“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 S Wright – (HOD)
Mrs K Harvey
Mrs L McFarlane
Mrs L White
Mrs E Cochrane
Mr R Swann
Mrs L Patton – (Numeracy Coordinator)
KS3:
(Subject/Topic Content)
YEAR 8
ANGLES
Understand and use the terms vertical, horizontal and perpendicular
Understand that an angle is a measure of turn
Recognise and name acute, obtuse and reflex angles
Know how to measure angles with a protractor up to 1800 (or 3600)
Draw angles accurately up to 1800 or 3600
Know that there are 3600 in a full turn, 1800 in a straight line, 1800 in a triangle and 3600 in a quadrilateral
Calculate missing angles e.g. right angles, straight lines, around a point, triangles, quadrilaterals and angles outside a shape
Understand and use the 8 points of a compass and use the terms clockwise and anticlockwise
ALGEBRA
Know the difference in an expression, equation and formula
Use a letter to represent an unknown quantity
Collect ‘like’ terms
Multiply and expand simple expressions involving brackets
Factorise simple expressions
Identify and describe simple sequences (not to include Nth Term)
Solving simple equations
DATA HANDLING
Collect and record data within the class
Display and interpret data on Bar Charts, Bar Line Graphs, Pictograms, Pie Charts, Stem and leaf diagram and Frequency Polygons
Scatter Graphs – draw, interpret, line of best fit, correlation and understand the meaning of “outlier”
Calculate the mean, mode, median and range from discrete data
Calculate mean, mode, median and range from a frequency table
Interpret statistics from real-life situations
FRACTIONS AND PERCENTAGES
Convert a fraction into an equivalent fraction
Write fractions in their simplest form
Change between improper fractions and mixed numbers
Calculate the fraction of a quantity
Add, subtract, multiply and divide fractions
Understand what is meant by decimals and decimal place value
Convert simple fractions to decimals
Understand percentage notation
Change a percentage to a fraction
Convert between percentages and decimals
Find the percentage of a quantity (include VAT)
Calculate percentage increase and decrease/Profit and Loss
NUMBER
Understand and use the term multiple and factor
Identify HCF and LCM
Identify prime numbers
Complete calculations using square/triangular/cube numbers
Understand square and cube roots
Order of operations (BODMAS)
Rules of negative numbers
Add, Subtract, multiply and divide positive and negative numbers
Round numbers using decimal places and significant figures
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
Drawing a line such as y=3, x=2, y=x and y=-x
Reflect shapes in a given line e.g. x=2
Rotate shapes given the angle and centre of rotation
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
Combined transformations
PROBABILITY
Use the words for probability – certain/likely/even/unlikely/impossible
Use a scale for probability
Calculate probabilities as a fraction, decimal and percentage
Complete sample space diagrams and answer questions based on this
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 and use timetables
Convert from 12 to 24-hour clock, and vice versa
Read calendars
ALGEBRA
Revision of Year 8 Algebra
Expanding brackets and collecting like terms
Factorising harder expressions i.e. with a letter on the outside (x2 + 2x factorises to x(x + 2))
Substitution (include negative numbers)
Solve multi-step equations
Solve equations after expanding brackets
Solve: 4x + 2 = x + 8 involving two operations
Use algebra to solve problems in real life
Translate word questions into equation form
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 and y axes
Read and interpret real-life graphs (conversion graphs)
Bearings
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
Define congruence and tessellation
Examine patterns occurring in different cultured (tessellations, Amish quilt design and Islamic tile patterns
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
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 formulae to find the area of a triangles, parallelograms, rhombuses, kites and trapeziums
Find the area of composite shapes
Be familiar with parts of a circle and be able to correctly label a circle
Understand the meaning of and use the relevant formulae to calculate the circumference and area of circles
Calculate the surface area of cubes and cuboids
VOLUME AND CAPACITY
Understand the concept of volume; be able to calculate volume by counting cubes
Use formula to calculate volume of cubes and cuboids
Understand the units of volume
Understand the distinction between capacity and volume, and their respective units
Compound measure calculations (speed/density/pressure)
Use prior knowledge or area and volume to calculate the volume of prisms e.g. cylinders, L-shaped prisms, triangular prisms
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)
Recognise and use rotational symmetry
Describe the order and centre of rotational symmetry
Planes of symmetry in 3D shapes
YEAR 10
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 ratio
Using ratio given the difference between
Using ratio given one quantity
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
Interior/exterior angles and number of sides of polygons
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
Finding the equation of a straight line graph (y = mx + c)
Draw and Interpret Distance-Time Graphs (includes speed, distance and time)
Plotting quadratic graphs
ALGEBRA
Revision of Year 8 and 9 Algebra
Nth term of a sequence
Forming and solving equations i.e. diagrams involving perimeter of shapes, angles, area etc..
Trial and Improvement
Reading and writing inequalities
Representing inequalities on a number line
Solving inequalities
Rearranging the subject of a formula
Index Laws
COLLECTING AND RECORDING DATA
Revision of Year 8 Data Handling to include:
Tally charts, pictograms, bar charts, line graphs, frequency polygons, stem-and-leaf diagrams, scatter graphs, two-way tables, simple averages
Distance Tables
Decision trees
Averages for grouped data (include estimated mean, median, modal group)
Two and Three circle Venn diagrams
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*, C, D, E, F or G
Higher Tier – Grades A*, A, B, C*, 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.
Post 16:
(Subject/Topic Content)
GCE AS and A2 Mathematics
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