Maths


Maths Curriculum Map

Intent

The Maths curriculum is designed to ensure that all students make good progress and achieve in Mathematics; to become numerate, analytical thinkers and to give them access to their next level of education and training. The curriculum is structured so that concepts are broken down into small steps, that essential skills are practised until they are fluent, then used in application to problem solving. We believe that all students can achieve at the highest level with perseverance and practice. Our curriculum provides for regular practice and monitoring, through classwork, homework, mini-tests, weekly skills tests and assessments. Evidence of all of these elements are in the front sheets of students’ exercise books, plus a list where students rate their understanding of objectives covered (with a link to video clips they can use to review a topic.) We encourage parents to check these documents to see their child’s progress throughout the year.

The  KS3 and KS4 the curriculum has 5 strands:

Number (N)

Algebra (A)

Ratio, Proportion and Rates of Change (R)

Geometry and Measures (G)

Statistics (S)

Probability (P)

Each term pupils will meet objectives from at least 3 of the 5 strands of the Mathematics Curriculum and these are detailed below. The course is designed to provide variety interleaving and to establish links between the different strands, so that students understand the subject as a whole.

For KS5 there are 3 areas of study

Pure Mathematics (P)

Statistics (S)

Mechanics (M)

 

Implementation

Autumn 1 Autumn 2 Spring 1 Spring 2 Summer 1 Summer 2
Year 7

(KS3)

Students’ first week is a week of ‘Inspirational Maths’ embedding our core value, that all students can achieve in Maths.

This term students revisit topics from primary school that they embed and extend.

 

Number focuses on the four operations; mental calculation, and written methods with integers and decimals. Students use the hierarchy of operations between addition/subtraction and multiplication/ division and brackets. Students use rounding and estimation to check calculations.

 

In algebra

students apply their arithmetic skills to use simple function machines, write arithmetic operations algebraically; they learn the meaning of ‘terms’ ‘like terms’ and ‘expressions’.

 

In statistics students practise their arithmetic calculating average and use averages to compare data sets.

Calculation with four operation skills extends to decimals, time, money, length mass and capacity; interpreting a calculator display ordering negative numbers, adding and subtracting negatives and some multiplication (no touching signs).

 

Students study factors, multiple, primes and square numbers; they practice finding square roots using mental methods and rounding and using a calculator; use index notation for numbers and the hierarchy of operations is extended to calculations with powers.

 

In algebra they revisit ‘like terms’ and simplify expressions by adding like terms; write expressions from worded descriptions and function machines, including using brackets; extend to substitution and writing simple formulae. All algebra provides an opportunity to link to calculation and practice calculation through substitution.

 

In geometry students find the perimeter and area of 2-d shapes; this also provides opportunities to practise their arithmetic, algebra and problem solving. Students choose appropriate units for problems.

Students read from scales and review coordinate grids, including negative axes.

 

In statistics students draw and interpret data as pictograms, bar charts, tally charts, grouped frequency tables, line graphs and compound bar charts. They now use charts and averages to compare data sets.

 

This term focuses on fractions in students’ number work. Fractions underpin many complex mathematical topics, including ratios, rates, proportionality and slope.  Fluency with fractions also has a number of real‐world applications which students will consider over the course of the term. They will revisit skills from primary school, describing parts using fraction notation and comparing simple fractions.

They will simplify fractions; convert between division and fractions; decimals and fractions; add and subtract simple fractions and find fractions of amounts.

Students work with ratio notation and reducing to its simplest form; making links with simplifying fractions.

 

Students work with direct proportion in the context of worded problems and solve problems with the unitary method; making links to fractions and ratio.

 

Students use the language of probability and describe probabilities using fractions and percentages. They evaluate the probability from given problems and the probability of an event not happening.

Students extend their understanding of fraction equivalence to percentages; they convert between percentages, decimals and fractions; find percentages of amounts. Interleaving with opportunities to practice their mental and written methods.

 

Students revisit ratio and divide an amount in a given ratio; making links to finding fractions and percentages of amounts.

 

Probability extends to listing outcomes and calculating the probability of an event not happening.

In algebra students revisit sequences; they use mathematical language to describe sequences and generate sequences from patterns and practical context. Knowledge of sequences supports the work students do with straight lines this term; they revisit using the coordinate grid; find midpoints of line segments; use substitution to generate coordinates and plot simple linear graphs and recognise some linear graphs.

 

In Geometry students improve their fluency estimating, measuring and drawing angles; they use precise geometrical language to describe shapes and their symmetry.  This is extended to congruence, scale-factor and enlargement; using their understanding of ratio.

In algebra students extend their work with sequences to more complex sequences and begin to identify position to term rules.

 

In geometry students use rulers and protractors to draw triangles accurately and solve problems using scale drawings, applying their previous work on ratio and scale.

Students move from measuring angles to using rules for the sum of angles in a triangle and then a quadrilateral; they can calculate the exterior and interior angles of triangles and quadrilaterals.

 

Students return to symmetry and the transformations (reflection, rotation and translation) of 2-D shapes on a coordinate grid.

Year 8

(KS3)

This term students revisit calculations with negative numbers and extend to using combinations of signs; multiplication and division.

In number students meet powers and roots and the hierarchy of operations again; they will use powers to revisit work with factors and to link to work with algebraic powers.

In algebra students will expand brackets, a key skill.

 

Students extend the work they did in year 7, substituting into more complex expressions and writing more complex expressions and formulae.

Students meet conversions as formulae and as graphs, they also read and interpret distance time graphs.

 

Students find the areas of triangles, parallelograms and trapeziums; emphasising the link between triangles and parallelograms.

This term students develop their skills manipulating algebra; factorising simple expressions and solving one step equations then two-step equations. Students plot line graphs, revisiting substitution, coordinates and making links to sequences and functions.

 

In geometry, students find the volume of cubes, cuboids and compound shapes; they find the surface area of cubes and cuboids. The difference between volume and surface area is emphasised.

In number this term students revisit their year 7 work with decimals and extend to negative decimals; they use inequality with decimals and review place value, multiplying by 0.1 and 0.01, which underpins calculation with decimals; students work confidently calculating with decimals of any size. Students revisit fractions, now adding and subtracting fractions with all denominators; multiplying any two fractions or fractions and integers. Students will develop the confidence to move between decimals and fractions for ease of calculation.

 

Students have met in triangles and quadrilaterals, they now work with angles in parallel lines and apply the skills to geometry problem solving; this also provides opportunities to practise simple calculation and generalising ideas algebraically.

In number this term focuses on dividing fractions, students use the term reciprocal and practical examples to justify the steps of dividing fractions; they start with dividing integers by a fraction, then fractions and then mixed numbers.

 

Students continue to work with ratio this term, including decimals in ratios. They also meet ratio in real-life problems

 

In Geometry students return to interior and exterior angles, but apply understanding of triangle geometry to interior and exterior angles of any polygon. Students can then explore more difficult problem solving geometry.

Students will revisit fraction and decimal equivalence; this will extend to recognising recurring and terminating decimals. Students will apply the equivalence of fractions to compare proportions.

This term students work with graphs and proportion; recognising direct proportion from a graph and using graphs to solve direct proportion calculations; they revisit the written ratio methods to compare the merits of each method. Working with direct proportion, students learn to work out the gradient and interpret its significance in direct proportion.

 

In statistics students use their knowledge of angle, calculation with fractions and ratio and presenting data with pie charts: to interpret; calculate angles and draw.

Students will also draw and interpret stem and leaf diagrams and scatter diagrams. Scatter diagrams will build on their skills with coordinate grids, scale, direct proportion and gradient.

In number students return to percentages, they revisit finding percentages of amounts; they now write proportions as fractions, percentages or ratio. Students practise calculator and mental methods to find percentage increase and decrease and extend their understanding of decimal and percentage equivalence to use decimal multipliers to calculate percentage increase and decrease.

 

In algebra students continue to work with straight lines and using links to their work with gradients and sequences, they can write the equation of simple linear graphs as y = mx +c

 

In statistics students consider how data is collected, they consider primary and secondary data, sample size and bias. Students evaluate and design questionnaires and data collections sheets.

Students use their skills with averages and charts to compare data sets; they consider misleading graphs and the most appropriate average to use.

Year 9

Foundation

(KS4)

Students review calculation, place value; hierarchy of operations; building confidence with application to worded problems and problem solving.

They practise skills using factors, multiples and primes and extend to problem solving.

Students secure their knowledge of algebraic notation and simplify expressions by adding like terms.

In geometry students will review angles; missing angles in triangles, quadrilaterals and parallel lines; interior and exterior angles.

Students read and draw bearings and revisit scale drawing

Students return to their KS3 work on ratio, using the equivalence of ratio and fractions; sharing an amount in a given ratio, using the unit ratio and solving problems with conversion, comparison and scaling.

Students return to index notation for numbers and practice recall of squares and square roots, for exact squares.

Students revisit ratio and use different strategies to solve proportion problems; including the unit ratio, conversion graphs and equivalent fractions.

In algebra students use notation accurately to expand over a single bracket, linking to multiplication and area of rectangles. They reverse this process to factorise a single bracket.

Students extend their work with algebraic notation to understand and derive simple formulae. This extends to substitution and applying methods of calculation; substituting into formulae, that includes brackets and powers. This work can be extended to substitute non-integer values, using written, mental and calculator methods.

 

Students revisit their key stage 3 work on averages and charts; focusing on frequency tables, bar charts and two-way tables. Completing, designing, interpreting and criticising.

In geometry students revisit the area of rectangles and parallelograms; triangles and trapezia. Students make strong links between multiplication and area of rectangles and how the area of a parallelogram is linked to a rectangle, a triangle to parallelogram. Students are using their skills with substitution and calculation in area formulae. Students deduce the lengths of missing sides in compound shapes.

 

Students revisit the important work with negative numbers from year 8. Ordering, adding, multiplying and dividing by positive numbers; students review dealing with ‘touching signs’ and multiplying or dividing by negative factors. They now substitute negative numbers in simple formulae, first integers, then non-integers.

 

Students revisit fractions: equivalent fractions, finding fractions of an amount and converting between mixed and improper fractions. They need to be secure with equivalent fractions, a skill which underpins the majority of work with proportion. They apply these skills in a greater variety of contexts.

 

Students will recall and use the formulae for the area and circumference of a circle. They are using substitution and inverse operations to solve problems.

 

Students will work with direct proportion and the unitary method; they will apply this to solve best buy problems.

Students will decide whether two variables are in direct proportion by both the unitary method and using their work on equivalent fractions.

 

In statistics students recall methods to find averages from lists; they can group data from a list, in a frequency table and understand how this links to methods to find averages from a frequency table. Students are practising their calculation methods, including brackets and order of operations. Students will also compare sets of data using averages and make reference to the context of the problem.

Students revisit their work with decimals; they require confidence with place value for all decimal calculation. They can now combine decimals with their work with negative numbers and with substitution.

 

Students also revisit place value, rounding numbers to a given number of decimal places and using rounded values to estimate calculations. Estimation is a valuable skill for checking all calculations. This work also includes more practice with the hierarchy of operations.

 

In algebra students return to the solving equations work they did in year 8. They solve by spotting solutions; reverse number machines; reverse operation and balancing. As students become more fluent with balancing and reverse operations. Students are practising their algebraic manipulation, using their knowledge of negative numbers; calculation and substitution to check solutions.

 

Students revise fundamental skills with a coordinate grid in all 4 quadrants. They find the midpoint of a line segment by sight and then use the rule; students make a link to their work with averages.
Students then use distance time graphs to draw and interpret journeys. In this context students use the gradient to calculate speed.

Students revisit percentages and their work with equivalent fractions to convert between percentages, decimals and fractions.

Students use conversion to compare numbers and quantities of an amount.

Students use decimal multipliers to find fractions of an amount and percentage increase or decrease. This practise is an opportunity to revisit decimals and calculation: mental, written and calculator methods.

 

In geometry students return to work with transformations; they describe a translation in words and then a vector, they recognise, describe and carry enlargements with positive integer scale factors.

 

Students last worked with probability in year 7. They revise and practise listing outcomes, including 2 independent events. Students work with experimental and theoretical probability. Students solve problems using equivalent fractions, finding fractions of amount to calculate expectation.

 

This term students meet 2 new topics.

Students have found the gradient of the line with distance time graphs, they now find the gradient of any line on the coordinate grid. This extends to find the equations of all lines of the form y =mx; they revisit the link between coordinate pairs and sequences; then draw and identify lines of the form y =mx + c. Students are practicing their substitution, calculation and algebraic manipulation within this topic.

 

Students learn and apply Pythagoras, using their skills with substitution, hierarchy of operations and solving equations.

 

For the remainder of this term students consolidate their work with proportion and algebra, focusing on problem solving and worded questions.

 

 

Year 9

Higher

(KS4)

Students will return to written calculation methods, including estimation and hierarchy of operations and apply these skills to worded questions and problem solving at GCSE level.

In algebra they will consolidate their understanding of algebraic notation, simplifying and factorising single brackets; students will now work regularly with fractions and negatives in algebra.  These skills underpin further work on solving linear equations. Students solve using reverse operations and balancing; equations include negatives, fractions and emphasis on the order of operations.

In ratio students continue converting between equivalent fractions and ratios from worded problems and a variety of context; to achieve fluency.

Students revisit angles in parallel lines, extending to ensure accurate written reasoning. Problems in year 9 will be in more complex geometry than at KS3.

Students will extend their work with scatter diagrams to include understanding of correlation, using and drawing a line of best fit. Students interpret the gradient and consider causation.

Students revisit factors and multiples, using factor trees and Venn diagrams; these problems from real world examples.

 

This half term students return to equations, setting up equations from word problems and geometry.

Students improve their fluency with substitution, using negatives, fractions, decimals into kinematics and increasingly more complex formulae. Students use brackets on their calculator for efficient substitutions.

 

Students work again with y=mx +c for straight lines; review methods to substitute and plot a straight line; recognise equations for vertical and horizontal lines; read the intercept from a graph and find the gradient between two points to write the equation of a line. Interpreting the meaning of the gradient and intercept in the context of a problem, including direct proportion.

 

Students return to compare data sets using averages and range and set these in the context of a given problem. Students review representations of data as graphs and extend to draw and interpret frequency polygons; comparing data using charts and averages read from charts.

Students revisit all calculations with fractions, including mixed fractions and problem set in a variety of contexts.

Students return to straight line graphs and test for parallel and perpendicular lines and apply use of y =mx +c to find the equation of a line through 2 given points.

Students meet sequences and find the nth term to generalise the sequence and apply solve problems; students make strong links between straight line graphs and arithmetic sequences. They also meet geometric sequences.

 

Students re-examine graphs as direct proportion and the unitary method; they meet the scale factor or equivalent fraction methods to solve direct proportion in a single step. Students are introduced to inverse proportion in worded problems.

 

Students re-visit bearings and scale drawings; drawing and interpreting scale drawings to solve increasingly difficult problems.

 

Students design and evaluate questionnaires and data collections sheets. They understand sampling, how data is collected and how bias may be introduced.

Students meet recurring decimals and convert between fractions and recurring decimals applying knowledge of equations.

 

Students review arithmetic and geometric sequences; they meet Fibonacci, quadratic sequences. They continue sequences and use the nth term to find given terms in a sequence.

 

Students extend their work with gradients to distance time graphs working with speed. In a wide range of graphs, students consider the gradient key points and their meaning in the given context.

 

Students extend their work with percentages using multipliers for percentage increase, decrease and reverse percentages. Students will also calculate percentage change and simple interest.

In geometry students extend their work with area and perimeter to problems where they deduce lengths, compound shapes and

In algebra students extend their work with expanding brackets to expand and simplify double brackets; grounding their work with number and area rectangles, then regular practice for fluency.

Students revisit ratio and choose the most efficient technique to solve problems.

In geometry students find the circumference and area of circles, they are using substitution in the given formulae, extending their calculator skills. They use fractions of circles and compound shapes. Students identify prisms, they extend their work with volume of cubes and cuboids, to find the volume of any prism including cylinders.

 

Students revisit probability; finding unknown probabilities using algebra and conditional probabilities focused on 2-way tables.

 

Students extend their skills with solving equations and algebraic manipulation to rearrange simple formulae, using reverse operations.

Students write error intervals for rounded values.

 

Students work with decimal multipliers that they have used with percentages to solve problems of growth and decay. Including compound interest and depreciation

 

In geometry students return to work with transformations; they work with precise descriptions and now represent translations as vectors, they recognise, describe and carry enlargements with positive, including fractional scale factors. Students also use combinations of transformation.

 

Students find all tree averages from frequency tables, and construct grouped frequency tables.

Year 10

Foundation

(KS4)

Students revisit and reinforce their year 9 work with conversions between fractions, decimals and percentages; comparing numbers and using them as operators. Students work with more complex and worded problems.

 

In geometry students represent 3D objects as 2D drawings, nets, plans and isometric drawings.

Students continue to work with substitution using compound measures and kinematic formulae. Students also consider change units with compound units; they need to review conversion with single units and equivalent fractions.

 

In statistics students revisit scatter diagrams, they use a line of best fit and describe correlation. They also represent data in pie-charts; this is an opportunity to practise calculating with fractions and equivalent fractions.

Students calculate percentage change, this links to previous work with percentage increase and decrease. They identify the original amount and 100% in a wide variety of contexts.

 

Students meet sequences and find the nth term to generalise the sequence and apply solve problems; students make strong links between straight line graphs and arithmetic sequences. They also meet geometric sequences, Fibonacci and quadratic sequences. They continue sequences and use the nth term to find given terms in a sequence. They revisit substitution and hierarchy of operations to do this.

 

 

Students have worked with enlargement in year 9, they extend this to work with similar shapes. They use scale factor and ratio skills to find missing lengths in similar 2-D shapes.

 

Students develop their fluency calculating with fractions; using equivalent fractions and converting between mixed and improper fractions to the four operations as simple calculations and problems in geometry or worded problems.

In algebra students extend their work with expanding single brackets to expand and simplify double brackets; grounding their work with number and area rectangles, then regular practice for fluency. They reverse this process to factorise a simple quadratic.

 

Students learn and use the notation of inequalities on a number line. They revise solving equations and extend to linear inequalities. Students need to recall the effect of negative operators.

 

At KS3 students made accurate constructions of triangles; they now use compasses and ruler for precise angle and constructions; these are applied to locus problems combining locus rules.

 

Students have met exterior and interior angles at KS3; they now use all rules for finding missing angles at points and parallel lines to solve geometric problems.

 

 

Students are introduced to inverse proportion in worded problems.

They use arithmetic and checking to solve problems.

 

Students return to probability, they find expected outcomes for future events, find probability using equally likely events; students need to appreciate the concepts of randomness, fairness and bias. Students use two-way tables and probability tables.

 

In geometry students return to similar shapes, they consider the effect of enlargement on angles, area and volume. They solve simple problems with similar areas.

 

Students combine previous works with area and circumference of circles with fractions to find areas of sectors and lengths of arcs; revising other plane shapes in compound shapes.

Students evaluate squares and cubes agnd link to squares and square roots, they use negative square roots.

 

Students have worked with formulae and algebraic manipulation; they rearrange formulas to change the subject, using reverse operations, balancing and application of the order of operations.

 

Students have represented linear equations, they nwo extend to graphical representations of quadratic, cubic and reciprocal functions.

 

In number students links powers of 10 and place value to convert large and small number from standard form to ordinary numbers and vice versa

 

Students extend their work with percentages increase using multiplier to repeated percentage change; applying to problems with compound interest, growth, depreciation and decay.

This term students will consolidate their learning and develop problem solving and application to worded questions. Students will meet only 3 new topics and are the most challenging on the Foundation course.

 

 

In algebra students will revisit their skills with solving linear equations, rearranging formulae and equations of straight lines to solve linear simultaneous equations algebraically

 

Students identify prisms, they extend their work with volume of cubes and cuboids, to find the volume of any prism including cylinders.

 

Students have worked with Pythagoras; they now meet right angle trigonometry. Students use their skills rearranging formulae and calculator skills to find missing sides; they develop reverse operation for trigonometric functions to find missing sides

 

Year 10

Higher

(KS4)

Students extend their year 9 work with percentages, choosing the appropriate skill for a wide variety of questions; they use fractions and multipliers appropriately.

Students learn and use the notation of inequalities on a number line and with set notation.

Students return to probability, they find expected outcomes for future events, find probability using equally likely events; students need to appreciate the concepts of randomness, fairness and bias. Probability increasingly uses algebra in problems; non-calculator problems require students to work with fractions and links with ratio.

Students learn and apply Pythagoras, using their skills with substitution, hierarchy of operations and solving equations.

Students extend their work with equations and inequality to notation, to now solve linear inequalities and work with negative multiplication and division on inequalities.

 

This term with direct proportion students link the graph and ratio to the formula y =kx. Students extend this formula to work with problems direct proportion to x squared, cubed and their reciprocals and inverse proportion, applying their work with equations and substitutions.

Students revisit their KS3 work with indices and number; this extends to the general rules of indices, using negative and fractional indices.

Students now move from expanding to factorising simple quadratics; this leads to solving quadratics by factorising .

 

Also in algebra students will revisit their skills with solving linear equations, rearranging formulae and equations of straight lines to solve linear simultaneous equations algebraically and graphically.

 

In geometry students represent 3D objects as 2D drawings, nets, plans and isometric drawings.

 

Probability extends to calculate the probability of 2 events; understand independent and conditional probabilities and use tree diagrams to solve probability problems.

 

Students apply knowledge of indices, place value and written calculation methods to work with standard form.

 

Students re-arrange more complex formulae; manipulating algebra fluently, factorising to isolate a particular term.

Students meet and solve more complex simultaneous equations, which lead to a quadratic. They substitute, rearrange and solve quadratics by factorising.

Students have used Venn diagrams to find highest common factors; they have used set notation with inequalities; they now interpret and use Venn diagrams to summarise probability problems, including conditional probabilities.

 

Students work with compound measures, speed, density and pressure; they do this successfully by rearranging formulae, substitution and calculation skills.

 

There is an opportunity to review direct and inverse proportion; choosing the most efficient method to solve a variety of problems.

Students review work with fractions; arithmetic, converting to recurring decimals.

 

In algebra students use skills with substitution and coordinate grids to sketch, recognise and interpret quadratic graphs. They review work with linear graphs. Students then link algebraic methods with inequalities, solving quadratics by factorising and simultaneous equations; students then solve quadratic inequalities using factorising and graphs; solve quadratic and linear equations graphically. Students recognise graphically whether a quadratic has real roots and identify the turning points and intercepts.

 

Students have considered the gradient of graphs as the rate of change and the speed in distance time graphs; students now find and interpret the gradient of non-linear graphs.

 

At KS3 students made accurate constructions of triangles; they now use compasses and ruler for precise angle and constructions; these are applied to locus problems combining locus rules.

In number students meet surds, they make links to algebra and indices, to simplify surds, multiply 2 surds and over brackets.

 

Students extend their work with linear and quadratic graphs to cubic, reciprocal and exponential graphs. They identify intercepts, asymptotes.

Students have met exterior and interior angles at KS3; they now generalise algebraically formulae in regular and irregular polygons; students then use rearranging formulae and algebraic methods to solve geometric problems.

 

In statistics students move from working with frequency graphs and tables to cumulative frequency; drawing and interpreting graphs. Students then link the median to the cumulative frequency and estimate the median from the graph. Students use simple percentages to understand the interquartile range and find this from a graph.

Students revisit indices, combining algebraic and number and simplifying negative and fractional indices.

Students have worked with Pythagoras, they now meet rIght angle trigonometry; they discover the ratios using similar triangles and ratio of pairs of lengths. Students use their skills rearranging formulae and calculator skills to find missing sides; they develop reverse operation for trigonometric functions to find missing sides

In geometry students develop their skills of logical argument to prove that 2 triangles are congruent; they use scale factor and ratio skills to find missing lengths in similar 2-D shapes.

Students learn the trigonometric values for key angles

Students extend work with cumulative frequency to draw and interpret box plots. Students have compared data using the mean and the range; they now use a box plot to compare two data sets, using median and inter quartile range; they contextualise their comparison in the given problem.

Year 11

Foundation

(KS4)

Students focus on calculator skills; revisiting work with standard form, substitution, trigonometry and fractions.

 

They revisit calculation in financial context, reviewing percentage change as profit and loss, percentage increase with VAT, simple interest and best buys using ratio or fractions.

Students revisit the quadratic graph and identify its key features and their link to the algebraic significance. They use substitution with quadratics to generate and plot a graph and solve a quadratic graphically.

 

Probability extends to calculate the probability of 2 events; understand independent and conditional probabilities and use tree diagrams to solve probability problems.

 

Students extend their work with volume to find the volume of spheres, pyramids and cones using the given formulae, practising substitution and finding the volume of compound shapes including hemispheres.

Students have met vectors to describe translation; they extend vectors to add vectors and multiply vectors by a scalar. Students use Pythagoras to find the magnitude of a vector.

 

Students pracitse finding the gradient of a line segment, in distance time graphs to find speed and in further real life contexts including scatter diagrams to find the rate of change and its meaning.

 

Students will meet no more new content, but drill key skills and practise in a variety of context; to develop fluency and confidence.

 

Lessons will focus on strengths and weaknesses identified in assessments.

Students will meet no more new content, but drill key skills and practise in a variety of context to develop fluency and confidence.

 

Lessons will focus on strengths and weaknesses identified in assessments.

 

 

Exam preparation continues Exam preparation continues
Year 11

Higher

(KS4)

Students return to quadratics, to factorise more complex quadratics using the ‘splitting the middle term’ method. Students then solve quadratics by completing the square, they revise expanding brackets, perfect squares and rearranging expressions. Students will meet the quadratic formula and use their skills with substitution and calculators to apply this skill.

Students then revisit previous work with simultaneous equations with quadratics; quadratic inequalities and graphs applying the all methods. Students return to the quadratic graph to link the turning point and complete the square.

 

Students have met Pythagoras and locus, this leads to the equation of a circle, centre (0,0) on a coordinate grid. Students apply the work they have done with gradients to find the gradient of a radius, then apply knowledge of perpendicular lines and the equation of a line to find the equation of the gradient.

Work in algebra formalises logical steps and rigour with manipulating algebra to algebraic proof.

In geometry students have worked with scale factors to find missing lengths in similar shapes; students now meet area and volume scale factors. Students need confidence with direct proportion to squared and cubed variables; rearranging formulae and scale factor

Students use their knowledge of fractions, circumference and areas of circle and areas of isosceles triangles to find the lengths of arcs, area of sectors and segments. In statistics students extend their work with unequal frequency tables and charts to histogram. This work relies on confidence with compound measures, proportion and rearranging formulae.

Students can simplify and add surds; students now multiply more complex surds and rationalise the denominator. This work relies on previous work with quadratics and the difference of 2 squares.

 

Students know how to identify the error intervals for rounded values, this work now extends to upper and lower bounds for expressions and formulae involving more than one rounded variable and arithmetic operations. Students use arithmetic skills, negative numbers substitution and percentage change.

Students have met various graphs, they now meet trigonometric graphs, they can sketch and identify the symmetry and intercepts of each graph. Students may extend this to find solutions to trigonometric equations using the symmetry of the graphs.

 

Students extend their work with area and nets to find the surface area of a cylinder; they find the surface area of spheres and cones using the given formulae, practising substitution and rearranging formulae.

 

Students find the volume of cones and spheres using the given formulae; this relies on substitution, rearranging formulae and links to previous work with volume of prisms and cylinders.

 

 

Students manipulate algebraic expression, which they now represent as functions; they work with inverse and composite functions. Students revisit algebraic and trigonometric graphs and consider transformations, reflections and translations.

Students have met iterations when solving problems with compound interest; they have found roots from a quadratic graph; they now use a repeated iteration to solve an equation, identifying a change of sign as a root; they rely on efficient use of a calculator.

 

Students have met vectors to describe translation; they extend vectors to add vectors and multiply vectors by a scalar. Students use Pythagoras to find the magnitude of a vector. Students use fractions to divide a vector in a given ratio. Students extend to complete vector proof using algebraic manipulation.

 

Students build on their work with right angled trigonometry to the sine and cosine rule and area of a triangle; this relies on accurate substitution and rearranging formulae including trigonometric functions. . Students meet circle theorems, this builds on geometry of triangles and quadrilaterals. Students apply the theorems to solve problems with missing angles.

Students use listing techniques, linked to previous work with probability and lowest common multiples, to find all combinations or permutations of a given problem; students generalise to the product rule; using a simple formulae and substitution

Students combine work with algebra and fractions; they build on their skills with factorising, linear and quadratic expressions; cancelling algebraic fractions; rearranging expressions and solving linear equations.

 

 

Students have found gradients of line segments and tangents, they apply this non-linear graphs; students know how to find the area of trapeziums and triangles; they find the area under of a graph to estimate the distance from a velocity time graph.

The exam season will start this term, so the limited time is given over to exam practice and preparation; identifying strengths and weaknesses in pupils’ exam performance to target specific topics. Students also spend time practising timed questions and evaluating their performance in terms of accuracy, recording their method.

 

Y12

A level

(KS5)

This term we will review and extend the bridging work that students competed at the end of year 11

P1 – algebraic expressions

–       Quadratic functions

–       Equations

–       Inequalities

–       Graphs

–       Transformations

P2 – straight line graphs

–       circles

This work will be extended to the more challenging topics

P3 – Algebraic division, factor theorem and Binomial expansion

 

Students will be introduced to statistics and Mechanics. In statistics they look at the large data set of weather, that is the context for some exam problems.

S1 – statistical sampling

S2a – Data presentation

M1 – Quantities and Units

M2a – Kinematics 1

 

P4 – Trigonometric ratios, graphs, equations and identities – students revisit their GCSE work on trigonometry and extend to more complex problem solving, including trigonometric equations.

 

S2b – Data presentation- students revisit histograms and scatter diagrams; students embed their interpretations in the context of a problem and build familiarity with the large data set.

 

M2b – Kinematics 1 (constant acceleration)

 

P5 – Vectors, this relies on students’ work last term with algebra, functions and trigonometry.

 

S3 – Probability

 

S4 – Statistical distributions – this work is an extension of students work on probability.

 

M3a – Forces and Newton’s Laws; this work brings together the previous work in Mechanics and vectors (P5)

P6 – Differentiation; the first module on calculus requires fluency in the first pure topics (P1, P2, P3)

P7 – Integration – the ‘reverse’ of differentiation is an extension and further practise of P6

 

S5a – Statistical hypothesis

 

M3b – Forces and Newton’s Laws

P8 – Exponentials and logarithms

 

S5b – Statistical hypothesis testing

 

M4 – Kinematics 2 (variable acceleration) students work with calculus in Mechanics (P6 and P7)

P1 (A2) Proof

P2 (A2) Algebraic and Partial Fractions – this term students return to P3; they learn and drill more proof and algebraic methods .

Y13

A level

Students continue to cover content seen in previous year and build upon it within the following topic areas:

 

P5 – Binomial Theorem

P6 – Trigonometry

P7 – Parametric Equations

 

S1 – Regression and Correlation

S2 – Probability

 

M1 – Moments

M2- Forces at any angle

 

P8 – Differentiation

 

S3a and b- Normal Distribution

 

M3 – Applications of kinematics

M4 – Applications of forces

 

P9 – Numerical Methods

P10 and 11- Integration

 

S3c – hypothesis testing with Normal distribution

 

M5 – Further Kinematics

 

 

Y12/13

GCSE Retake

GCSE retake students follow the Foundation GCSE course. Students who achieved a grade 3 in the summer will be entered for the November exam. Students will focus on exam-style questions and exam technique. Identifying common errors and misconceptions.

 

Students are expected to do significant independent study in preparation for the exam. Between the exam and the results in January, students are not expected to attend lessons, so that they can focus on their other courses.

 

Students drill the Foundation skill and apply them in exam questions.The course is covered by topic area; as all work is revision students’ strengths and weaknesses direct how class time is used. This sequence is a guide.

 

Number

N1 – Calculations with decimals, positive and negative integers

N2 – estimating rounding and accuracy

N3 – Fractions, decimals and percentages

N4 – nth term, prime factorisation, LCM and HCF

N5 – Standard form

 

 

Ratio and Proportion

R1 – Conversion and exchange rates

R2 – Percentages for simple and compound interest and depreciation

R3 – Compound measures

 

Algebra

A1 – Algebraic notation, expand and simplify expressions, solve equations, laws of indices

A2 – Factorisation, substitution.

A3 – Solve and represent inequalities

A4 – Solve and represent simultaneous equations

A5 – Coordinates and straight line graphs

 

Geometry

G1 – Angle rules, measuring and drawing angles

G2 – Area and volume

G3 – Basics of 2D/3D shapes/ symmetry

G4 – Bearings

G5 – Circumference and Area of circles

G6 – Loci and constructions

G7 – Perimeter and scale

G8 – Pythagoras

G9 – Transformations

G10 – Similarity and congruence

G11 – Surface area

G12 Right angled trigonometry

 

Probability

P1 – Probability and relative frequency

P2 – Venn diagrams

 

 

Statistics

S1 – Averages from lists and frequency table

S2 – Graphs, charts and tables

S3 – Scatter diagrams

 

 

Impact

Students will drill new skills in lessons and at home to ensure they are engrained. ‘Weekly skills tests’ review skills from previous terms to ensure they are kept fluent. Links to Mr Hegarty clips are included in lessons and PLC documents at the front of their book, so they have ready access to reminders of ‘how to’ do all skills. Student exercise books are a record of key examples plus errors, misconceptions, tips and checks that they can use to support revision and further practice. New skills are assessed through classroom ‘mini- test’ every 3 weeks; students are required to re-do any test if they do not achieve 50%; formal extended assessments, as per the school assessment calendar, include assessment on all topics covered so far in that key stage. Pupil reflection and teacher analysis inform independent learning for individuals and topics to be re-visited in review periods for classes.