“There should be no such thing as boring mathematics”. (Edsger Dijkstra)

Mathematics equips young people with a diverse set of tools to understand and change the world. These tools include problem-solving skills, logical reasoning, and the ability to think in abstract ways. Mathematics, therefore, is a creative discipline. It can stimulate moments of delight and wonder when a student solves a problem for the first time, unearths a more efficient solution to a problem or suddenly sees hidden connections.

Throughout history, mathematics has shaped the way we view the world and remains as important today. Many life stages and skills require a solid grasp of mathematics, from entering university to balancing a household budget, applying for a home loan, or assessing a possible business opportunity. When students eventually leave education and seek out a career, they will inescapably need to use the mathematical skills and strategies they have mastered at school. They will quickly realise that many careers require a solid understanding of mathematics. Doctors, computer game designers, astronauts, forensic scientists and other professionals use maths on a daily basis, as do builders, plumbers and engineers. Mathematics, therefore, opens a world of opportunity for young people.

**Subject:**

**Mathematics**

**Levels Taught:**

KS3

GCSE/KS4

Post 16

**Staff:**

Mrs Wright – **(HOD)**

Mr Boyd

Mrs Harvey

Mrs McFarlane

Miss Peacock

**KS3:**

(Subject/Topic Content)

**Year 8**Introduction to Maths – Employability

1. ALGEBRA

- Use a letter to represent an unknown quantity.
- Collect ‘like’ terms.
- Multiply and expand simple expressions involving brackets.
- Identify and describe simple sequences.
- Solving simple equations.
- Know the difference in an expression, equation and formula
- Simplifying expressions by gathering together like terms
- Simplify expressions by multiplying and dividing terms
- Expanding brackets revision
- Solve equations
- Solve equations after expanding brackets
- Solve: 4 x + 2 = x + 8 involving two operations
- Use algebra to solve problems in real life
- Factorise expressions
- Translate word questions into equation form

2. ANGLES

- Understand that angle is a measure of turn.
- Recognise and name acute, obtuse and reflex angles.
- Know that there are 360 in a full turn.
- Know how to measure angles with a protractor up to 180 (or 360)
- Draw angles accurately up to 180 or 360 degrees.
- Understand angles in a straight line and angles at a point.
- Understand that angles in a triangle add up to 180.
- Understand and use 8 points of compass, and the terms clockwise and anticlockwise.
- Understand and use the terms vertical, horizontal and perpendicular.

3. DATA HANDLING

- Collect and record data within the class.
- Display data on Bar Charts, Pictograms, Pie Charts, Scatter graphs, Stem and leaf diagram and Frequency Polygons.
- Interpret graphs and charts.
- Calculate the mean from discrete and/or grouped data.
- Find the median from the discrete and/or grouped data.
- Calculate the range.
- Calculate mean from a frequency table.
- Interpret statistics from real-life situations.

4. FRACTIONS AND PERCENTAGES

- Pupils will understand the term equivalent and be able to convert a fraction into an equivalent fraction.
- Pupils would be able to write fractions in their simplest form.
- Pupils will be able to find the fraction of a quantity.
- Pupils will be able to add and subtract fractions.
- Pupils understand what is meant by decimals.
- Pupils should be able to convert simple fractions to decimals.
- Pupils understand percentage notation.
- Pupils will be able to change a percentage to a fraction.
- Pupils will be able to change between percentages and decimals.
- Pupils will be able to find the percentage of a quantity.

5. NUMBER

- Understand and use the term multiple and factor.
- Identify HCF and LCM.
- Identify prime numbers.
- Investigate square/triangular numbers.
- Investigation of cubic numbers.
- Understand square and cube roots.
- Order of operations (BODMAS).
- Index laws
- Rules of negative numbers.
- Round numbers using decimal places and significant figures.
- Use knowledge of square numbers, square roots and rounding to apply Pythagoras Theorem.

6. METRIC UNITS AND SCALE DRAWING

- Understand and use metric units of length.
- Know the connection between units.
- Measure lengths of objects
- Estimate lengths of objects
- Understand and use metric units of mass/weight.
- Know connections between units
- Measure weights of objects
- Estimate weights of objects
- Be aware of connections between units.
- Make a simple scale drawing.

**Year 9**TRANSFORMATIONS

- Recognise the four types of transformation – translation, reflection, rotation, enlargement
- Translate shapes given the vector
- Calculate the vector given the shape and its image after transformation
- Reflect shapes by drawing mirror image
- Revision of drawing a line such as y=3
- Reflect shapes in a given line, eg. x=2
- Rotate shapes given the angle and centre of rotation
- Combined transformations
- Calculate centre of enlargement and scale factor from given shape and its enlargement
- Enlarge shapes with whole number scale factor
- Enlarge shapes with fractional scale factor

PROBABILITY

- Use the words for probability – certain/likely/even/unlikely/impossible
- Use a scale for probability
- Calculate probabilities as a fraction, decimal and percent

SCATTER GRAPHS

- Understand and identify the types of correlation in real life situations.
- Plot scatter graphs and decide the appropriate correlation.
- Understand and draw a line of best fit.
- Use the line of best fit for missing data.

TIME

- Read the time from a clock face.
- Show times on a clock face.
- Understand am/pm times.
- Add time.
- Calculate the time lapse from on time to another.
- Convert minutes to hours, and vice versa.
- Interpret timetables and convert from 12 to 24-hour clock, and vice versa.
- Read calendars

STRAIGHT LINE GRAPHS

- Plot co-ordinates in all four quadrants.
- Represent simple functions for vertical and horizontal lines.
- Understand substitution with formulas and linear equations. Find points that line on a line and list the coordinates.
- Represent linear equations on x, y axes.
- Read and interpret real-life graphs (conversion graphs).

SHAPE AND CONSTRUCTION

- Recognise and define a polygon.
- Recognise different types of polygons
- Define a triangle and know the properties of each type of quadrilateral.
- Define a quadrilateral and know the properties of each type or quadrilateral.
- Determine the parts of a polygon.
- Use a compass to draw circles.
- Construct triangles and some regular polygons using a compass.
- Define congruence and tessellation.
- Recognise common 3D objects.
- Draw 3D shapes on Isometric paper.
- Draw, cut and fold nets of cubes and cuboids.
- Create other 3D shapes given net templates.

SYMMETRY

- Recognise line symmetry
- Draw lines of symmetry on shapes and letters.
- Reflect 2D shapes in horizontal and vertical mirror lines.
- Know the symmetrical properties of regular/irregular 2D shapes (including quadrilaterals and special triangles).
- Understand terms object, image, line of reflection, congruent.
- Draw the horizontal and vertical mirror line, given the object and the image.
- Reflect 2D shapes in diagonal lines (equivalent to y = x and y = – x)
- Reflect 3D shapes in a face and a line.
- Examine patterns occurring in different cultured (tessellations, Amish quilt design and Islamic tile patterns.
- Recognise and use rotational symmetry.
- Describe the order and centre of rotational symmetry.

AREA AND PERIMETER

- Calculate the perimeter and area by counting squares.
- Use the formula for the area of a rectangle and a square.
- Estimate the area by counting whole squares and part squares.
- Use the formula to find the area of a triangle.
- Find the area of parallelograms.
- Find the area of composite shapes.
- Be familiar with parts of a circle.
- Understand the meaning of and discover the formula to calculate circumference of a circle
- Understand and use appropriate formula to calculate circumference and area of a circle.
- Understand, use and apply Pythagoras Theorem.

VOLUME AND CAPACITY

- Understand the concept of volume; be able to calculate volume by counting cubes; and discover a formula to calculate volume of cubes and cuboids.
- Understand the units of volume.
- Understand the distinction between capacity and volume, and their respective units.

Pythagoras theorem

- Understand, use and apply in 2D
- Find the midpoint of two co-ordinates, or the midpoint of a line
- Find the length of a line given in co-ordinates

Ratio

- Use the term ratio and ratio notation
- Simplify ratios
- Share a quantity in a given ration
- Use ratio in real-life examples: including maps, recipes, etc

Angles, Triangles and Parallel Lines

- Name the types of triangles using their sides and angles
- Use letters to give the name of angles
- Calculate interior and exterior angles
- Calculate the missing angles in triangles and quadrilaterals
- Recognise, label and draw parallel lines
- Name angles made by intersecting lines
- Construct triangles with compass/protractor and ruler

Co-ordinates and Straight line graphs

- Plotting and identifying points in all four quadrants
- Locate position (including maps, angles and turns)
- Generate co-ordinates for a line
- Explore linear functions and make tables of linear function
- Plot straight line graphs
- Find the gradient of a straight line graph

Collecting and recording data

- Survey: design; know good question structure and answer options; sensitivity to data collection
- Access and retrieve data from a variety of sources
- Be able to group data into given class intervals
- Collect, organise and record data by using and designing recording sheets, using tallying methods where appropriate
- Use a decision tree diagram to sort items
- Draw and interpret frequency tables and diagrams; pictograms; charts and line graphs
- Draw and interpret stem and leaf diagrams
- Draw and interpret pie charts
- Two way tables: construct and use
- Scatter graphs: draw, line of best fit, estimate, distinguish correlation
- Two and Three circle Venn diagrams

Databases, tables and lists

- Interrogate data in a database
- Represent information graphically using IT
- Mean, median, mode and range: calculate and appreciate their suitability; use to compare data sets
- Calculate mean, modal and median class from grouped frequency table

Product of primes, HCF and LCM

- Express a positive number as a product of primes
- Find highest common factor or Lowest common multiple of two whole numbers

Financial Capability

- Understand key terms of finance
- Calculate using money including rounding and change
- Calculate percentages
- Calculate percentage increase/decrease
- Calculate profit and loss
- Exchange rates and foreign currency
- Wages including PAYE
- Debit and credit cards, hire purchase, mortgage and savings
- Calculate interest on savings/loans – APR/AER
- Complete cheques
- Read and calculate from bank statements
- Budgeting

**GCSE/KS4:**

(Subject/Topic Content)

**CCEA GCSE Mathematics**

This compulsory course provides pupils with the confidence to handle the application of the five elements of Mathematics – Number, Data Handling, Algebra, Shape, Space and Measure in everyday life. Mathematics also provides a powerful means of communication in terms of representation, explanation and prediction. It builds on topics covered at KS3. Mathematics is a very important subject as a ‘C’ grade at GCSE is necessary for almost every pathway beyond fifth form irrespective if that is looking for employment or continuing further in education.

Pupils take GCSE Mathematics with CCEA, the Northern Ireland Examination Board at the appropriate level to their ability, either Higher or Foundation level. Higher level pupils normally sit paper T3 or T4 at the end of Year 11 and T6 at the end of Year 12. Foundation level pupils sit either paper T1 or T2 at the end of Year 11 and T5 at the end of Year 12.

**Examination Details**

**Level:**

Foundation Tier – Grades C, D, E, F or G

Higher Tier – Grades A*, A, B, C or D

**Assessment:**

All levels – This course comprises of one module examination (45%) and a complete examination (55%).

The completion examinations consist of two papers – one non-calculator paper and one calculator paper. The module examination is a calculator paper.

**CCEA Essential Skills Application of Number**

This qualification is offered for pupils who would experience difficulty with the demands of GCSE. It forms a key part of all post-16 College, community and work-based learning provision in Northern Ireland, including apprenticeships and work preparation courses.

Pupils take Essential Skills Level 1 and 2 Application of Number with CCEA, the Northern Ireland Examination Board.

Students in Year 11 work towards achieving Level 1 in Application of Number and move onto Level 2 in Year 12.
Essential Skills is a national qualification, recognised by employers and Further Education Colleges.

**Examination Details**

**Level:**

Level 1 equivalent to E grade GCSE

Level 2 equivalent to C grade GCSE

**Assessment:**

Each level of this course comprises of one terminal examination paper with calculator.

**Post 16:**

(Subject/Topic Content)

GCE AS and A2 Mathematics encourages students to extend their range of mathematical skills and techniques. They use their mathematical knowledge to reason logically and recognise incorrect reasoning. They draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions.

Students investigate algebra and functions, geometry, trigonometry, exponentials and logarithms, differentiation and vectors. They also examine quantities and units in mechanics, kinematics, forces and Newton’s laws, statistical sampling, data presentation and interpretation, probability, statistical distributions.

Studying mathematics develops students’ analytical, research and problem-solving skills. It provides a firm foundation for scientific, technical, engineering and mathematical careers. It gives students the knowledge and logic they need to solve scientific, mechanical and coding problems. This course is taught as part of the Ballymena area learning community.

Examination Details

This CCEA GCE in Mathematics has four externally assessed units. Students can take the AS course as a final qualification or the AS (40%) units plus the A2 units (60%) for a full GCE A level qualification.

The specification has four externally assessed units:

- AS 1: Pure Mathematics
- AS 2: Applied Mathematics
- A2 1: Pure Mathematics
- A2 2: Applied Mathematics.

**Assessment:**

Each unit consists of an external written examination:

AS 1 – Paper 1hr 45 mins

AS 2 – Paper 1hr 15 mins

A2 1 – Paper 2hr 30 mins

A2 2 – Paper 1hr 30 mins