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 ax2 + 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 x2 = 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.

Mathematics A-Level 2017 Onwards