Mathematics

“'The acquisition of at least basic mathematical skills - commonly referred to as ‘numeracy’ - is vital to the life opportunities and achievements of individual citizens.”

Professor Adrian Smith 'Making Mathematics Count' 2004

But Maths is so much more than numeracy! Mathematics has changed the world we live in: it pushes the evolution of our understanding of the world around us; it forms the basis for all of our monetary systems and controls the way in which countries interact and exchange financially; it helps us to create the latest blockbuster computer game as well as life-saving, medical magnetic resonance imaging; it is the basis for future technological and scientific breakthroughs. Mathematics equips students with powerful ways to describe, analyse, formulate and understand the world around them in ways they couldn't possibly imagine; the way a flower grows, the infinity of space, artificial intelligence and so much more. Students take great pleasure when they solve a problem for the first time, adapt to discover a more elegant solution or see hidden connections and we need to ensure that our students develop and empower their mathematical ways of thinking. Mathematics is a creative discipline, in itself a language that is international, knows no cultural boundaries and has even been used in contacting life on other planets! It makes an enormous contribution to society, developing the mind, honing the cognitive skills desired by many employers, and is a significant life skill.

The ability to analyse information and to solve problems are key skills embedded in our curriculum, both in the classroom and through visits or enrichment activities such as the World Maths Tests. Students leave the school well equipped to progress and be successful in the world of education or employment. In a world evolving, changing and developing exponentially, an understanding of and enthusiasm for mathematics helps prepare students with the necessary skills and determination to embrace the challenges of an unpredictable future.

Key Stage 3:


What will I learn?
What will I do?
Year 7How to solve problem solving style questions using mathematical skills already obtained.
Develop mastery in mathematical skills and a deeper understanding.
Work on developing fluency in maths
Term 1
  
Number skills
• Understand and use place value
• Apply the four operations to integers
• Order of operations
• Work with factors, multiples and primes
• Write a prime number as a product of its prime factors

Decimals and measures
• Apply the four operations to decimals using formal written methods
• Round numbers to the nearest 10,100 etc., decimal places and significant figures
• Use rounding to estimate answers

Expressions, functions and formulae
• Interpret algebraic expressions
• Simplify expressions
• Multiply and expand out a single bracket
• Factorise expressions into a single bracket
• Substitute values into formula and expressions
• Solve linear equations

Analysing and displaying of data
• Calculate averages from a list and table
• Understand sampling
• Draw several charts to represent data

Term 2

Angles and shapes
• Measure and draw angles accurately
• Find missing angles on a line, around a point, in polygons and on parallel lines

Area, perimeter and Volume
• Find the area and perimeter of simple shapes
• Find area and circumference of a circle
• Calculate areas of compound shapes
• Understand properties of solids and their nets
• Calculate the volume and surface areas of prisms

Fractions (operations) and FDP
• Simplify fractions
• Apply the four operations to fractions
• Convert between fractions, decimals and percentages

Ratio and proportion
• Use ratio for recipe questions
• Share a quantity into a ratio
• Convert between ratio and fractional parts

Term 3

Probability
• Find relative frequencies
• Understand the probability scale and be able to place events on it.
• Complete probability spaces
• Find probabilities from Venn and tree diagrams

Factors, multiples and primes (RECAP)

Transformations
• Perform and describe reflections, rotations, translations and simple enlargements.

Sequences and graphs
• Plot coordinates
• Plot straight line graphs in the form y=mx+c
• Interpret gradient and intercept
• Find the midpoint of a line between two coordinates
• Find the next terms in a sequence
• Find the nth term of a linear sequence
• Use a nth term rule to generate a sequence
• Work with special sequences such as the Fibonacci sequence.
Year 8How to solve problem solving style questions using mathematical skills already obtained.
Develop mastery in mathematical skills and a deeper understanding.
Work on developing fluency in maths
Term 1
Number Skills – Review
• Understand and use place value
• Apply the four operations to integers
• Order of operations
• Work with factors, multiples and primes
• Write a prime number as a product of its prime factors

Fractions, decimals and percentages (review)
• Simplify fractions
• Apply the four operations to fractions
• Convert between fractions, decimals and percentages
• Order fractions, percentages and decimals
• Calculate fractions and percentages of amounts
• Work out compound interest

Probability
• Find relative frequencies
• Understand the probability scale and be able to place events on it.
• Complete probability spaces
• Find probabilities from Venn and tree diagrams
• Stratified sampling

Graphs
• Plot coordinates
• Plot straight line graphs in the form y=mx+c
• Interpret gradient and intercept
• Find the midpoint of a line between two coordinates
• Draw and solve quadratic graphs
• Recognise equations of cubic and reciprocal graphs

Real life graphs
• To be able to sketch graphs of real life situations - examples include speed, distance time graphs, water depth graphs

Ratio Review
• Use ratio for recipe questions
• Share a quantity into a ratio
• Convert between ratio and fractional parts
• To be able to draw and interpret Graphs of ratios

Term 2

Transformations Review
• Perform and describe reflections, rotations, translations and simple enlargements.

Statistics, graphs and charts
• Calculate averages from a list and table
• Understand sampling
• Draw several charts to represent data, e.g. bar charts, frequency polygons and pie charts etc.

Sequences – Review
• Find the next terms in a sequence
• Find the nth term of a linear sequence
• Use a nth term rule to generate a sequence
• Work with special sequences such as the Fibonacci sequence.

Expressions and equations (forming and solving equations)
• Understand the difference between expressions, equations and formulae
• Interpret algebraic expressions
• Simplify expressions
• Multiply and expand out a single bracket
• Factorise expressions into a single bracket
• Substitute values into formula and expressions
• Solve linear equations
• Expand out double brackets to form a quadratic expression
• Solve and factorise quadratic equations

Term 3

Shape and measure 2D and 3D solids
• Find the area and perimeter of simple shapes
• Find area and circumference of a circle
• Calculate areas of compound shapes
• Understand properties of solids and their nets
• Calculate the volume and surface areas of prisms
• Calculate the volume and surface area of a sphere and cone

Angles (Review)
• Measure and draw angles accurately
• Find missing angles on a line, around a point, in polygons and on parallel lines

Scale drawings and measures
• Read scales
• Construct and interpret plans and elevations of 3d shapes
• Interpret maps and scale drawings and use bearings.

Constructions and Loci
• To be able to bisect a straight line and an angle
• To be able to bisect a straight line through a point
• To be able to construct triangles.
Key Stage 4

GCSE Mathematics

What will I learn? (the skills that this subject develops at KS4)


What will I learn?
What will I do?
Year 9Moving into your GCSE specification we will start to look at the following skills

• Developing fluent knowledge, skills and understanding of mathematical methods and concepts
• Being able to acquire, select and apply mathematical techniques to solve problems
• Being able to reason mathematically, making deductions and inferences and drawing conclusions
• To be able to comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context

The following areas will be assessed:
Number
Algebra
Ratio, proportion and rates of change
Geometry and measures
Probability
Statistics
• Apply the four operations to positive and negative numbers
• Work with induces
• Write recurring decimals as fractions
• Work with factors, multiples and primes
• Write a prime number a product of its prime factors
• Represent data in different charts and tables
• Interpret data and make conclusions
• Perform operations with fractions
• Convert between fractions, decimals and percentages
• Calculate percentages and percentage change
• Calculate missing angles on lines, around a point, in a triangle, in polygons and on parallel lines
• Find averages from listed and grouped data and apply to real life situations
• Find the area of simple and compound shapes
• Find the volume and surface area of prisms
• Find the volume and surface area of cones and spheres
• Finding missing lengths in a right angled triangle using Pythagoras’ Theorem
• Find missing lengths or angles using trigonometry
• Perform and describe transformations
• Find bearings and read scale drawings
• To be able to draw loci and construct angles and triangles.
Year 10At GCSE you will learn to apply your mathematical knowledge alongside the following skills:

• Recalling facts, terminology and definitions
• Interpreting notation correctly
• Accurately carrying out routine procedures or set tasks requiring multi step solutions
• Making deductions, inferences and draw conclusions from mathematical information
• Constructing chains of reasoning to achieve a given result
• Interpreting and communicating information accurately and presenting arguments and proofs, whist assessing the validity of an argument and critically evaluating a given way of presenting information

The following areas will be assessed:
Number
Algebra
Ratio, proportion and rates of change
Geometry and measures
Probability
Statistics
• Plot coordinates and straight line graphs
• Find the equation of a straight line and interpret the gradient and intercept
• Plot and interpret distance time graphs and relate to type of correlation
• Perform and describe transformations
• Simplify ratios
• Share quantities into a ratio
• Be able to plot a ratio graph and read conversion graphs whilst relating the problems to real life
• Pythagoras’ theorem
• Find missing lengths and angles in a right angled triangle using trigonometry
• Probability – be able to complete Venn diagrams and probability trees whilst calculating with fractions
• Direct and inverse proportion
• Growth and decay
• Compound measure e.g. speed
• Draw Loci and construct angles and triangles
• Plot quadratic graphs
• Expand and factorise quadratic expressions
• Complete the square on quadratic expressions to find the minimum and maximum turning points
• Use the sine and cosine rule
• Apply and prove circle theorems
• Simplify and solve algebraic fractions
• Rearrange formula
• Simplify and rationalise surds
• Find an estimate for a solution using iteration
• Composite functions
• Identify and prove similarity and congruence.
Year 11At GCSE you will learn to apply your mathematical knowledge alongside the following skills:

• Recalling facts, terminology and definitions
• Interpreting notation correctly
• Accurately carrying out routine procedures or set tasks requiring multi step solutions
• Making deductions, inferences and draw conclusions from mathematical information
• Constructing chains of reasoning to achieve a given result
• Interpreting and communicating information accurately and presenting arguments and proofs, whist assessing the validity of an argument and critically evaluating a given way of presenting information

The following areas will be assessed:
Number
Algebra
Ratio, proportion and rates of change
Geometry and measures
Probability
Statistics
• Apply the four operations to fractions
• Laws of indices
• Write numbers in standard and perform calculations
• Identify and prove similarity and congruence
• Add and subtract column vectors
• Plot and interpret cubic and reciprocal graphs
• Solve simultaneous equations algebraically and graphically
• Rearrange formula
• Algebraic proofs
• Recall and use Pythagoras’ theorem in 2d and 3d
• Simplify and rationalise surds
• Convert between ratio and fractional parts
• Direct and inverse proportion
• Translate graphs of functions
• Find the gradient of a line between two points
• Apply the trapezium rule and recognise under and over estimation.