of 2 pure papers and 1 combined mechanics and discrete paper. All exams are 2 hours long.

Year 12

Term 1

Term 2 

Term 3

Content - GCSE higher recap on algebra, geometry and number. Coordinate geometry, differentiation.  


Skills - using previous GCSE knowledge and extending understanding 

Content - rates of change, integration, trigonometric graphs, vector geometry

Content - Logarithms, exponentials. Mechanics - SUVAT, newton’s 1st and 2nd laws

Term 4 Term 5 Term 6

Content - Proof Statistics - revision of GCSE handling data, using the large data set, binomial distribution, hypothesis testing.


 Skills - analysing and deducing

Revision - using gaps identified from mocks to teach

Content - moving on to A level content. Functions review, partial fractions, sequences and series. 
Skills - using prior knowledge to build further
 

 

Year 13 

Term 1

Term 2 

Term 3

Content - differentiation - chain rule, product rule and quotient rule. Radians, trigonometric functions. 

Content - mocks and review. Integration. Mechanics - constant and variable acceleration.

 
Skills - being able to use mock exam to show areas of need and focusing revision.

Content - Integration by parts, differential equations. Mechanics - motion under gravity, resolving forces, 3D vectors. 


Skill - putting all learnt knowledge into answering exam questions and being able to recall year 12 learning

Term 4 Term 5 Term 6

Mocks and review.

Revision - using gaps identified from mocks to teach

Course complete.

 

Example of skill progression

Interpreting data display, such as histograms and cumulative frequency graphs progresses on to being able to use large data sets to analyse date effectively using these methodologies and then apply the knowledge gained from the analysis to interpret and hypothesise further.

Careers and progression

Qualification pathways 

The department has responded to student requirements and changed the offer to include Further Mathematics at KS5 and Additional Maths at KS4.

The GCSE offered at KS4 prepares students perfectly for the A level offered at KS5, which in turn prepares students for further study at degree or employment in a wide variety of jobs. An A Level Mathematics qualification is a valuable key to any scientific degree (Physics, Engineering, Biology, Chemistry, Economics and of course Mathematics) as successful students will have developed good powers of analysis, the capacity to think logically and the ability to solve problems. Mathematics plays a key role in many areas, for example, within science and industry, financial management, accountancy, construction, aviation, hospitals, marketing, meteorology, manufacturing and computer programming.

Example of successful progressions

67% of students that studied A level maths progressed to higher education/careers in mathematics related area in 2019.

 

Examples of links to Gatsby benchmark 4 (Linking curriculum to careers) 

The maths department are working with students to make the links between GCSE and real world maths, to make it more relatable and relevant, discussing where maths is in use in daily jobs. We give real life contexts and examples, we link topics to where they would be used in careers. We have career lessons where we talk about where maths could take them.

 

Examples of link to Gatsby benchmark 5 (encounters with employers)

As a department we support students in looking at careers with local employers. Students in year 11 have a carousel day where they meet different employers and talk about different job roles. Year 12 and 13 students took part in a day with Anglian water.

 

Employability skills

Numeracy, problem solving & tactics, analysis & evaluation, resilience.

Extra-curricular

We offer students a range of enrichment opportunities outside of lessons designed to ignite a passion for Mathematics.

Students can participate in the UKMT individual and team challenges which are separated into junior, intermediate and senior divisions.

Opportunities to go to conferences.

STEM opportunities both in and out of school.

Intervention offered to students with a maths teacher available every lunchtime for drop in sessions.

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