# Mathematics

Head of Subject: Mr Vettiankal (vettiankal@williamellis.camden.sch.uk)

The main aims of our Department are:

• To interest and motivate our students in their mathematical studies by ensuring they experience success using a wide range of courses and a variety of teaching and learning styles.
• To maximise the personal mathematical potential of each of our students and enable them to achieve good examination results by challenging them to work hard and consistently in a pleasant environment.
• To ensure that students feel at ease with any basic mathematical concepts encountered either inside or outside of the classroom. They are exposed to a wide variety of relevant and useful mathematics.
• To arouse a sense of mathematical wonder in our students by sharing our enthusiasm and exploring mathematics for its own sake.
• To prepare our students for the wider responsibilities of adult life by a classroom ethos which encourages responsibility, initiative, concentration, perseverance, co-operation and respect for others.

Key Stage 3

Year 7

• Simplify fractions by cancelling all common factors; identify equivalent fractions.
• Recognise the equivalence of percentages, fractions and decimals.
• Extend mental methods of calculation to include decimals, fractions and percentages.
• Multiply and divide three-digit by two-digit whole numbers; extend
• Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations and methods.
• Check a result by considering whether it is of the right order of magnitude.
• Know and use the order of operations and understand that algebraic operations follow the same conventions
• Plot the graphs of simple linear functions.
• Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle.
• Convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring instruments.
• Compare two simple distributions using the range and one of the modes, median or mean.
• Understand and use the probability scale from 0 to 1
• Solve word problems and investigate in a range of contexts, explaining and justifying methods and conclusions

Year 8

• Add, subtract, multiply and divide integers
• Use the equivalence of fractions, decimals and percentages to compare proportions
• Divide a quantity into two or more parts in a given ratio
• Use standard column procedures for multiplication and division of integers and decimals
• Simplify or transform linear expressions by collecting like terms
• Substitute integers into simple formulae.
• Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c
• Identify alternate and corresponding angles
• Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor.
• Use straight edge and compasses to do standard constructions
• Deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid
• Construct, on paper and using ICT, a range of graphs and charts;

Year 9

• Add, subtract, multiply and divide fractions.
• ·   Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole
• Make and justify estimates and approximations of calculations.
• Construct and solve linear equations with integer coefficients, using an appropriate method.
• Generate terms of a sequence using term-to-term and position-to- term definitions of the sequence, on paper and using ICT
• Know and use the formulae for the circumference and area of a circle.
• Design a survey or experiment to capture the necessary data from one or more sources
• Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems.
• Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques
• Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text.

Year 9 objectives for more able pupils

• Know and use the index laws for multiplication and division of positive integer powers.
• Understand and use proportionality and calculate the result of any proportional change using multiplicative method
• Square a linear expression and expand the product of two linear expressions of the form x ± n; establish identities.
• Solve a pair of simultaneous linear equations by eliminating one variable
• Change the subject of a formula.
• Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.
• Understand and apply Pythagoras’ theorem.
• Know from experience of constructing them that triangles given SSS, SAS, ASA or RH

Key Stage 4 – GCSE Specification Edexcel Maths 1MA1

Year 10

• Calculation, checking and rounding
• Indices, roots, reciprocals
• Factors, multiples, primes, standard form and surds
• Algebra: the basics, setting up, rearranging and solving equations
• Sequences
• Averages and range
• Fractions and percentages
• Representing and interpreting data and scatter graphs
• Ratio and proportion
• Polygons, angles and parallel lines
• Pythagoras’ Theorem and trigonometry
• 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

Year 11

• Transformations
• Constructions, loci and bearings
• Solving quadratic and simultaneous equations
• Inequalities
• Probability
• Similarity and congruence  in 2D and 3D
• 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
• Rearranging the subject of formulae, algebraic fractions, rationalising surds
• Vectors and geometric proof
• Reciprocal and exponential graphs ; gradient and area under graphs
• Direct and inverse proportion

Assessment –

• The qualification consists of three equally-weighted written examination papers at either Foundation tier or Higher tier.
• All three papers must be at the same tier of entry and must be completed in the same assessment series.
• Paper 1 is a non-calculator assessment and a calculator is allowed for Paper 2 and Paper 3.
• Each paper is 1 hour and 30 minutes long.