Linear scheme of work Higher Topic list. Topic/Content/References

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1 Linear scheme of work Higher Topic list Topic/ontent/References Shape 1: Lines, Angles & Shapes Recognise acute, obtuse and right angles Understand the terms perpendicular and parallel Identify scalene, isosceles, equilateral and right-angled triangles Recognise and name shapes such as parallelogram, rhombus, trapezium Recognise reflex angles stimate angles and measure them accurately Use properties of angles at a point and on a straight line Use angle properties of triangles including the sum to 180 Show that the exterior angle of a triangle is equal to the sum of the interior opposite angles alculate interior and exterior angles of a quadrilateral Recognise corresponding, alternate and interior angles on parallel lines Understand and use three-figure bearings lassify a quadrilateral using geometric properties alculate exterior and interior angles of a regular polygon Number 1: Types of number, estimating and approximating including surds Understand place value in large numbers Add and subtract large numbers (up to 3 digits) Understand positive and negative numbers ind the factors of a number Round to the nearest integer Multiply and divide whole numbers by 10, 100, 1000 Multiply large numbers (2 digits by 2 digits) Add and subtract positive and negative numbers Use inverse operations to check answers Use hierarchy of operations to carry out calculations (IMAS) Round numbers to given powers of 10 and to a given number of decimal places Multiply and divide positive and negative numbers Recognise prime numbers Round a number to one significant figure stimate answers to solve problems Round numbers to significant figures Round numbers to different degrees of accuracy, decimal places and significant figures Write a number as a product of prime factors ind the highest common factor (H) of two numbers ind the least common multiple (LM) of two simple numbers ind upper and lower bounds ind the least common multiple (LM) of two or more numbers ind the highest common factor (H) of two or more numbers Use upper and lower bounds in calculations Use surds and π in exact calculations without a calculator. Rationalise the denominator of a surd such as Simplify surds such as write 2 in the form: a + b

2 Algebra 1: Making sense of algebra and sequences Topic/ontent/References ontinue a sequence of diagrams or numbers Write the terms of a simple sequence Simplify an expression such as 5a + 2a 3a Work out the value of an expression such as 3x + 2y when x = 4 and y = 3 Simplify expressions like: 5a + 5b a + 2b Understand the rules of arithmetic as applied to algebra, such as x y is not equal to y x Work out the value of an expression such as 2x - 3y for negative3 values of x and/or y ind a term in a sequence with negative or fractional numbers xpand brackets such as 4(x 3) actorise an expression such as 6x 8 Write the terms of a sequence or a series of diagrams given the nth term xpand and simplify an expression such as 3(3x 7) 2(3x + 1) Write the nth term of a sequence or a series of diagrams xpand and simplify two brackets such as (x 3)(x + 5) xpand and simplify two brackets such as (3x + 1)(2x - 3) Simplify fractions such as and Number 2: ractions, decimals and ratio Understand positive and negative integers ind the fraction of a shape shaded Put integers and simple fractions in order ind equivalent fractions xpress simple decimals and percentages as fractions Add and subtract negative numbers Simplify fractions alculate fractions of quantities Arrange fractions and decimals in order Write place value of decimal digit such as 3 in 0.63 Order decimals such as 0.46 and 0.5 Multiply and divide negative numbers xpress fractions as decimals and percentages Add and subtract fractions Add, subtract and multiply decimals onvert simple fractions to decimals and decimals to fractions ind one quantity as a fraction or percentage of another Solve problems involving fractions Solve problems involving decimals ind one quantity as a fraction of another Use ratio notation including reduction to its simplest form and its various links to fraction notation ivide a quantity in a given ratio Solve simple ratio and proportion problems, such as finding the ratio of teachers to students in a school Add and subtract fractions and decimals Multiply and divide decimals Add and subtract mixed numbers ind the reciprocal of a number Round numbers to a given power of 10, up to three decimal places and one significant figure

3 Topic/ontent/References Multiply and divide fractions Multiply and divide mixed numbers onvert fractions to decimals Solve more complex ratio and proportion problems such as sharing money in the ratio of peoples ages Solve more ratio and proportion problems using the unitary method Recognise that recurring decimals are exact fractions and that some exact fractions are recurring decimals Understand the effect of multiplying and dividing by numbers between 0 and 1 onvert recurring decimals to fractions Solve direct and indirect proportion problems Interpret graphs showing direct and indirect proportion problems Handling ata 1: Statistical measures ind the mode for a set of numbers ind the median for an odd set of numbers Work out the range for a set of numbers alculate the mean for a set of numbers ind the median for an even set of numbers alculate the fx column for a frequency distribution ompare the mean and range of two distributions alculate mean and range for a frequency distribution ind the modal class of grouped data ind the mean for grouped data ind the median class for grouped data ind the upper and lower quartiles and calculate the inter-quartile range for a frequency distribution Algebra 2: Index Notation Work out or know simple squares and square roots Work out or know simple cubes and cube roots Use terms square, positive square root, negative square root, cube and cube root Recall integer squares from 2 x 2 to 15 x 15 and the corresponding square roots Recall the cubes of 1, 2, 3, 4, 5 and 10 and the corresponding cube roots Use index notation and index laws for positive and negative powers including 10³ x 10⁵and 10³ 10⁷ onvert between ordinary and stand index form numbers Use standard index form for calculations Algebra 3: Solving quations Set up and solve a simple equation such as: 5x = 10 or x + 4 = 7 Set up and solve more complicated equations such as: 3x + 2 = 6 x or 4(2x 1) = 20 istinguish between an expression, an equation, an identity and a formula erive complex expressions and formulae Substitute numbers into formulae such as: Solve equations such as 3x 12 = 2(2x - 5)

4 Topic/ontent/References Shape 2: Nets, elevations and Pythagoras Theorem Recognise the net of a simple solid raw the net of a simple shape such as a matchbox tray raw a simple shape such as a cuboid on isometric paper raw the elevations of a solid on squared paper Use Pythagoras Theorem to find the third side of a right-angled triangle Use Pythagoras Theorem to prove that a triangle is right angled Use 3- coordinates ind the distance between two points from their coordinates Use Pythagoras Theorem in 3- problems Number 3: Working with Percentages Understand that percentage means number of parts per 100 and use this to compare hange a percentage to a fraction or a decimal and vice versa Work out a percentage of a given quantity ompare percentages, decimals and fractions Increase or decrease by a given percentage. or example, find the new price of a 490 TV after a 15% reduction. xpress one quantity as a percentage of another Use ratio notation, including reduction to its simplest form and its links to fraction notation Solve simple ratio and proportion problems, such as finding and simplifying a ratio ompare harder percentages, fractions and decimals Work out a percentage increase or decrease Solve more complex ratio and proportion problems using the unitary method Solve ratio and proportion problems using the unitary method Use a multiplier raised to a power to solve problems involving repeated percentage changes Understand how to use successive percentages Work out reverse percentage problems Work out values and draw graphs in situations involving exponential growth. or example, draw a graph to show the way in which a population of bacteria grows. Solve direct and indirect proportion problems Interpret graphs showing direct and indirect proportion problems Shape 3: Measures ecide which is the most appropriate unit of measurement to use in everyday situations overt between metric units Measure the length of a line onvert between metric and imperial units such kilograms and pounds Measure and scale a line Make sensible estimates of lengths onvert between metric and imperial units such as speed, for example, convert 80km/h to mph alculate average speed Use compound measures such as speed Recognise that measurements to the nearest unit may be inaccurate by up to one half unit in Use either compound direction measure, such as density, for example find density given cross sectional area, length and mass ind upper and lower bounds Use upper and lower bounds in calculations

5 Topic/ontent/References Algebra 4: Using expressions and formulae Use a formula in words such as: Total pay = rate per hour no. of hours + bonus Substitute positive numbers into a simple formula such as: P = 2L + 2W Use formulae from other subjects such as : v = u + at erive simple expressions Use formulae such as: P = 2L + 2W to find W given P and L Substitute negative numbers into simple formulae such as: = Topic/ontent/References Use formulae from mathematics and other subjects erive expressions and formulae such as: = 35h + 55 Substitute numbers into more complicated formulae such as: = erive more complex expressions and formulae istinguish between an expression, an equation and a formula Rearrange linear formulae such as p = 3q + 5 Rearrange formulae involving brackets, indices, fractions and square roots A Rearrange formulae where the variable appears twice Shape 4: Area, perimeter and volume ind the perimeter of a shape by counting the sides of squares ind the area of a shape by counting squares stimate the area of an irregular shape by counting squares and part squares Name the parts of a circle ind the volume of a shape by counting cubes Work out the area and perimeter of a simple rectangle such as 5m by 4m ind the volume of a cuboid Work out the area and perimeter of a simple rectangle such as 2.6cm by 8.3cm ind the area of a triangle, trapezium and parallelogram ind the area and perimeter of shapes made from triangles and rectangles alculate the circumference and area of a circle onvert between square units such as changing 2.6m 2 to cm 2 Work out the perimeter and area of a semicircle and compound shapes made from parts of a onvert circle between cube units such as changing 3.7m 3 to cm 3 ind the volume of prisms including cylinders A ind the surface area of simple prisms alculate the lengths of arcs of circles alculate the areas of sectors of circles Solve problems involving surface areas and volumes of pyramids, cones and spheres Solve problems involving complex shapes and solids, including segments of circles and Handling frustum ata of cones 2: ollecting data esign and use tally charts for discrete and grouped data Understand and name different types of data esign and use data collection sheets, surveys and questionnaires esign and use two-way tables for discrete and grouped data Understand and name other types of data collection methods Identify possible sources of bias in the design and use of data collections sheets and questionnaires

6 Understand the data-handling cycle Topic/ontent/References A Understand that increasing sample size generally leads to better estimates Select and justify a sampling scheme and a method to investigate a population Use sampling methods including random and stratified sampling Algebra 5: oordinates, plotting and sketching graphs Use coordinates in the first quadrant Use coordinates in all four quadrants raw lines such as: x = 3 and y = x Produce a table of values for equations such as: y = 3x 5 or x + y = 7 and draw their graphs Solve problems such finding where the line y = 3x 5 crosses the line y = 4 ind the coordinates of the midpoint of a line segment raw graphs of quadratics such as: y = x 2 + 2x + 1 Use a graph to estimate x and y values, giving answers to an appropriate degree of accuracy raw graphs of harder quadratics such as: y = x 2 + 2x + 1 ind the gradients of straight line graphs Solve problems using equations such as: x2 + 3x + 2 = 5 by graphical methods Shape 5: Trigonometry Use sine, cosine and tangent to calculate a side in a right Use sine, cosine and tangent to calculate an angle in a right Use trigonometry to solve problems, including those involving bearings Use trigonometry to find sides and angles in three dimensions Use the sine and cosine rules to solve 2- problems alculate the area of a triangle using: absin Use the sine and cosine rules to solve 3- problems Number 4: Ratio and proportion Use ratio notation including reduction to its simplest form and its links to fraction notation Solve simple ratio and proportion problems, such as finding and simplifying a ratio e.g. the ivide a quantity in a given ratio Solve more complex ratio and proportion problems, such as sharing money in the ratio of people s ages Solve ratio and proportion problems using the unitary method Solve direct and indirect proportion problems Interpret graphs showing direct and indirect proportion problems Algebra 6: quations with fractions and simultaneous equations Set up and solve an equation involving fractions such as = 4 or 2x 3 = 8 Solve equations such as: Solve equations such as = = Solve a pair of linear equations graphically; identifying the point of intersection as the solution Solve a pair of simultaneous equations such as x + 3y = 9 and 3x 2y = 9 Solve a pair of simultaneous equations such as y = 4x + 5 and y = x² ind the point of intersection of a linear and a quadratic equation; recognising that the solution could be found from the points of intersection of the graphs

7 A Shape 6: Transformations and vectors raw a line of symmetry on a 2- shape raw the reflection of a shape in an mirror line raw all the lines of symmetry on a 2- shape Topic/ontent/References ive the order of rotational symmetry on a 2- shape Name, draw or complete 2- shapes from information about their symmetry State the scale factor of an enlargement Reflect shapes in the axes of a graph nlarge a shape by a positive scale factor ind the measurements of the dimensions of an enlarged shape Reflect shapes in lines parallel to the axes, such as x=2 and y=-1 Rotate shapes about the origin escribe fully, reflections in a line and rotations about the origin Translate a shape using a description such as 4 units right and 3 units down nlarge a shape by a positive scale factor from a given centre ompare the area of an enlarged shape with the original area Reflect shapes in lines such as y=x and y=-x Rotate shapes about any point escribe fully, reflections in any line parallel to the axes, y=x or y=-x and rotations about any point ind the centre of a rotation and describe it fully Translate a shape by a vector such as ind the ratio of corresponding lengths in similar shapes and identify this as the scale factor of enlargement Use ratios in similar shapes to find missing lengths Use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations nlarge a shape by a positive scale factor nlarge a shape by a negative scale factor ompare lengths, areas and volumes of enlarged shapes Use the effect of enlargement on perimeter, area and volume in calculations A Add, subtract and multiply vectors Use addition, subtraction and multiplication of vectors to solve simple geometric problems Understand the relationship between parallel vectors Solve more difficult problems using vectors Handling data 3: rawing graphs and charts onstruct and interpret a pictogram onstruct and interpret a bar chart onstruct and interpret a dual bar chart Interpret a pie chart onstruct a pie chart Interpret a stem-and-leaf diagram onstruct a histogram (frequency diagram) with equal class intervals onstruct and interpret an ordered stem-and leaf diagram onstruct and interpret line graphs Interpret a line graph raw a scatter graph by plotting points on a graph

8 Interpret the scatter graph onstruct a frequency polygon raw a line of best fit on the scatter graph Topic/ontent/References A Interpret the line of best fit Identify the type and strength of the correlation onstruct and interpret a cumulative frequency diagram for continuous or grouped data Use a cumulative frequency diagram to estimate median and inter-quartile range onstruct and interpret a box plot ompare two sets of data using a box plot referencing average and spread onstruct a histogram with unequal class intervals Interpret a histogram with unequal class intervals Handling data 4: Probability Understand and use the language of probability onstruct and interpret a bar chart Understand and use a probability scale xpress a probability as a fraction isplay outcomes systematically Understand the differences between experimental and theoretical probability Use a two way table to find a probability Understand mutually exclusive events Identify different mutually exclusive events and know, if they cover all the possibilities, then the sum of probabilities is 1 Use probability to estimate outcomes for a population Understand and use relative frequency raw tree diagrams A Understand independent and non-independent events ind probabilities of successive independent events ind probabilities of successive dependent events Shape 7: ircle properties Know the angle and tangent properties of a circle A Understand the angle and tangent properties of a circle Understand the alternate segment theorem Algebra 7: Real life graphs Plot points on conversion graphs Read values from conversion graphs Read a value from a conversion graph for a negative value Interpret horizontal lines on a distance-time graph arry out simple interpretation of graphs such as finding a distance from distance-time graphs arry out more advanced interpretation of graphs such as finding a simple average speed from onstruct distance linear functions from real-life situations and plot their corresponding graphs urther interpret real-life graphs, for example the average speed in km/h from a distancetime graph over time in minutes

9 iscuss and interpret graphs modelling real situations Topic/ontent/References Algebra 7: Real life graphs Plot points on conversion graphs Read values from conversion graphs Read a value from a conversion graph for a negative value Interpret horizontal lines on a distance-time graph arry out simple interpretation of graphs such as finding a distance from distance-time graphs arry out more advanced interpretation of graphs such as finding a simple average speed onstruct linear functions from real-life situations and plot their corresponding graphs urther interpret real-life graphs, for example the average speed in km/h from a distance- iscuss and interpret graphs modelling real situations Shape 8: onstructions and loci Select congruent shapes Measure a line accurately to the nearest millimetre Measure and draw lines accurately Use simple scale drawings Measure and draw an angle to the nearest degree Measure and draw angles accurately Understand congruence and similarity Use scales, such as scale on a map Use map scales to find a distance raw scale drawings raw a triangle given three sides (SSS), two sides and the included angles (SAS) or two raw a quadrilateral such as kite, parallelogram or rhombus with given measurements Understand that giving the lengths of two sides and a non-included angle may not produce a unique triangle Understand the idea of locus onstruct perpendicular bisectors and angle bisectors Recognise that measurements to the nearest unit may be inaccurate by up to one half unit onstruct the locus of points equidistant from two fixed points onstruct the locus of points equidistant from two fixed lines Solve loci problems, for example the locus of points less that 3cm from a point P Match one side and one angle of congruent triangles given some dimensions onstruct perpendicular line from a point to a line, perpendicular at a point on a line and an angle Match of sides 60⁰ and angles of similar triangles A Prove two triangles are congruent Prove construction theorems Algebra 8: Quadratic, cubic, circular and exponential functions raw graphs of quadratics such as: y = x 2, y = x 2 4 and y = 3x 2

10 raw graphs of quadratics such as: y = x 2 + 2x + 1 Use a graph to estimate x and y values, giving answers to an appropriate degree of accuracy raw graphs of harder quadratics such as: y = 2x 2-7x + 5 Topic/ontent/References actorise an expression such as x 2-5x + 14 or x 2 9 Solve an equation such as x 2-5x + 14 = 0 omplete tables for, and draw graphs of, cubic functions and use the graphs to solve equations A actorise an expression such as 3x 2 + 7x + 2 or 3x 2 27 Solve problems using equations that factorise such as 3x 2 + 7x + 2= 0 Solve problems using equations such as: 2x 2-6x + 1= 0 by using the quadratic formula Solve problems using equations such as: x 2 + 3x + 2= 0 by graphical methods omplete tables for, and draw graphs of, reciprocal functions and use the graphs to solve Sketch and draw circular graphs such as sin x and cos x Use the graphs to solve equations Solve problems using equations such as = Sketch and draw graphs of exponential functions and use them to solve equations Understand the graphs of circular functions for angles of any size Use symmetry of circular functions to solve equations Recognise the shapes of graphs of functions including cubic functions, reciprocal functions, Recognise functions when solving problems Algebra 9: Inequalities Represent and interpret inequalities on a number line Substitute numbers into formulae such as: Solve an equality such as 2x 7 <9 ind the integer solutions of an inequality such as: -8 < 2n 5 Solve an inequality such as: 3x x Represent linear inequalities in two variables, such as: x + y < 7, as a region on a graph Algebra 10: Transforming graphs Understand and apply function notation iven y = f(x) or a sketch of y = f(x), draw transformations of f(x) Understand that and y = f represent a one way stretch with a scale factor a Understand that y = f(x) + a and y = f(x a) represent translations of y = f(x) parallel to the y and x axes respectively of y = f(x)