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

Maths is so much more than numeracy! Mathematics has changed the world that 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

Year 7 Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied
Number Work Develop understanding and mastery of basic number work, the four operations, place value and priority of operations. Developing Number Work Further develop understanding and mastery of more complex number work including indices and real roots, estimations of roots, factors and multiples, HCF and LCM, prime numbers and their applications. More Complex Number Work Further develop understanding and mastery of more complex number work including the product rule for counting and calculations involving fractions and mixed numbers. Algebraic Terms An introduction to algebraic vocabulary, algebraic simplification and manipulation, algebraic laws of indices, expansion and factorisation of single bracket expressions. Expansion of double bracket expressions. Delving Deeper Further develop number skills to encompass ratios, linking in with the earlier skills developed in fractional calculations and to solve problems involving ratios (bar model methodology). Introduction to linear sequences and delving deeper into problem solving and examining Fibonacci sequences. Project Work Linked with Technology Department regarding the use of mathematics in designing in 3D, taking measurements, nets, terms used to describe 3D shapes, scales etc. The term ends with some work on bar charts and frequency tables.
Skills and
Key
Knowledge
Taught
Topics areas:

-Ordering positive & negative numbers

-Four operations

-Place value

-Inverse operations

-Directed numbers

-Order of operations

Topic areas:

-Positive integer powers and associated real roots

-Estimate powers and roots of any positive integer

-Factors & multiples

-HCF and LCM

-Prime numbers Prime factorisation

-Apply systematic listing strategies

Topic areas:

-Product rule for counting

-Multiplying fractions, mixed numbers

-Dividing fractions, mixed numbers

-Add/subtract fractions/mixed numbers with same/different denominators

Topic areas:

-Algebraic vocabulary

-Forming expressions and equations

-Simplify and manipulate expressions

-Index laws

-Expansion of single/double brackets

-Factorising a single bracket expression

Topic areas:

-Use of ratio notation

-Simplifying ratios

-Dividing quantities into a given ratio

-Generate terms in a sequence

-Term to term/position to term rule

-Deduce expressions for the nth term of a linear sequence

-Fibonacci sequences

Topics areas:

-Conversion of related standard units

-Construct, interpret plans and elevations of 3D objects

-Interpret maps and scales

-Draw and interpret bar charts and frequency tables

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 8  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied
Rounding Introduction to rounding and its uses in estimating calculations. Round integer and decimal numbers to decimal places and significant figures. Students utilise skills learned for rounding to significant figures to estimate calculations. Students learn to understand how to calculate error intervals when given a rounded quantity. Calculations Students learn to express one quantity as a fraction of another and know how to determine a percentage of an amount with or without the aid of a calculator, interpreting fractions and percentages as operators. Students learn to list outcomes in a systematic manner and use the product rule to calculate the number of possible outcomes. Plotting Students learn Cartesian axes, coordinates and how to plot them. Students plot a linear equation by creating a table of coordinates and plotting them on a suitable set of axes. To understand the concepts of gradient, y- intercept and the general equation of a straight line y=mx+cy=mx+c and how to determine them graphically and algebraically. Angles Students learn of standard ruler constructions. They calculate missing angles in a range of contexts, such as on a straight line, at a point and vertically opposite angles. Students learn of the properties of triangles and quadrilaterals and use these for problem solving. Synoptic Term Review time for work on ratio. Students calculate the perimeter and area of basic shapes, understanding the various characteristics of 3D shapes and become fluent with the mathematical vocabulary used to describe these characteristics. Students focus on transformations, including the introduction of vector notation for translations. Probability Students explore the concept of randomness, bias and fairness. Students use the probability scale to define probabilistic outcomes (decimal, fraction, or percentage). Students learn that probabilities range from zero to one and how to calculate probabilities involving equally likely and independent events. Students are introduced to the differences between theoretical and experimental probabilities.
Skills and
Key
Knowledge
Taught
Topic areas:

-Rounding to decimal places

-Rounding to significant figures

-Estimation

-Error intervals

Topic areas:

-Converting between FDPs

-Express one quantity as a fraction of another

-Calculate percentage of an amount without/ with the use of a calculator

-Systematic listing strategies

-Use the product rule to determine the number of outcomes

-Expansion and simplification of one or two sets of brackets

-Solving linear equations (increasing complexity)

-Transposition of formulae/equations

Topic areas:

-Work with coordinates in all four quadrants

-Plot straight line graphs

-Identify gradients and intercepts graphically or algebraically

-Definition of congruency

-Name, measure and draw angles

Topic areas:

-Name, measure and draw angles

-Determination of angle properties

-Properties of a triangle

-Properties of a quadrilateral

Topic areas:

-Perimeter and area of basic shapes

-Describe the characteristics of 3D shapes

-Carry out simple transformations

-Draw and interpret frequency trees/tables

Topic areas:

-Understand the probability scale and how to define a probability in numerate form

-Understand how to calculate probabilities in a range of contexts, both theoretical and experimental

-Use relative frequency to make predictions

-Calculate the various statistical averages and the range to interpret statistical data

-Use a variety of diagrams and charts to calculate probabilities (sample space diagrams, Venn diagrams, two-way tables and pie charts)

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 9  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied at
Standard-
level (sets
9Q4/R4/9S
and lower)
Number Building to the prior knowledge and exploring FDP, percentage skills, error intervals and limits of accuracy Number Building to the prior knowledge acquired and exploring ratio (including graphically), transformations, numerical indices and standard form Graphs, Tables and Charts Students study stem and leaf diagrams, converting and calculating between standard units as well as compound units whilst understanding algebraic terminology Equations and Inequalities Students expand brackets, factorise expressions, study substitution, rearrange formula and solve equations (algebraically and graphically) Linear Equations and Linear Sequences Students learn to plot linear graphs, interpreting them alongside studying estimation review and sequences Real-life Graphs and Properties of Polygons Students use real-life graphs as well as developing their use and knowledge of angles in polygons and parallel lines as well as understanding bearings
Skills and
Key Knowledge Taught 
Topic areas:

-Understanding equivalent values

-Ordering fractions and equivalent fractions

-Converting between fractions, decimals and percentages

-Ordering fractions, decimals and percentages

-Calculating percentages of amounts with and without a calculator.

-Calculating reverse percentages

-Finding error intervals of numbers rounded to decimals places

-Finding error intervals of numbers rounded to significant figures

-Using error intervals in problem solving

-Truncation of numbers

-Finding bounds and use within calculations

Topic areas:

-Unitary method

-Recipe ratio proportions

-Sharing amounts in a ratio

-Relating ratios, fractions and graphs

-Reflections

-Rotations -Translations with column vectors

-Describing transformations

-Combining transformations

-Enlargements with integer and fractional scale factors

-Adding and subtracting using column vectors

-Calculating powers of 10

-Calculating square and cube numbers/roots

-Writing ordinary numbers in standard form and back as an ordinary number

-Solving worded problems involving standard form

Topic areas:

-Drawing and interpreting stem and leaf diagrams

-Conversion of units of time

-Conversion of units of mass, length and capacity

-Using compound units such as rate of pay

-Calculating densities and when you need to find the volume of a prism

-Calculating average speeds and involving numbers in standard form

-Calculating speeds for two-part journeys

-Conversion between units of speed

-Identifying the difference between equations, expressions, identities and formulae

-Multiplying and dividing expressions

-Collecting like terms in algebraic expressions

Topic areas:

-Expanding single brackets (and multiple single brackets)

-Expanding double brackets

-Factorising expressions into single brackets

-Substituting values in formula

-Working with negative numbers in substitution

-Changing the subject of a simple equation or formula

-Solving one and two-step equations

-Solving equations with the variable on both sides

-Finding solutions to equations graphically

-Interpreting inequalities and draw them on a number line

-Solving one and two-step inequalities and draw the solutions on a number line

Topic areas:

-Plotting a straight-line graph from a table of values

-Calculating the gradient of a given straight line

-Finding the equations of a straight-line graph

-Identifying gradient and intercepts algebraically

-Identifying parallel lines algebraically through a given point

-Finding approximate solutions to linear equations using a graph

-Interpreting the gradient of a straight line as a rate of change

-Rounding numbers to one significant figure

-Estimating calculations using significant figures

-Finding the nth term of a linear sequence

-Using the nth term of a linear sequence to generate terms

-Understanding geometric progressions and use their nth term rules.

Topic areas:

-Using conversion graphs

-Plotting and interpreting distance-time graphs

-Calculating speed from a distance-time graph

-Drawing real-life graphs and interpreting gradient as rates of change

-Understanding the properties of regular and irregular polygons

-Finding exterior angles in polygons

-Finding the interior sum of angles

-Identifying alternate angles on parallel lines

-Identifying corresponding angles on parallel lines

-Identifying co-interior angles on parallel lines

-Finding missing angles on parallel lines using known angle facts

-Measuring bearings between two points

-Finding bearings using angles on parallel lines

-Marking points on a map using bearings and scales

-Solving problems involving bearings.

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 9  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied at
Challenge-
Level (sets
9Q1-Q3
and 9R1-
R3)
Number Building to the prior knowledge and exploring indices laws and powers, fractions, decimals and percentages, working with money and error Intervals Algebra Building to the prior knowledge acquired whilst also exploring bounds, transformations, expanding brackets and sequences Data: Interpreting and representing data/ Number Students learn of stem and lead diagrams, changing the subject of formula, linear graphs and standard form Compound Measures Students learn of compound units, real life graphs, understanding area under graphs and gradient Further Algebra Students learn of substitution, solving equations and iteration Area and Volume, Transformations Students learn of inverse and composite functions, angles in polygons and parallel lines as well as bearing
Skills and
Key Knowledge Taught 
Topic areas:

– Calculating numerical powers (including fractional and negative)

-Laws of indices

-Converting between fractions, decimals and percentages

-Ordering fractions, decimals and percentages

-Converting between a recurring decimal and fraction

-Finding a percentage of an amount

-Calculating percentage change

-Calculating reverse percentages

-Evaluating best buys and value for money

-Exchanging between different currencies

-Finding error intervals when rounded to decimal places and significant figures

-Truncation

Topic areas:

-Upper and lower bounds of a given measurement

-Bounds in calculations

-Reflections

-Rotations

-Translations using column vectors

-Enlargements with negative and fractional scale factors

-Describing all transformations

-Expanding single and multiple sets of single brackets

-Expanding double and triple brackets

-Finding and use the nth term of a linear sequence

-Finding and use the nth term of a quadratic sequence

-Finding and use the nth term of a geometric sequence

Topic areas:

-Drawing an ordered stem and leaf diagram

-Interpreting single and double stem and leaf diagrams

-Changing the subject of an equation or formula

-Calculating the gradient of a given straight line

-Finding the equation of a straight line from a graph

-Identifying gradient and intercepts algebraically

-Identifying parallel and perpendicular lines algebraically

-Ordinary numbers in standard form

-Writing standard form numbers then back as ordinary numbers

-Performing the four operations in standard form

Topic areas:

-Conversion of units of time, mass, length, and capacity

-Calculating density

-Calculating multiple mixed densities

-Calculating density using the volume of a prism

-Calculating average speeds

-Calculating average speeds in standard form

-Calculating average speeds of two-part journeys

-Conversion between units of speed

-Using conversion graphs

-Calculating gradients of real

-life graphs and interpret them as rates of change

-Interpreting real

-life graphs

-Plotting real-life situations on to graphs

-Reading calculations within graphs (velocity, acceleration, distance, area etc)

-Using the trapezium rule to calculate area under a curve

Topic areas:

-Expanding double and triple brackets

-Rearranging formula

-Solving one and two step equations

-Solving equations with the variable on both sides

-Demonstrating that there is a solution between two values

-Rearranging to find an iterative formula

-Using iteration to find a solution to an equation

Topic areas:

-Substitute into functions

-Finding inverse functions

-Finding composite functions

-Find exterior angles in polygons

-Finding the interior sum of angles (and in polygons)

-Identifying alternate angles on parallel lines

-Identifying corresponding angles on parallel lines

-Identifying co-interior angles on parallel lines

-Finding missing angles on parallel lines using known angle facts

-Measuring bearings between two points

-Finding bearings using angles on parallel lines facts

-Marking points on a map using bearings and scales

-Solving problems involving bearings

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Key Stage 4

Year 10 Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied in
Edexcel
GCSE Maths –
Foundation
(set 10H3
and lower)
Graphs and Transformations Students use knowledge of linear graphs to interpret and describe linear relationships, both academic and in real-life situations. Students learn the concepts of gradient, parallel and perpendicular, linking this with distance-time graphs and use this to describe and calculate rates of change Ratio and Proportion Students learn to understand ratios and use them to divide amounts into a given ratio. Students use the unitary method to solve best value problems and links to proportionality Right-Angled Triangles Students use Pythagoras’ Theorem to determine missing sides for right angles triangles. Students use the trigonometrical ratios to determine sides and angles in right angled triangles (calculator and non-calculator) Probability and Multiplicative Reasoning Students calculate probabilities in a range of contexts, including mutually exclusive and exhaustive events. Students calculate percentage changes, reverse percentages, increases/decreases, applying this knowledge to simple and compound interest problems Constructions, Loci and Bearings, Quadratic Equations and Graphs Students develop their understanding of 3D shapes. Students draw loci and solve practical problems. Students also explore quadratic equations Perimeter, Area and Volume Students explore circumference and use of maths language for circles and perimeters. Volume calculations within a variety of shapes are also studied
Skills and
Key
Knowledge
Taught
Topic areas:

-Finding the midpoint of a line segment

-Recognising, naming and plotting straight-line graphs parallel to the axes

-Generating and plotting coordinates from a rule

-Plotting straight-line graphs from tables of values

-Drawing graphs to represent relationships

-Finding the gradient of a line

-Identifying and interpreting the gradient from an equation

-Understanding what m and c represent in y = mx + c

-Finding equations of straight-line graphs

-Use distance-time graphs to solve problems

-Draw and interpret a range of graphs

-Translating a shape on a coordinate grid

-Drawing reflections

-Enlarging shapes

Topic areas:

-Ratio notation/form

-Solving problems using ratios

-Using ratios to convert between units

-Writing ratios for shapes and their enlargements

-Dividing a quantity into 3 parts in ratio

-Solving word problems using ratios

-Using ratios involving decimals

-Solving ratio and proportion problems

-Solving proportion problems in words

-Recognising and using direct proportion on a graph

-Understanding the link between the unit ratio and the gradient

-Recognising different types of proportion

-Solving word problems involving direct and inverse proportion

Topic areas:

-Pythagoras’ theorem

-Calculating the length of the hypotenuse in a right-angled triangle

-Calculating the length of a line segment AB

-Calculating the length of a shorter side in a right-angled triangle

-Using the sine ratio to calculate the length of a side in a right-angled triangle and to problem solve

-Using the cosine ratio to calculate an angle in a right-angled triangle and problem solve

-Using the tangent ratio to calculate the length of a side in a right-angled triangle and calculate angle

-Solving problems using an angle of elevation/depression

-Understanding trigonometric ratios in right-angled triangles and using to problem solve

-Knowing the exact values of the sine, cosine and tangent of some angles.

Topic areas:

-Calculating simple probabilities from equally likely events

-Understanding mutually exclusive and exhaustive outcomes

-Using two-way tables to record the outcomes from two events

-Working out probabilities from sample space diagrams

-Finding and interpreting probabilities based on experimental data

-Using Venn diagrams to work out probabilities

-Using frequency trees and tree diagrams

-Solving probability problems involving events that are not independent

-Calculating a percentage profit or loss

-Finding an amount after repeated percentage change.

-Solving growth and decay problems.

-Calculating average speed, distance and time

-Using formulae to calculate speed and acceleration

Topic areas:

-Describing 3D shapes using the correct mathematical words

-Understanding the 2D shapes that make up 3D objects

-Understanding and drawing plans and elevations of 3D shapes

-Identifying SSS, ASA, SAS and RHS triangles as unique from a given description

-Identifying congruent triangles.

-Bisecting angles and lines using rulers and compasses

-Drawing loci for the path of points that follow a given rule

-Multiplying double brackets

-Using quadratic graphs to solve problems

-Solving quadratic equations ax2 + bx+c=0 using a graph

-Solving quadratic equations ax2 +bx+c= k

-Solving quadratic equations algebraically via factorisation

Topic areas:

-Calculating the circumference of a circle

-Solving problems involving the circumference of a circle

-Calculating the circumference and radius of a circle

-Working out percentage error intervals

-Giving answers in terms of π

-Working out areas of semicircles and quarter circle and perimeters

-Solving problems involving areas and perimeters of 2D shapes

-Working out the volume and surface area of cylinders

-Working out the volume of a pyramid.

-Working out the surface area of a pyramid

-Working out the volume and surface area of a cone

-Working out the volume and surface area of a sphere

-Working out the volume and surface area of composite solids

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 10  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied in
Edexcel
GCSE
Maths – Higher (set 10W1- 10W4 and 10H1-2) 
Equations and Inequalities Students learn how to find the roots of a quadratic expression via factorisation, completing the square, graphically, or using the quadratic formula. Probability, Multiplicative Reasoning Students learn to determine all the possible outcomes for two or more events via the use of the product rule. Students learn to identify all possible outcomes for two events using a sample space diagram, utilising this to determine probabilistic outcomes for these events. Similarity and Congruence, More Trigonometry Students learn the rules of governing congruency and use these to prove congruence in shapes. Students understand the concept of similar shapes and link together the linear scale factor to that of area and volume in order to solve problems. Students learn trigonometrical ratios and how to utilise these in finding sides and angles in problems, knowing the graphs for the trigonometrical ratios. Students learn how to use the sine and cosine rules to solve problems and to transform trigonometric graphs and sketch them. Further Statistics Students learn the sampling processes, including stratified sampling. Students learn about cumulative frequency diagrams and box plots to compare sets of data, looking at the IQR and the median. Students learn to draw and interpret histograms and understand the concept of frequency density. Equations and Graphs, Circle Theorems Students learn skills to solve simultaneous equations, graphically alongside representing inequalities graphically. Students learn to use graphs of quadratic functions, solving quadratic equations graphically. Within graph use, students learn about graphs of cubic functions. Within circles, students learn of radii and chords, Tangents, angles in circles and applying circle theorems. More Algebra Students learn to rearrange formulae. Students develop their understanding of algebraic fractions and simplifying algebraic fractions and solving algebraic fraction equations. Students also learn of surds, functions and proof.
Skills and
Key
Knowledge
Taught
Topic areas:

-Finding the roots of quadratic functions.

-Rearranging and solving simple and more complex quadratic equations.

-Using the quadratic formula to solve a quadratic equation

-Completing the square for a quadratic expression.

-Solving quadratic equations by completing the square

-Solving simple simultaneous equations (for real-life situations)

-Using simultaneous equations to find the equation of a straight line

-Solving linear simultaneous equations where both equations are multiplied

-Interpreting real-life situations involving two unknowns and solve them

-Solving simultaneous equations with one quadratic equation.

-Solving inequalities and show the solution on a number line and using set notation

Topic areas:

-Product rule

-Sample space diagrams

-Identifying mutually exclusive outcomes and events

-Probability of an event not happening

-Comparing real results with theoretical expected values to see if a game is fair

-Using frequency trees

-Calculating probabilities of repeated events

-Using probability tree diagrams

-Deciding if two events are independent

-Tree diagrams

-Using two-way tables to calculate conditional probability

-Using Venn diagrams to calculate conditional probability

-Using set notation

-Percentage changes

-Growth and decay problems

-Calculating rates

-Converting between metric speed measures

-Using formula to calculate speed and acceleration

-Solving problems involving compound measures

-Using relationships involving ratio

-Using direct and indirect proportion

Topic areas:

-Congruence

-Proving shapes are congruent and solving problems

-Using ratio of corresponding sides to work out scale factors

-Finding missing lengths on similar shapes

-Using similar triangles to work out lengths in real-life

-Using the link between linear scale factor and area scale factor to solve problems

-Linking scale factors for length, area and volume to solve problems

-Using upper and lower bounds in calculations involving trigonometry

-Finding the sine/cosine of any angle

-Knowing the graph of the sine/cosine function and use it to solve equations

-Finding the tangent of any angle (and the graph of the tangent function for equations)

-Finding the area of a triangle and a segment of a circle Use the sine/cosine rule to solve 2D problems

-Solving bearings problems using trigonometry Use Pythagoras’ theorem/trigonometry in 3D

-Trigonometric graphs

Topic areas:

-Understanding how to take a simple random sample

-Understanding how to take a stratified sample

-Drawing and interpreting cumulative frequency tables and diagrams

-Working out the median, quartiles and interquartile range from a cumulative frequency diagram

-Finding the quartiles and the interquartile range from stem-and-leaf diagrams

-Drawing and interpret box plots

-Understanding frequency density

-Drawing and interpreting histograms

-Comparing two sets of data

Topic areas:

-Solving simultaneous equations graphically

-Representing inequalities on graphs

-Interpreting graphs of inequalities

-Drawing quadratic functions

-Finding approximate solutions to quadratic equations graphically

-Solving quadratic equations using an iterative process

-Finding the roots of cubic equations

-Cubic functions and equations

-Using facts about chords and their distance from the centre of a circle

-Solving problems involving chords and radii

-Using facts about angles subtended at the centre and the circumference of circles

-Using facts about the angle in a semicircle being a right angle

-Finding missing angles using these theorems and give reasons for answers

-Proving the alternate segment theorem

-Solving angle problems using circle theorems

-Finding the equation of the tangent to a circle at a given point

Topic areas:

-Changing the subject of a formula where the power of the subject appears

-Changing the subject of a formula where the subject appears twice

-Adding/ subtracting/ multiplying/dividing subtracting algebraic fractions

-Changing the subject of a formula involving fractions where all the variables are in the denominators

-Simplifying algebraic fractions

-Adding/ subtracting/ multiplying/dividing more complex algebraic fractions

-Simplifying and expanding expressions involving surds

-Rationalising the denominator of a fraction

-Solving equations that involve algebraic fractions

-Function notation

-Finding composite functions

-Finding inverse functions

-Proving a result using algebra

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 11  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied in
Edexcel
GCSE Maths
Foundation
(set 11H3
and lower)
Fractions, Indices and Standard Form Students deal with fractions and mixed numbers using the four operations, applying the laws of indices to simplify calculations involving powers. Students learn the concept of a standard form number and apply the laws of indices to these when performing calculations involving standard form. Students multiply/divide fractions and mixed numbers. Students use the laws of indices to simplify numerate and algebraic expressions and use standard form numbers in calculations Congruence, Similarity and Vectors Students use the rules governing similarity to determine similar shapes, determine the linear scale factor involved in similar shapes to find missing sides. This requires students to understand congruency and use this to determine missing sides and angles in congruent shapes. Students develop their understanding of vectors as well as similarity, enlargement, scale factors and apply this to solve problems involving similar shapes More Algebra Students focus on plotting and sketching the graphs of cubic, reciprocal graphs and interpret them. Students understand the concept of simultaneous equations and solve them using an algebraic approach or via their graphs. Students develop their ability to rearrange ever increasingly complex equations, understand the differences of expressions, equations & formulae, using the skills acquired in the algebra content to prove results and conditions. Class-specific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning. Class-specific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning. Exams undertaken
Skills and
Key
Knowledge
Taught
Topic areas:

-Multiplying and dividing mixed numbers and fractions

-Using the laws of indices

-Writing large numbers in standard form

-Converting large numbers from standard form into ordinary numbers

-Writing small numbers in standard form

-Converting numbers from standard form with negative powers of ordinary numbers

-Multiply/ divide/add and subtract numbers in standard form

Topic areas:

-Using similarity to solve angle problems

-Finding the scale factor of an enlargement

-Using similarity to solve problems

-Understanding the similarity of regular polygons

-Calculating perimeters of similar shapes

-Recognising congruent shapes

-Congruence to work out unknown angles

-Congruence to work out unknown sides

-Adding and subtracting vectors

-Finding the resultant of two vectors

-Finding multiples of a vector

Topic areas:

-Drawing and interpreting graphs of cubic functions

-Drawing and interpreting graphs of y = 1/x

-Drawing and interpreting non-linear graphs to solve problems

-Solving simultaneous equations by drawing a graph

-Solving simultaneous equations.

-Solving simultaneous equations algebraically

-Changing the subject of a formula

-Identifying expressions, equations, formulae and identities

-Proving results using algebra.

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs

Year 11  Autumn Term 1 Autumn Term 2 Spring 1 Spring 2 Summer 1 Summer 2
Topics
Studied in
Edexcel
GCSE Maths
– Higher (set
11W1- 11W4
and 11H1-2)
Vectors and Geometric Proof Students develop their ability to solve problems involving vectors in a range of contexts, understanding vector notation and the difference between a vector and scalar quantity. Students understand how to determine the magnitude of a vector and find the resultant of two or more vectors. Students learn the determination of parallel and collinear vectors and apply vectors to simple geometric proofs. By the end of the unit, students know how to prove whether vectors are parallel. Proportion and Graphs Students learn to solve problems involving direct/indirect proportionality (including square, square roots, cubes and cube root) in a range of contexts. Students sketch and interpret exponential graphs and understand how to determine the gradient at a stationary point on a curve. Students use suitable mathematical methods to estimate the area under a curve and develop their understanding of the various transformations of graphs and their associated function notations. Students solve problems involving direct and indirect proportion, including squared, cubed, square root and cube root relationships to functions and their graphs. Class-specific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning. Class-specific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning. Class-specific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning. Exams undertaken
Skills and
Key
Knowledge
Taught
Topic areas:

-Vector notation

-Calculating the magnitude of a vector

-Calculating using vectors and represent the solutions graphically

-Calculating the resultant of two vectors.

-Solving problems using vectors

-Using the resultant of two vectors to solve vector problems

-Expressing points as position vectors

-Proving lines are parallel

-Proving points are collinear

-Solving geometric problems in two dimensions using vector methods

-Applying vector methods for simple geometric proofs

Topic areas:

-Using equations to solve problems involving direct proportion

-Solving problems involving square and cubic proportionality

-Using equations to solve problems involving inverse proportion

-Using and recognising graphs showing inverse proportion and exponential functions

-Calculating the gradient of a tangent at a point

-Estimating the area under a non-linear graph

-Understanding the relationship between translating a graph and the change in its function notation

-Understanding the effect stretching a curve parallel to one of the axes has on its function form

-Understanding the effect reflecting a curve in one of the axes has on its function form

Links for
Support/
Help at
Home
Numeracy Practice together, even the times table to develop mental maths

Use of accounts from school such as: MathsWatch, Numeracy Ninjas, Corbett Maths and GCSEPod

Help with measuring in the home (ingredients on recipes through to measuring within DIY)

Support during weekly homework

Correspondence with class teacher through Synergy, especially after data entries or assessments for additional personalised support

Attend any workshops or parent-teacher offers from the Maths department to support core numeracy

Use of Apps on tablets/phones that support numeracy, search ‘numeracy’ within the App store for a range of free apps to spend 10 minutes a day on

Encouragement, the biggest blocker to our students developing their maths is their mindset that they ‘can’t do Maths’ – help us change that mindset

Any study guides (available to loan from the library)

Reading: books of famous mathematicians or the greater study of numbers

Use of additional homework booklets, therapy work packs and/or additional resources from the class teacher via Synergy

Use of student resources located within WHS SharePoint for students

Participation in numeracy competitions in school alongside enrichment and extra-curricular clubs