Mathematics at Durham Johnston School
The Mathematics department at Durham Johnston consists of 9 full time teachers and two part-time teachers. We are also supported by a member of the leadership group who teaches 9 hours per week. All members of the department have both mathematics and teaching qualifications and the department is able to offer a complete range of mathematics courses at all levels. Students also have the opportunity to take part in national mathematics contests and our students have a very good record of success.
Students receive three lessons of maths per week in year 7,8 and 9. In each Year we cover the five main areas of mathematics. Number, Geometry and Measures, Ratio and Proportion, Algebra and Data Handling.
KS3 Mathematics
KS3 Setting
In year 7 the students are arranged into three bands; 7X, 7Y and 7Z. This reduces to two bands in Years 8 and 9.
The table below shows the change in sets from year 7 into 8.
We are currently following AQA GCSE Specification (8300).
Summary of the key content
Year 10 Topics | ||
Foundation | Higher | |
Half Term 1 |
Form and solve linear equations Collecting like terms Single brackets, common factors Expanding double brackets Arithmetic with negative numbers, BIDMAS Substituting numbers into formulae and expressions Form and solve simultaneous equations Solving linear inequalities (1 variable), show on number line |
Linear Equations (inc. fractional coefficients) Rearranging formulae Linear Simultaneous Equations Multiplying Brackets (including 3 brackets) Factorising and solving ax^{2} + bx + c = 0 Solving using the quadratic formula Solving by completing the square |
Half Term 2 |
Factors, multiples. HCF, LCM, Prime factor decomposition Written methods for four ops, powers and roots Generate terms of a sequence Recognise well-known sequences (see spec) Finding nth term of a linear sequence Plot linear graphs Identify gradient and intercept (from graph and equation) Graphs in real contexts (inc reciprocal) |
nth Term of a Sequence (linear and quadratic) Equations of line graphs, parallel and perpendicular lines Interpret areas under graphs and gradients in real-life context Quadratic Graphs, Identify roots (by factors) Solving and representing linear inequalities graphically Solving and representing simple quadratic inequalities graphically Finding approx soutions to an equation using iteration |
Half Term 3 |
Order positive/negative integers, decimals, fractions Four ops with decimals Convert between fractions and terminating decimals Fractions and percentages of amounts Rounding to a given decimal place or any sig fig, Inequality error intervals Estimating, using a calculator |
Fractions, converting to/from recurring decimals Percentages (reverse and compound) Ratio, proportion (direct, indirect), percentage change Fractional and negative indices Standard Form Surds |
Half Term 4 |
Use of protractor, measuring/drawing angles, scale drawing Angles at a point, straight line, opposite, alternate, corresponding Derive sum of angles in a triangle, angle sum in other polygons Metric conversions (length, area, volume), compound units Area of triangles, parallelograms, trapezia Area and circumference of circles, compound shapes Volume of prisms (inc. cylinders) Pythagoras |
Convert metric units in area and volume, compound units (e.g. density, pressure) Similar shapes (inc. area and volume) Arc lengths, area of sectors, volume and surface area Pythagoras Theorem Right-Angle Trigonometry (in 3D) Congruence Circle Theorems (inc. proofs) |
Half Term 5 |
Four ops with fractions, mixed numbers Revision (2 weeks) Summer Exam Probability scale, calculating probability, sum to 1 Relative frequency, expectation Venn diagrams, tree diagrams Sampling, and it's limitations |
Exclusive and Independent Events, AND and OR rules Revision (2 weeks) Summer Exam Tree Diagrams Relative Frequency Constructions |
Half Term 6 |
Frequency tables, bar charts, pie charts, Time series data Scatter graphs Averages and range Plans and elevations Construct angle of 60, perp bisector of a line/angle, loci Bearings Transformations (inc fractional SF) (revise equation of st. lines) |
Cummulative Frequency, quartiles and box plots, compare distributions Histograms Mean from a grouped table TEST 3D, coordinates, Enlargement (fractional and negative), describing combined Distance between 2 points Dividing a line in a given ratio (inc. midpoints) |
Year 11 Topics | ||
Foundation | Higher | |
Half Term 1 |
Simple percentages Solution by cross-multiplying (e.g. x/2 = 3/4, 2/x = 3/4) Percentage change, quantity as a percent of another Percentage increase/decrease, change, reverse Growth and decay problems, Compound interest Ratio (simplifying, dividing a given quantity), Scale diagrams Express a relationship between 2 quantities as a ratio or fraction Understand and use proportion as equality of ratios Direct and inverse proportion |
Algebraic Fractions Equations Leading to Quadratics Simultaneous Equations with Quadratics Completing the square and identities Identify turning points of quadratics (by comp. square) Equation of a circle centre (0,0), equation of tangent at given point Upper + Lower Bounds Vectors |
Half Term 2 |
Basic congruence for triangles (SSS, SAS, ASA RHS) Similar shapes, scale factors Surface area and volume of 3D shapes (see list) ( in terms of pi) Arc lengths, angles, sectors Pythagoras Right-angled trig finding sides and angles Exact trig values Vectors |
Sine and Cosine rule, area of a triangle Exact trig values, Graphs of Trig Functions (inc. tan x) Trig equations and identities Recognise and sketch cubic, reciprocal, and exponential graphs Graph Transformations, inc exponential |
Half Term 3 |
Index laws Standard form Simplifying expressions with surds Factorising quadratics (coeff x^{2} = 1) Solve quadratic equations by factorising Identify roots and intercepts, turning pts of quadratics graphically Rearranging formulae y = mx + c, to identify parallel lines Equationn of a line (point/line form) Rate of change |
Function notation, inverse and composite functions Domain and range Piecewise graphs Rates of change (gradient of a chords/tangents of a curve) Tangents and Normals Recognise and use geometric sequences (where ratio can be a surd) Set up, solve, and interpret growth and decay problems |
Revision | Revision |
Revision Websites
Mr Hegarty Maths
https://mathswebsite.com/register
Clearly presented videos on topics or past papers. It is possible to sign up to this website, for free, and complete videos and tasks on different topics.
Corbett Maths
www.corbettmaths.com/contents/
Clearly presented videos and additional questionscpresented in a more "exam style".
Mathed up
www.mathedup.co.uk/classes/10n2/gcse-maths-takeaway/
Past exam questions arranged by topic, with an interactive quiz linked in videos and solutions.
Assessment Details
A-Level 2017 Onwards
The mathematics department will be following the OCR Linear specifications for A level maths and further maths.
We have chosen Mathematics A H230/240
http://www.ocr.org.uk/qualifications/as-a-level-gce-mathematics-a-h230-h240-from-2017/
We have chosen Further Mathematics A H235/H245
http://www.ocr.org.uk/qualifications/as-a-level-gce-further-mathematics-a-h235-h245-from-2017/
These are new courses that started in September 2017. All year 12 students of mathematics or further mathematics will take the AS exam in the summer of year 12.