## CURRICULUM

## Maths

## Maths Curriculum Intent

Mathematics teaches students to solve problems when they do not appear to have all the information required to do so. It teaches them how to think and work systematically, critically analyse information and effectively communicate the steps within their thinking. Our curriculum adopts a ‘no tricks’ approach to teaching, as we believe everybody can do mathematics.

## MATHS STRANDS

## Number

Number is interleaved throughout the five years. Number includes teaching students about numerical structure and calculation, fractions, decimals and percentages and measures and accuracy.

Algebra is interleaved throughout the five years. Algebra includes teaching student’s algebraic notation, vocabulary and manipulation, graphs, solving equations and inequalities and sequences.

## Algebra

## Ratio, Proportion, and rates of change

## Geometry and Measures

## Probability

## STATISTICS

## Maths SKILLS

## Develop fluency

In y7, 8 and 9 students are taught to:

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

• Select and use appropriate calculation strategies to solve increasingly complex problems

• Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

• Substitute values in expressions, rearrange and simplify expressions, and solve equations

• Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

• Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

• Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics

In y10 and y11 students are taught to:

• Consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}

• Select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy

• Consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}

• Extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities

• Move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal, {exponential and trigonometric} functions

• Use mathematical language and properties precisely.

In y7, 8 and 9 students are taught to:

• Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

• Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

• Identify variables and express relations between variables algebraically and graphically

• Make and test conjectures about patterns and relationships; look for proofs or counter-examples

• Begin to reason deductively in geometry, number and algebra, including using geometrical constructions

• Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

• Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

In y10 and y11 students are taught to:

• Extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically

• Extend their ability to identify variables and express relations between variables algebraically and graphically

• Make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}

• Reason deductively in geometry, number and algebra, including using geometrical constructions

• Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

• Explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally

Assess the validity of an argument and the accuracy of a given way of presenting information

## Reason Mathematically

## Solve Problems

In y7, 8 and 9 students are taught to:

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

• Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

• Begin to model situations mathematically and express the results using a range of formal mathematical representations

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

In y10 and y11 students are taught to:

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

• Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts

• Make and use connections between different parts of mathematics to solve problems

• Model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem

## Year 7

##### Calculations

• Use place value to multiply and divide by 10, 100, 1000 etc.

• Understand that division can also be written as a fraction.

• Multiply and divide integers and decimals mentally.

• Use formal written methods for short division.

• Divide any whole number by any other whole number accurately using long division.

• Multiply any whole number by any other whole number using column multiplication.

• Add and subtract using integers and decimals mentally.

• Use formal written methods for addition and subtraction.

• Understand place value from thousandths through to thousands.

• Use place value to multiply and divide by 0.1, 0.01, 0.001 etc.

• Multiply one decimal number by another using column multiplication.

• Divide decimal numbers by integers using long division.

• Understand and apply inverse operations to solve problems.

• Use estimates to check answers are reasonable.

• Know divisibility tests for the 2,4,5, 8 and 10 times tables.

Tier 1 students will also be taught to: • Know divisibility tests for the 3, 6 and 9 times tables.

• Use answers to one calculation to work out the answer for other related calculations (including division).

• Divide decimals by decimals using both long and short division.

• Understand that to divide by decimal numbers, equivalent fractions can be used to convert to an integer divisor.

• Multiply and divide integers by decimals (terminating) between 0 and 1 mentally e.g. 0.5, 0.25, 0.2.

##### Number Sense

• Convert fractions to decimals accurately without a calculator.

• Order negative numbers including decimals on a number line.

• Order simple fractions and decimals on a number line.

• Place simple fractions in the correct place on a number line.

• Identify equivalent fractions and cancel fractions to their simplest form.

• Order simple fractions and decimals.

• Order negative numbers on a number line.

• Understand and apply the concept of temperature and money less than zero.

• Count forwards/backwards around zero

• Order fractions by converting to decimals/percentages.

•Convert a fraction to a percentage using a calculator.

•Convert a fraction to a percentage by writing them with a denominator of 100 and where this isn't possible, converting them to a decimal number first.

• Covert a decimal number to a fraction.

•Convert a decimal number to a percentage.

• Multiply and divide using negative numbers.

• Add and subtract with negative numbers.

• Convert fractions to decimals accurately with a calculator.

• Order fractions by writing them with a common denominator (including negative fractions). Tier 1 students will also be taught to: • Represent a given inequality on a number line. • Create an inequality from information shown on a number line. • Convert fluently between fractions, decimals, and percentages with and without a calculator. • Convert fractions to recurring decimals with and without a calculator and understand recurring decimal notation. • Complete the four operations fluently with negative numbers in context.

##### Algebraic Notation

• Use the correct order of operations to interpret numeric calculations and algebraic expressions. (BIDMAS)

• Write an expression from a problem.

•Understand and simplify expressions through multiplication and division with more than one variable.

•Understand and simplify expressions through multiplication and division with one variable.

• Understand and simplify expressions (addition and subtraction) with more than one variable by collecting like terms.

• Understand and simplify expressions (addition and subtraction) with one variable by collecting like terms.

• Understand the difference between variables, expressions, and terms. • Use correct algebraic notation to represent unknown numbers or variables.

Tier 1 students will also be taught to:

• Multiply out linear expressions with brackets.

• Factorise any expression into a single bracket.

• Expand and simplify expressions containing more than one single bracket.

##### 2D Shape, Angles and Symmetry

• Identify the order of rotational symmetry and number of lines of reflectional symmetry within a given shape.

• Use knowledge of different types of quadrilateral to solve missing angle problems with all types of common quadrilateral.

• Use knowledge of different types of triangle to solve missing angle problems with all types of triangles.

• Be able to classify, and name angle facts, for all common quadrilaterals (square, rectangle, rhombus, parallelogram, kite, and trapezium).

• Be able to classify, and name angle facts, for all types of triangle.

• Tessellate a shape, combinations of shapes.

• Identify which shapes tessellate.

• Identify a shape from given properties, such as line of symmetry, order of rotational symmetry, parallel sides, number of sides, angle properties etc.

• Understand and use the terms parallel and perpendicular accurately.

• Solve composite angle problems involving both triangles and quadrilaterals.

Tier 1 students will also be taught to:

• Work out the angle sum within any regular or irregular polygon when given the number of sides.

• Work out the size of each individual interior and exterior angle within a regular polygon.

• Identify exterior and interior angles of polygons.

##### Fractions

• Add and subtract fractions with different denominators.

• Convert fluently between improper fractions and mixed numbers.

• Find a fraction of an amount.

• Convert between fractions, decimals, and percentages with and without a calculator.

• Write one quantity as a fraction of another including when the fraction is greater and less than 1.

• Know standard fraction / decimal/ percentage equivalences (e.g. ½ = 0.5 = 50%, ¼ = 0.25 = 25%, 1/10 = 0.1 = 10%, 1/100 = 0.01 = 1%).

• Order fractions on a number line.

• Add and subtract fractions with the same denominator. • Write a fraction in its lowest terms.

• Identify equivalent fractions.

• Multiply and divide with mixed numbers

• Add and subtract with mixed numbers.

• Multiply and divide a fraction by a fraction.

• Multiply and divide an integer by a fraction.

• Multiply and divide a fraction by an integer.

• Use calculator and non-calculator methods to find a fraction of an amount. Tier 1 students will also be taught to: • Multiply fractions such as 1/2 x 1/3 relating them to 'a half of a third'. • Understand mental arithmetic methods for multiplying and dividing by terminating decimal values between -1 and 1, linking this to fractions.

##### Time

• Solve basic functional time problems.

• Understand a leap year and know when they occur.

• Know how many days are in each month.

• Know how to convert from hours to minutes; minutes to seconds; years to months; weeks to days.

• Know how many days in a year, weeks in a year, days in a week, hours in a day, minutes in an hour and seconds in a minute there are.

• Convert fluently between the 12- and 24-hour clock.

• Tell the time on a digital clock.

• Tell the time on an analogue clock.

• Understand the concept of different time zones and use these to convert between instantaneous times in different countries around the world.

• Understand how to write time in different forms e.g. 1 hour 45 minutes as 1 and 3/4 of an hour or 1.75 hours.

• Solve problems that involve conversions between adjacent units of time i.e. seconds to minutes or minutes to hours.

• Solve problems using timetables.

Tier 1 students will also be taught to:

• Solve problems that involve conversions between non-adjacent units of time i.e. seconds to weeks or minutes to months. Include examples that have to take into account different numbers of days in each month and leap years.

• Solve complex planning problems that draw on other aspects of maths. e.g. planning a journey to another country to attend a meeting. Timings. costs, travel plans etc. all included.

##### Formulae

• Simplify expressions with more than one variable.

• Simplify expressions containing one variable.

• Write an expression from a problem.

• Use correct algebraic notation to represent unknown numbers or variables.

• Use the correct order of operations to interpret (BIDMAS)

•Interpret the information from substituting into a formula.

•Set up and substitute into a formula from given information.

• Set up a formula from given information.

• Substitute into a formula with negative integer values with and without a calculator.

• Substitute into a formula with fractional values with and without a calculator.

• Substitute into a formula with decimals with and without a calculator.

• Understand the difference between a variable, term, expression, and formula.

Tier 1 students will also be taught to:

•Multiply out single brackets.

• Rearrange a two-step formula.

• Rearrange a one-step formula.

• Substitute into a formula with negative non-integer values without a calculator.

##### Rounding and Estimating

• Understand and use estimation to check the validity of answers.

• Round numbers to up to 2 decimal places.

• Approximate any number by rounding to the nearest 10, 100 or 1000, 10 000, 100 000 or 1 000 000.

• Approximate any number with one or two decimal places by rounding to the nearest whole number.

• Solve real life problems using estimations and rounding (everything rounded to 1 significant figure).

• Round any decimal number to a given number of significant figures (including numbers between -1 and 1).

• Round any whole number to a given number of significant figures.

• Round any number to any given number of decimal places.

Tier 1 students will also be taught to:

• Express error intervals using inequalities.

• Understand the difference in the way the upper bound is expressed for discrete and continuous data.

• Identify upper and lower bounds.

##### Measure

• Convert one metric unit to another.

• Use a protractor to measure and draw angles, including reflex angles, to the nearest degree.

• Choose which units and instruments to use for everyday measurements.

• Be able to read and interpret scales on a range of measuring instruments.

• Measure lengths accurately using a ruler.

• Draw and interpret scale drawings.

• Convert numbers using a given scale or scale factor.

•Know how to read a map scale and create scales.

• Convert between metric and imperial measures when given the conversion.

Tier 1 students will also be taught to:

• Construct a triangle given three sides, two angles and a side or two sides and the included angle.

• Convert between non-adjacent metric units, e.g. kilometres and centimetres

##### Equations (Tier 1 only)

• Substitute answers back into equations to check solutions.

• Set up and solve a one-step equation

• Solve a one-step linear equation

• Understand the meaning of the equals sign and its role in mathematics.

• Understand the meaning of and difference between a variable, coefficient, term, expression, formulae, and equation.

• Set up and solve multi-step equations in a given context.

• Solve a 2-step equation involving expanding a bracket.

• Simplify and solve an equation.

• Solve any linear 2-step equation.

##### Algebraic Notation 2 (Tier 2 and 3)

• Factorise any expression into a single bracket.

• Expand and simplify expressions containing more than one single bracket.

• Multiply out linear expressions with brackets.

##### Percentages

• Find 5, 10, 25 and 50 percent of a quantity without a calculator.

• Convert between fractions, decimals, and percentages with and without a calculator.

• Know standard fraction / decimal/ percentage equivalences (e.g. ½ = 0.5 = 50%, ¼ = 0.25 = 25%, 1/10 = 0.1 = 10%, 1/100 = 0.01 = 1%).

• Order percentages on a number line.

• Solve real-life problems using percentages.

• Increase or decrease a quantity by a percentage using a calculator using the multiplier method.

• Find any percentage of a given quantity using a calculator using the multiplier method.

• Increase or decrease a quantity by a percentage without a calculator.

• Find any percentage of a given quantity without a calculator.

Tier 1 students will also be taught to:

• Express a change in quantity as a percentage change.

• Express one quantity as a percentage of another.

##### Coordinates

• Plot and read positive coordinates.

• Know the meaning of horizontal and vertical.

• Know how to write a coordinate.

• Be comfortable placing positive and negative numbers on a number line (written vertically and horizontally)

• Use coordinates with the properties of shapes to solve problems for missing vertices of shapes on a set of axes.

• Know the term origin and its location on a set of axes as well as the coordinate it corresponds to.

• Understand the x-axis and y-axis on a coordinate grid and know which value in a coordinate corresponds to each axis.

• Plot and read coordinates in all four quadrants.

Tier 1 students will also be taught to:

• Solve coordinate problems that use coordinates in 3 dimensions.

• Know and understand what a plane is.

• Plot and write coordinates in 3 dimensions.

• Understand that there is a third dimension, and this is represented by a z coordinate.

• Find the midpoint of a pair of coordinates.

• Draw lines parallel to the axis and understand how to write their equations.

##### Area and Perimeter

• Find a missing length when given the area or perimeter and other lengths in a square, rectangle, or parallelogram.

• Calculate the area of simple rectilinear compound shapes.

• Recognise that shapes with the same areas can have different perimeters and vice versa.

• Calculate the area of rectangles, triangles, parallelograms.

• Know that the area of a rectangle is given by the formula area = length × width

• Work out the perimeter of any shape (when given the measurements).

• Solve problems linking to other contexts such as cost of a gardening project that draw on using area and perimeter.

• Find a missing length when given the area or perimeter and other lengths including with triangles.

• Write an algebraic expression for the area/perimeter of a shape.

• Convert to consistent units of measurement within the metric system where necessary to solve area and perimeter problems.

•Know that when solving area and perimeter problems, the units of measurement must be consistent.

Tier 1 students will also be taught to:

• Find a missing length when given the area or perimeter and other lengths including with trapezia.

• Set up and solve equations linked to the area and perimeter of shapes.

• Find the area of a trapezium and learn the formula.

##### Data and Frequency Tables

• Sort and classify data into sets.

• Design and use two-way tables (Carroll diagrams) for ungrouped data.

• Design and use two-way tables (Carroll diagrams) for grouped & ungrouped data.

• Complete a table from given information.

• Complete a tally chart for qualitative data.

• Group data in equal class intervals.

• Use Venn diagrams to represent sorted data.

Tier 1 students will also be taught to:

• Use inequalities for grouped data.

##### 3D Shape

• Recognise and name 3D objects.

• Recognise vertices, edges, and faces.

• Construct isometric drawings of 3D objects.

• Draw the net of a 3D object.

• Draw plans and elevations for 3D objects.

Tier 1 students will also be taught to:

• Find the surface area of a cuboid and a right-angled triangular prism.

##### Financial Awareness

• To calculate the annual cost of subscriptions and services

• To know and understand what constitutes the cost of living

• To be able to plan make financial decisions that take possible future events into account

• To be able to plan within a monthly budget

## Year 8

##### Types of Number

• Recognise prime numbers and know tests for primes.

• Make mental estimates of the answers to calculations; use checking procedures to monitor the accuracy of their results.

• Round to any number of significant figures.

• Find factors and multiples of any number.

• Multiply and divide numbers by 01, 0.01, 0.001, 10, 100 and a 1000.

• Round a number to any number of decimal places.

• Know up to the 12 x 12 times tables and associated division facts.

• Understand and use BIDMAS

• Be able to use written methods for the four operations• Know the index laws for multiplication and division of powers with the same base (numbers only no algebra).

• Use product notation to write numbers as products of their prime factors.

• Use the concepts and vocabulary of highest common factor (HCF) and lowest common multiple (LCM).

• Round numbers and measures to an appropriate degree of accuracy and understand this statement.

• Know tests of divisibility for 1-10 (Not for 7)

• Estimate Square Roots

• Calculate cubes and cube roots with and without a calculator.

• Calculate square and square roots with and without a calculator.

Tier 1 students will also be taught to:

• Know the index laws for raising a power to a power (numbers only no algebra).

• Use Venn diagrams and prime factorisation to find HCF and LCM.

##### Algebraic Expressions

• Multiply out linear expressions with brackets.

• Understand the difference between expressions, equations, formula, and term.

• Simplify expressions involving multiplication and division using more than one variable.

• Understand and simplify expressions with more than one variable using addition and subtraction.

• Simplify expressions with one variable using addition, subtraction, and multiplication.

• Write an expression from a problem.

• Use correct algebraic notation to represent unknown numbers or variables.

• Factorise into one bracket.

• Expand and simplify expressions containing more than one single bracket.

• Simplify algebraic expressions by cancelling down.

• Use and apply the index laws for multiplication and division to algebra problems.

Tier 1 students will also be taught to:

• Set up and simplify from problems involved multiplying multiple terms by other terms (thus requiring the use of expanding double brackets).

• Multiply out double brackets (quadratic expressions) - include brackets containing three terms.

• Use and apply the index laws for raising a power to a power to algebra problems.

##### Proportion

• Be able to find a multiplier to use in a proportion problem.

• Find the value of a single item in a comparison problem

• Be able to recognise when two values are in proportion.

• Be able to use fractions in situations involving proportion.

• Identify when a comparison problem requires both division and multiplication

• Identify when a comparison problem can be solved using multiplication

• Identify when a comparison problem can be solved using division

• Use exchange rates to convert between currencies with a calculator.

• Identify value for money by matching prices or quantities.

• Solve proportion problems using the unitary method.

• Identify when proportional reasoning needs to be used in a real-life problem/exam question

Tier 1 students will also be taught to:

• Be able to solve simple inverse proportion problems.

• Use comparisons to be able to identify best buys for multi-step problems. Including those where different combinations of deals can be used.

##### Angles, Polygons and Parallel Lines

• Know the meaning of ‘regular’ polygon.

• Solve composite angle problems involving both triangles and quadrilaterals.

• Understand and use the terms parallel and perpendicular accurately.

• Tessellate a shape, combinations of shapes.

• Use knowledge of different types of quadrilateral to solve missing angle problems with all types of common quadrilateral.

• Use knowledge of different types of triangle to solve missing angle problems with all types of triangles.

• Be able to classify, and name angle facts, for all common quadrilaterals (square, rectangle, rhombus, parallelogram, kite and trapezium).

• Be able to classify, and name angle facts, for all types of triangle.

• Calculate missing angles around a point and on a straight line.

• Identify shapes that will tessellate and explain why.

• Recognise acute, obtuse, right, and reflex angles.

• Use a protractor to measure and draw angles to the nearest degree.

• Form and solve equations to find angles 2D shapes.

• Understand and use angle notation.

• Work out the angle sum within any regular or irregular polygon when given the number of sides.

• Work out the size of each individual interior and exterior angle within a regular polygon.

•Identify exterior and interior angles of polygons.

• Identify vertically opposite angles. Tier 1 students will also be taught to: • Use geometric arguments in simple proofs. • Calculate missing angles in parallel lines problems and explain reasoning • Identify alternate, corresponding, and interior angles in parallel lines.

##### Equations

• Substitute answers back into equations to check solutions.

• Solve 1-step equations (the coefficient and the answer may be positive or negative and fractional).

• Write an equation from a problem.

• Understand the meaning of the equals sign and its role in mathematics.

• Understand the meaning of and difference between a variable, coefficient, term, expression, formulae and equation.

• Multiply out linear expressions with brackets

• Write an expression from a problem. (express missing number problems algebraically)

• Use the correct order of operations to interpret numeric calculations and algebraic expressions. (BIDMAS)

• Solve fractional 3-step equations where the unknown once (one fraction only).

•Form and solve equations from a problem

• Solve linear equations with brackets.

• Solve 2-step equations Tier 1 students will also be taught to: • Use the basic principles of substitution to set up and solve equations with unknowns on both sides. E.g. two sides of a square labelled and 3x + 5 and 6x -2. Find x • Solve equations with the unknowns on both sides such as 3x-4 = 5 + x

##### Averages and Range

• Calculate median, mode and range from a bar chart.

• Understand the difference between averages and range.

• Calculate the mean, median, mode and range for a set of simple numbers.

• Solve missing number problems when given certain averages or the range.

• Know which average to choose and why.

• Compare two groups’ averages in context.

• Compare two groups’ ranges in context.

Tier 1 students will also be taught to:

• Find a mean of part of a group when given the mean of the whole group and other necessary information.

• Understand how changing the data will change the averages/range.

• Calculate the mean, median, mode and range from a frequency table.

##### Transformations

• Know the meaning of ‘congruent’, ‘congruence’, ‘object’, ‘image’.

• Rotate a shape by a given amount of turn.

• Reflect shapes in a mirror line (including diagonals).

• Reflect a shape using a mirror line parallel to the axes.

• Design a shape with given symmetrical properties.

• Give the order of rotational symmetry of a 2D shape.

• Recognise reflection symmetry of 2D shapes and draw lines of symmetry on.

• Describe a rotation fully.

• Finding the centre of rotation.

• Describe a translation using vector notation.

• Understand that reflections, translations and rotations produce congruent images.

• Rotate shapes around a given centre.

• Translate a shape when given a vector.

• Understand vector notation.

• Reflect a shape when given the equation of the line of reflection (lines parallel to the axis only)

• Draw lines parallel to the axis from the equation (x = n and y = n)

Tier 1 students will also be taught to:

• Combine reflections, rotations, and translations.

• Describe the equation of the line of reflection. (y= n, x = n, y = x and y = -x).

• Reflect shapes in the in lines such as x = 2, y = 4, y=x and y=-x.

• Understand and plot the line y = x and y = -x

##### Fractions, Percentages and Decimals review

• Multiply and divide with mixed numbers

• Add and subtract with mixed numbers.

• Multiply and divide a fraction by a fraction.

• Multiply and divide an integer by a fraction.

• Multiply and divide a fraction by an integer.

• Use calculator and non-calculator methods to find a fraction of an amount.

• Find 5, 10, 25 and 50 percent of a quantity without a calculator.

• Convert between fractions, decimals, and percentages with and without a calculator.

• Know standard fraction / decimal/ percentage equivalences (e.g. ½ = 0.5 = 50%, ¼ = 0.25 = 25%, 1/10 = 0.1 = 10%, 1/100 = 0.01 = 1%).

• Order percentages on a number line.

• Add and subtract fractions with different denominators.

• Convert fluently between improper fractions and mixed numbers.

• Find a fraction of an amount.

• Convert between fractions, decimals, and percentages with and without a calculator.

• Write one quantity as a fraction of another including when the fraction is greater and less than 1.

• Order fractions on a number line.

• Add and subtract fractions with the same denominator.

• Write a fraction in its lowest terms.

• Identify equivalent fractions.

• Express a change in quantity as a percentage change.

• Express one quantity as a percentage of another.

• Multiply fractions such as 1/2 x 1/3 relating them to 'a half of a third'.

• Understand mental arithmetic methods for multiplying and dividing by terminating decimal values between -1 and 1, linking this to fractions.

•Solve real-life problems using percentages.

• Increase or decrease a quantity by a percentage using a calculator using the multiplier method.

•Find any percentage of a given quantity using a calculator using the multiplier method.

• Increase or decrease a quantity by a percentage without a calculator.

• Find any percentage of a given quantity without a calculator.

##### Formulae

•Interpret the information from substituting into a formula.

•Set up and substitute into a formula from given information.

• Set up a formula from given information.

• Substitute into a formula with negative integer values with and without a calculator.

• Substitute into a formula with fractional values with and without a calculator.

• Substitute into a formula with decimals with and without a calculator.

• Understand the meaning of the equals sign and its role in mathematics.

• Understand the difference between a variable, term, expression, equation and formula.

• Expand single brackets.

• Simplify expressions with more than one variable.

• Simplify expressions containing one variable.

• Write an expression from a problem.

• Use correct algebraic notation to represent unknown numbers or variables.

• Use the correct order of operations to interpret (BIDMAS)

• Rearrange a two-step formula.

• Rearrange a one-step formula.

• Substitute into a formula with negative non-integer values without a calculator.

Tier 1 students will also be taught to:

• Rearrange a formula with unknowns on both sides. (not situations where factorising is required to isolate the unknown).

• Rearrange a formula with more than two steps required.

• Substitute into common scientific formulae. - speed, density and pressure with the values and formulae given

##### Area and Perimeter

• Solve problems linking to other contexts such as cost of a gardening project that draw on using area and perimeter.

• Find a missing length when given the area or perimeter and other lengths including with triangles. • Write an algebraic expression for the area/perimeter of a shape.

• Convert to consistent units of measurement within the metric system where necessary to solve area and perimeter problems.

•Know that when solving area and perimeter problems, the units of measurement must be consistent.

• Find a missing length when given the area or perimeter and other lengths in a square, rectangle or parallelogram.

• Calculate the area of simple rectilinear compound shapes.

• Recognise that shapes with the same areas can have different perimeters and vice versa.

• Calculate the area of rectangles, triangles, parallelograms.

• Know that the area of a rectangle is given by the formula area = length × width

• Work out the perimeter of any shape (when given the measurements).

• Find a missing length when given the area or perimeter and other lengths including with trapezia.

• Set up and solve equations linked to the area and perimeter of shapes.

• Find the area of a trapezium and learn the formula.

Tier 1 students will also be taught to:

• Find the area and perimeter of semi circles and quarter circles.

• Leave answers for circle problems in terms of pi.

• Find the circumference of a circle.

• Find the area of a circle.

• Know the formulae for finding the area and circumference of circles

• Know and label the parts of a circle (only area, circumference, diameter and radius at this point)

##### Probability

• Express a probability as a fraction, decimal or percentage.

• Understand probability must be between 0 and 1 and can be expressed as a fraction, decimal or percentage.

• Identify equally likely outcomes.

• Understand the vocabulary of chance including impossible, unlikely, evens, likely, certain.

• List all the possible outcomes for an experiment (e.g. rolling a dice).

• Understand the equivalence between fractions, decimals, and percentages.

• Understand that if the probability of an event occurring is p then the probability of it not occurring is 1 – p.

• Identify different mutually exclusive outcomes and know that the sum of these probabilities is 1.

• Know that probability is a way of measuring likeliness and that experimental probability will not always match theoretical probability.

• List all the outcomes for two successive events in a systematic way and derive probabilities from this.

• Understand the probability scale and place events on it.

• Work out the theoretical probabilities for events with equally likely outcomes.

Tier 1 students will also be taught to:

• Understand that increasing the sample size generally leads to better estimates of probability.

• Use a two-way table (sample space diagram) to find a probability.

• Use a single probability to find an estimate of frequency.

• Know how to work out the number of possible combinations for combined events.

##### Volume and Surface Area

• Construct isometric drawings of 3D objects.

• Visualise and describe the properties of 3D shapes (number of edges, vertices, and faces).

• Recognise and name 3D objects.

• Recognise vertices, edges, and faces.

• Find the area of squares, rectangles, triangles, and parallelograms.

• Recognise and sketch nets of 3D shapes.

• Draw plans and elevations for 3D objects

• Find a missing length in a volume question

• Use area to find the volume of a prism and vice versa

• Find the volume of rectangular, square, trapezia, triangular and parallelogram-based prisms

• Find the surface area of a cuboid and a right-angled triangular prism.

• Find the volume by counting cubes and stating units.

(Know the units for volume and the abbreviations cm3 and m3)

• Use the area of shapes to find other dimensions

Tier 1 students will also be taught to:

• Find the surface area of a cylinder

• Find the volume of a cylinder

• Solve algebraic problems including Volume/Surface Area (linear algebraic equations)

• Know the formulae for circumference and area of a circle.

• Recognise the symbol π and understand the number it represents to at least 2.d.p.

##### Sequences

• Continue a non-numerical sequence.

• Recognise and continue non-linear sequences.

• Continue a sequence of numbers (including decimals, fractions, and negatives).

• Calculate cubes and cube roots with and without a calculator.

• Recognise the squares of numbers to 12x12 and the corresponding roots.

• Know and understand the language even, odd, prime, factor, multiple.

• Begin to write expressions for position-to-term rule (nth term).

• Be given the position-to-term rule and write the terms of the sequence.

Tier 1 students will also be taught to:

• Prove or disprove that a term is in a sequence by solving.

• Be given the position-to-term rule for non-linear sequences and write the terms of the sequence.

##### Kinematics

• Convert between metric and imperial measures when given the conversion.

• Convert fluently between metric units of length.

• Convert fluently between metric units of mass.

• Convert fluently between metric units of volume/capacity.

• Know the conversions for units of metric measurement.

• Solve worded number problems with or without a calculator and with numbers of any type (money, time etc).

• Fluently recall time conversions.

•Know the connection between speed, distance and time and use the speed = distance / time formula in simple 1-stage problems.

• Read/Solve problems using a conversion graph.

•Convert between non-adjacent metric units, e.g. kilometres and centimetres.

• Convert to consistent units of measurement within the metric system where necessary to solve a problem.

•Identify when it is necessary to convert quantities in order to use a sensible unit of measure.

Tier 1 students will also be taught to:

• Find the average speed over a distance time graph.

•Know the connection between speed, distance and time and use the speed = distance / time formula for multi-stage problems.

• Describe a journey from a given distance/displacement time graph.

• Draw a distance/displacement time graph.

• Understand the difference between distance and displacement.

##### Constructions and Congruence

• Construct both angle, line and point to line bisections.

• Apply bisections to problems.

• Construct a locus of a given area.

• Construct congruent triangles using ASA, SAS, SSS & RHS.

• Prove two triangles are congruent using the rules ASA, SAS, SSS or RHS.

• Know the difference between congruent and similar shapes.

• Know what similar and congruent mean.

Tier 1 students will also be taught to:

Apply congruence, similarity, and triangle constructions to solve problems.

• Construct a locus of a points from a fixed point, line or shape.

• Apply bisections and loci to solve problems.

##### Financial Awareness

• Be able to understand bank statements, what a balance, credit and debit is.

• Understand wages and how much of their salary they see after tax and National Insurance.

• Understand pensions and other deductible amounts from their wage.

• Distinguish between the public and private sector, and understand the profit and loss of a business.

## Year 9

##### Foundation

##### Higher

##### Types of Number (Decimals and Indices)

• Know how to find LCM and HCF using Venn Diagrams.

• Know what HCF and LCM are and how to use them to solve problems.

• Know the definitions of multiples, factors, and prime numbers.

• Know the cube numbers from 1 - 6 and square numbers from 1 - 15.

• Know that square numbers can have both a positive and a negative root.

• Be able to multiply and divide by powers of 10 (inc. 10, 100, 1000, 0.1, 0.01, 0.001)

• Understand decimal place value.

• Be able to convert large and small numbers to standard form and vice versa.

• Calculate with numbers in index form i.e. 43 + 52

• Be able to use a calculator.

• Round a number to the nearest whole number.

• Round a number to a given decimal place.

• Round a number to a given number of significant places.

• Use approximations to 1 significant figure to estimate answers.

##### Algebraic Expressions

• Be able to simplify an expression involving sums, products, and powers

• Expand a single and double bracket.

• Expand a bracket and simplify.

• Factorise a linear expression.

• Substitute values into expressions and equations

• Rearrange equations to change the subject of a formula

• Form an expression

• Form an equation to solve a problem.

• Recognise and calculate with algebra using index notation.

• Know the index laws for multiplication and division of powers with the same base.

##### Proportion

• Understand direct proportion

• Solve problems involving direct and inverse proportion, understand a graphical representation of something in direct proportion.

• Use and convert standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate.

• Use a multiplier when solving problems involving direct proportion or proportional increase/decrease.

• Use comparisons to be able to identify best buys for multi-step problems. Including those where different combinations of deals can be used.

##### Averages

• Find the mean, median and mode from a list of data.

• Know when to use each average and why.

• Find the mode and median from frequency data.

• Find the mean from a frequency table.

• Find the mean, mode, median and range from a bar chart.

• Find the interval that contains the model group from grouped data.

• Find the interval that contains the median from grouped data.

• Find the estimated mean from grouped frequency data.

##### Ratio

• Understand what a ratio means and its link to fraction notation.

• Understand what a ratio means and its link to proportion

• Simplify ratios and understand equivalence between ratios.

• Write a ratio from a worded problem.

• Simplify a 2 or 3 part ratio

• Write a ratio in the form 1: n and n: 1

• Divide a quantity into a 2 or 3 part ratio

• Use ratio notation to work out the whole amount shared (Part to whole).

• Use ratio to find a quantity when other quantities are known (part to part).

##### Area and Perimeter

• Use standard formulae to solve problems involving areas of parallelograms, triangles, trapezia, and compound shapes.

• Know and recognise the parts of circle.

• Know and apply the formulae for area of a circle.

• Know and apply the formulae for circumference of a circle.

• Work backwards in a circle problem to find the radius or the diameter.

• Solve a circle problem, leaving answers in terms of pi.

##### Frequency Diagrams

• Draw and interpret two-way tables

• Complete and interpret frequency trees

• Draw dual and composite bar charts

• Draw and interpret line graphs.

• Draw and interpret Venn Diagrams.

• Compare and contrast the same type of and different types of frequency diagram

• Interpret specific information from a frequency diagram including mode, total frequency, highest and lowest value etc.

##### Fractions

• Know and find equivalent fractions.

• Simplify a fraction.

• Convert between mixed numbers and improper fractions.

• Multiply fractions.

• Divide fractions.

• Find a fraction of an amount.

• Add and subtract proper, improper fractions and mixed numbers.

• Use a scientific calculator to calculate with fractions, both positive and negative.

##### Solving Equations

• Know the difference between an expression, an identity, and an equation.

• Write an expression and an equation.

• Expand two brackets and simplify. eg 2(x+4) - 3(x+2).

• Solve one and two step linear equations using 1 variable.

##### Percentages

• Understand fractions or percentages as operators.

• Calculate a fraction or percentage of an amount.

• Write one amount as a fraction or percentage of another.

• Calculate a percentage change.

• Calculate a percentage increase or decrease.

• Convert between fractions, decimals and percentages and understand their equivalence.

##### Inequalities

• Know and understand the inequality symbols < ≤ > ≥ = ≡.:

• Find integer solutions to an inequality.:

• Solve a linear inequality.:

• Represent inequalities on a number line.

##### Pie Charts and Scatter Diagrams

• Understand that pie charts are used to show proportions.

• Use a template to construct a pie chart by scaling frequencies.

• Construct pie charts when the total frequency is not a factor of 360.

• Interpret data shown on in a pie chart.

• Plot a scatter diagram.

• Understand the meaning of ‘correlation’.

• Identify positive, negative and no correlation.

• Interpret a scatter diagram using understanding of correlation.

• Understand that correlation does not indicate causation.

• Construct a line of best fit on a scatter diagram.

• Use a line of best fit to estimate values.

• Know when it is appropriate to use a line of best fit to estimate values.

• Choose appropriate graphs or charts to represent data.

##### Linear Graphs

• Work with co-ordinates in all four quadrants.

• Draw the lines, y=x, y=-x, y=n and x=n and understand which lines are parallel to the axes.

• Draw a line in the format y=mx + c.

• Find the gradient of a straight line from the equation and graph.

• Deduce the equation of a straight line and write it in the form y=mx+c.

• Use the linear equation to identify parallel lines.

##### Scale Drawing, Nets and Plans and Elevations

• Understand what a scale factor is.

• Use scale factors to solve problems.

• Convert between miles and kilometres when given the conversion.

• Draw & interpret plans and elevations.

• Draw and identify nets of shapes.

##### Volume

• Identify 3D shapes from both picture and description.

• Find the Volume of a prism by counting squares and by calculation.

• Find the Volume of a cylinder.

• Solve problems involving Volume.

##### Probability

•Write probabilities in words, fractions, decimals and percentages and place these on a scale from 0 to 1.

• Compare the probabilities of events by comparing sizes of fractions, decimals, and percentages.

•Systematically list all outcomes for single and combined events.

•Use and draw sample space diagrams.

• Use theoretical models to include outcomes using dice, spinners, and coins.

##### Financial Awareness

• Understand the importance of their Credit Rating and how this affects their financial options.

• Understand that borrowing money costs interest and be able to calculate monthly interest charges.

• Understand that Buy Now Pay Later schemes and Store Cards are forms of credit which can lead to debt.

• Understand how Payday Loans work.

• Calculate interest charges on Payday Loans.

• Understand the dangers of falling into debt associated with gambling.

• Understand that probabilities when gambling are never favourable.

##### Types of Number

• Know the definitions of multiples, factors and primes. Know the cube numbers from 1 - 6 and square numbers from 1 - 15.

• Know that square numbers can have both a positive and a negative root.

• Breakdown any number into its prime factors.

• Know that every positive integer can be written as a product of its prime factors.

• Know how to find LCM and HCF using Venn Diagrams.

• Know what HCF and LCM are and how to use them to solve problems.

• Convert large and small numbers into standard form and vice versa.

• Use a calculator to work with standard form.

• Know the index laws for multiplication, division, raising a power to another power and that anything to the power of zero is always one.

##### Algebraic Expressions

• Expand a bracket.

• Factorise a linear expression.

• Expand and simplify double brackets.

• Factorise a quadratic expression when a=1.

• Simplify an algebraic fraction.

##### Proportion

•Understand direct proportion

•Solve problems involving direct and inverse proportion, understand a graphical representation of something in direct proportion.

•Use and convert standard units of mass, length, time, money, and other measures (including standard compound measures) using decimal quantities where appropriate.

• Use a multiplier when solving problems involving direct proportion or proportional increase/decrease.

• Solve more complex proportion problems where there are partial limits/more than 2 factors to consider

• Use comparisons to be able to identify best buys for multi-step problems. Including those where different combinations of deals can be used.

##### Averages

• Find the mean, median and mode from a list of data.

• Know when to use each average and why.

• Use the mean to find a missing number in a set of data

• Understand the range as a measure of spread (or consistency)

• Estimate the range from a grouped and ungrouped frequency table

• Find the mode and median from a frequency table.

• Find the mean from a frequency table.

• Find the interval that contains the model group median from grouped data.

• Find the estimated mean from grouped frequency data.

• Find the estimated mean from a graph.

##### Ratio

• Understand what a ratio means and its link to fraction notation.

• Understand what a ratio means and its link to proportion

• Simplify ratios and understand equivalence between ratios.

• Write a ratio from a worded problem.

• Simplify a 2 or 3 part ratio.

• Write a ratio in the form 1: n and n: 1

• Divide a quantity into a 2 or 3 part ratio

• Use ratio notation to work out the whole amount shared (Part to whole).

• Use ratio to find a quantity when other quantities are known (part to part).

##### Area and Perimeter

• Use standard formulae to solve problems involving areas of parallelograms, triangles, trapezia and compound shapes.

• Calculate area and circumference of circles.

• Find the length of an arc and the area of a sector.

• Work backwards from area, perimeter problems to find missing lengths (including arcs, sectors and circles).

##### Frequency Diagrams

• Draw and interpret two-way tables.

• Complete and interpret frequency trees.

• Draw and interpret a composite bar chart.

• Draw and interpret dual bar charts.

• Draw and interpret time series graphs.

• Draw and interpret Venn Diagrams.

• Draw frequency polygons.

• Interpret frequency polygons.

##### Equations and Inequalities

• Know the symbols < ≤ > ≥ = ≡.

• Know the difference between an expression, an identity, and an equation.

• Write an expression and an equation.

• Expand two brackets and simplify. e.g. 2(x+4) - 3(x+2).

• Solve two step linear equations using 1 variable.

• Solve an equation with unknowns on both sides.

• Solve an inequality.

• Represent inequalities on a number line.

• Apply solving linear equations to other aspects of maths.

##### Decimals

• Multiply by a number between 0 and 1 without a calculator.

• Round to a given number of decimal places.

• Round to a given number of significant figures.

• Estimate answers to calculations.

• Solve problems which require answers to be rounded to specified degrees of accuracy.

• Convert between recurring decimals and fractions.

##### Bearings and Scale Drawings

• Draw and read bearings.

• Know the difference between an angle and a bearing.

• Calculate bearings from problems using parallel lines angle facts.

• Understand what a scale factor is.

• Use scale factors to solve problems.

• Convert between miles and kilometres when given the conversion.

• Draw & interpret plans and elevations.

##### Inequalities

• Know and understand the inequality symbols < ≤ > ≥ = ≡.:

• Find integer solutions to an inequality.:

• Solve a linear inequality.:

• Represent inequalities on a number line.

##### Linear Graphs

• Know and use the equations of lines parallel to the axes.

• Generate and plot coordinates for any linear function.

• Solve an equation in the form y=mx+c graphically or otherwise.

• Recognise that y=mx+c corresponds to a linear graph and know how the parts of this equation determine the line.

• Calculate the gradient of a straight-line segment using dy/dx.

• Be able to find the equation of any straight line.

• Understand the gradients of parallel lines and use this knowledge to solve problems.

• Understand how to work out the gradient of perpendicular lines and use this to work out the equations of perpendicular lines.

##### Types of Data, Sampling and Bias

•Be able to describe and identify different types of data: qualitative, quantitative, discrete, continuous, primary and secondary.

•Use the data handling cycle to plan an investigation to test a hypothesis.

•Know how to use different sampling methods including stratified sampling.

##### Compound and Reverse Percentages

• Convert between fractions, decimals and percentages.

• Write one amount as a fraction or percentage of another amount.

• Calculate percentages increase or decrease.

• Solve problems involving percentage change • Calculate reverse percentage problems.

• Solve problems involving repeated percentage change, including compound interest.

##### Solving Simultaneous Equations

• Understand and use the order of operations to form equations and expressions.

• Understand and use the concept of inverse operations in order to solve equations.

• Solve any linear equation including those with brackets or where the unknown appears as a denominator.

• Solve linear equations where the unknown appears twice.

• Use elimination to solve a pair of simultaneous equations, including those where one or both equations need to be multiplied.

• Form a pair of simultaneous equations from a worded question, or from a geometric diagram.

• Plot a pair of simultaneous equations on a set of axes and know that the point of intersection is the solution for that pair of equations.

##### Pythagoras

• Identify and label different parts of a triangle including the hypotenuse and use conventional notation for this.

• Recall and use the formula a2+ b2=c2 to find any of the side lengths of a right-angled triangle.

• Use Pythagoras’ theorem in context or to solve other geometrical problems.

• Apply Pythagoras Theorem in 3D.

##### Pie Charts and Scatter Diagrams

• Understand that pie charts are used to show proportions.

• Use a template to construct a pie chart by scaling frequencies.

• Construct pie charts when the total frequency is not a factor of 360

• Interpret data shown on in a pie chart.

• Plot a scatter diagram.

• Understand the meaning of ‘correlation’.

• Identify positive, negative and no correlation.

• Interpret a scatter diagram using understanding of correlation.

• Understand that correlation does not indicate causation.

• Construct a line of best fit on a scatter diagram.

• Use a line of best fit to estimate values.

• Know when it is appropriate to use a line of best fit to estimate values.

• Choose appropriate graphs or charts to represent data.

##### Graphs

• Plot and interpret Distance Time graphs.

• Plot and interpret Velocity Time graphs.

• Use Distance Time to calculate and estimate Speed.

• Estimate distance and acceleration from a Velocity Time graph.

##### Financial Awareness

• Understand the importance of their Credit Rating and how this affects their financial options.

• Understand that borrowing money costs interest and be able to calculate monthly interest charges.

• Understand that Buy Now Pay Later schemes and Store Cards are forms of credit which can lead to debt.

• Understand how Payday Loans work.

• Calculate interest charges on Payday Loans.

• Understand the dangers of falling into debt associated with gambling.

• Understand that probabilities when gambling are never favourable.

## Year 10

##### Foundation

##### Higher

##### Factors Multiples and Primes

• Identify factors, multiples and primes including being able to recognise prime numbers up to 100.

• List factors and multiples systematically and use lists to find common factors and multiples of two numbers.

• Find the prime factor decomposition of a positive integer and write as a product of its prime factors (understand that each number has a unique prime factor decomposition).

• Find LCM and HCF of two numbers: by listing, Venn diagrams, and using prime numbers – including using the prime factor decomposition of two numbers.

##### Equations

• Solve one and two step linear equations using 1 variable.

• Solve any linear equation where the unknown appears once - including with brackets or fractions.

• Solve an equation with unknowns on both sides.

• Apply solving linear equations to other aspects of maths.

##### Indices

• Understand and use index notation including finding (or estimating) values of calculations involving square roots, cube roots, and positive indices.

• Use indices correctly in the hierarchy of operations including with brackets.

• Use the index law for raising a power to a power.

• Recall and use the index laws of multiplication and division.

• Use a calculator for all operations including powers, roots, and brackets.

##### Angles and Bearings

• Use the standard conventions for labelling and referring to the sides and angles of a triangle.

• Apply the properties of angles at a point, on a straight line, vertically opposite angles, including when represented algebraically.

• Understand and use alternate, co-interior and corresponding angles on parallel lines.

• Derive and use the sum of angles in a triangle to deduce and use the angle sum in any polygon, and to derive properties of regular polygons.

• Measure, draw and read bearings.

• Know the difference between an angle and a bearing.

• Calculate bearings from problems using parallel lines angle facts.

• Know compass directions and related angles.

• Know that Bearings are always given as 3 figures and measured clockwise from North.

• Understand and use the scale for distance on a map.

##### Sequences

• Generate terms of a sequence from a term-to-term rule.

• Generate terms of a sequence from a position-to-term rule.

• Find the term-to-term rule and position-to-term rule for a linear sequence.

• Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions.

• Recognise and use Fibonacci type sequences and quadratic sequences.

##### Types of data, sampling and Bias

•Be able to describe and identify different types of data: qualitative, quantitaive, discrete, continuous, primary and secondary.

•Use the data handling cycle to plan an investigation to test a hypothesis.

•Design or criticise a suitable data collection sheet for different types of data.

•Understand what is meant by a sample and population and how sample sizes and type of sample can affect results.

•Know and be able to use different types of sampling including stratified sampling.

•Understand bias and how it can be minimised to ensure the sample is representative.

##### Ratio

•Understand the link between ratio and fractions and be able to use fractions to solve ratio problems.

•Use ratio notation, including reduction to simplest form.

•Divide a given quantity into two parts in a given part: part or part: whole ratio; apply ratio to real contexts and problems.

• Write three part or two-part ratios by combining two other ratios e.g. Find A: C given A: B and B: A.

•Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

• Relate ratios to linear functions

##### Formulae

• Know the hierarchy of operations and be able to use this to form expressions and formulae.

• Substitute numerical values into scientific formulae.

• Understand and use standard mathematical formulae.

• Rearrange formulae to change the subject.

• Change the subject of a formula with brackets or when the subject appears twice.

• Translate simple situations or procedures into algebraic formulae.

##### Similarity and Congruence

•Be able to identify congruent shapes, and to show that two shapes are congruent.

•Be able to produce a congruent shape by reflecting, rotating, or translating a shape and understand why it is congruent.

•Be able to produce similar shapes by enlargement – including with a fractional scale factor and explain why these shapes are similar.

•Solve problems involving similar shapes where the scale factor is known or can be found.

•Compare lengths using ratio notation.

•Use and convert units of metric units of length, area and volume e.g. cm2 to m2

•Apply the concepts of congruence and similarity, including the relationships between lengths of similar objects.

##### Proportion

• Understand direct proportion and its link to equivalent ratios.

• Use and convert standard units of mass, length, time, money, and other measures (including standard compound measures) using decimal quantities where appropriate.

• Use a multiplier when solving problems involving direct proportion or proportional increase/decrease.

• Solve problems involving direct and inverse proportion, including graphical and algebraic representations.

• Understand that x is inversely proportional to y is equivalent to x is proportional to 1/y

• interpret equations that describe inverse and direct proportion

##### Compound Units

•Use compound units such as speed and rates of pay.

•Use compound units such as density and pressure.

•Change freely between compound units e.g. from km/h to metres/second or from wage per hour to wage per annum.

•Change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts.

• Draw and interpret a distance-time graph.

• Draw and interpret any compound measures graph (e.g. cost per mile for a taxi company).

##### Factorising Quadratics

• Simplify an expression - including the laws of indices.

• Multiply a term over a single bracket.

• Factorise a linear expression by taking out a common factor.

• Expand the product of two linear brackets.

• Factorise a quadratic expression of the form x² + bx + c.

• Factorise the difference of two squares.

##### Pythagoras’ Theorem

• Identify and label different parts of a triangle including the hypotenuse and use conventional notation for this.

• Recall and use the formula a²+b²=c²to find the hypotenuse right angled triangle.

• Recall and use the formula a²+b²=c² to find one of the shorter side lengths of a right-angled triangle.

• Be able to use the formula a²+b²=c²to show whether a triangle is right-angled or not.

• Use Pythagoras’ theorem in context or to solve other geometrical problems - for example to find the distance between two coordinates.

##### Fractions Decimals and Percentages

• Understand and find a reciprocal.

• Perform all four operations with decimals.

• Perform all four operations with fractions.

• Convert between improper fractions and mixed numbers.

• Find a fraction of a quantity.

• Convert fluently between fractions, decimals, and percentages.

• Find a percentage of a quantity.

• Increase or decrease a quantity by a given percentage.

• Calculate a repeated percentage change.

• Calculate a change in quantity as a percentage change.

• Calculate reverse percentages

##### Linear and Quadratic Functions

• Generate and plot coordinates for any linear function.

• Recognise that y=mx+c corresponds to a linear graph and know how the parts of this equation determine the line.

• Calculate the gradient of a straight-line segment using dy/dx.

• Be able to find the equation of any straight line. • Recognise and plot simple quadratic functions

##### Probability

• Compare the probabilities of events by comparing sizes of fractions, decimals, and percentages.

• Use theoretical models to include outcomes using dice, spinners, and coins.

• Record outcomes of probability experiments in tables.

• Compare experimental data and theoretical probabilities.

• Compare relative frequencies from samples of different sizes.

• Find the probability of an event happening using relative frequency.

•Estimate the number of times an event will occur, given the probability and the number of trials - both for experimental and theoretical probabilities.

• Use two way tables and frequency trees to record information and calculate probabilities.

##### Surface Area and Volume

• Identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

• Know and understand units for volume, area and length.

• Use standard formulae to solve problems involving areas of parallelograms, triangles and trapezia.

• Calculate area and circumference of circles.

• Calculate the volume of any prism.

• Calculate the surface area of any prism.

• Find the surface area and volume of composite solids.

• Calculate the volume of spheres, cones, and pyramids.

• Calculate the surface area of spheres, cones, and pyramids.

##### Financial Awareness

• Be able to understand the real-life cost of renting a property.

• Understand what a mortgage is and what interest rates mean.

• Understand how a student loan works, on be able to work out what sort of support they can get at university

• Work out the cost of financing a car. Students will understand the different payment options available to them.

##### Indices

• Understand and use index notation including finding (or estimating) values of calculations involving square roots, positive, negative, and fractional indices.

• Use indices correctly in the hierarchy of operations including with brackets.

• Recall and use the index laws of multiplication, division, and powers of powers.

• Recall and use laws of fractional and negative indices.

• Use a calculator for all operations including powers, roots, and brackets.

##### Standard Form

• Interpret and compare numbers in standard form a x 10n, where 1≤a<10 and n is a positive or negative integer.

• Calculate with numbers in standard form.

• Interpret a calculator display in standard form and know how to enter numbers in standard form.

##### Trigonometric ratios

• Identify and label adjacent, opposite, hypotenuse and theta on a right-angled triangle.

• Recall and use the correct trigonometric ratio to find a missing side length or angle in a right-angled triangle.

• Use the trigonometric ratios to solve problems in 2D or 3D.

##### Probability

•Write a probability as a fraction, decimal or percentage.

•Systematically list all the possible outcomes for single events and combined events and know how to work out the number of possible combinations for combined events.

•Construct and use two-way tables to calculate probabilities.

•Construct and use frequency trees to calculate probabilities.

##### Quadratic Sequences

• Generate terms from a linear nth term rule.

• Find the nth term rule for a linear sequence.

• Identify a linear, quadratic or Fibonacci type sequence.

• Identify a geometric progression.

• Generate terms from a quadratic nth term rule.

• Find the nth term rule for a quadratic sequence.

##### Surds

• Be aware of the concept of an irrational number and understand that the use of surds allows us to maintain accuracy.

• Understand surd notation, including interpreting calculator display given in surd form.

• Be able to simplify a surd such as √12 = √(4 × 3) = √4 × √3 = 2√3.

• Simplify expressions involving surds such as 4√3 + √75.

• Manipulate expressions involving surds, including expanding double brackets with surds.

• Rationalise the denominator of an expression.

• Know the exact values of sinɵ, cosɵ and tanɵ when ɵ=0, 30, 45 and 60. Know that sin90° = 1 and cos90° = 0.

##### Ratio

•Understand the link between ratio and fractions and be able to use fractions to solve ratio problems.

•Use ratio notation, including reduction to simplest form.

•Divide a given quantity into two parts in a given part: part or part: whole ratio; apply ratio to real contexts and problems.

•Express a multiplicative relationship between two quantities as a ratio or a fraction.

• Write three part or two-part ratios by combining two other ratios e.g. Find A: C given A: B and B: A.

• Solve problems involving ratios in which one quantity is changed to find an original or new total.

• Write a ratio as a linear equation

##### Cumulative Frequency and Box Plots

• Work out the cumulative frequency from a grouped frequency table.

• Draw a cumulative frequency graph/curve from a grouped frequency table.

• Use a cumulative frequency graphs/curves to estimate the median.

• Use a cumulative frequency graphs/curves to estimate the interquartile range.

• Draw a box plot.

• Interpret a box plot and know that each section represents 25% of the data.

• Compare two data sets from cumulative frequency graphs/curves and box plots and make reasoned conclusions.

##### Similarity and Congruence

•Be able to identify congruent shapes, and to show that two shapes are congruent.

•Be able to produce a congruent shape by reflecting, rotating, or translating a shape and understand why it is congruent.

•Be able to produce similar shapes by enlargement – including with a negative or fractional scale factor and explain why these shapes are similar.

•Solve problems involving similar shapes where the scale factor is known or can be found.

•Compare lengths, areas and volumes using ratio notation.

• Use and convert units of metric units of length, area and volume e.g. cm2 to m2

•Apply the concepts of congruence and similarity, including the relationships between lengths, area and volume of similar objects.

##### Solving Quadratics by Factorising

• Know the difference between linear and quadratic, and an expression and equation.

• Expand the product of two linear brackets.

• Factorise a quadratic expression of the form x2 + bx + c.

• Factorise the difference of two squares.

• Factorise a quadratic expression of the form ax2 + bx + c.

• Solve any quadratic equation set =0 by factorising.

• Form and/or rearrange a quadratic in order to solve it.

##### Compound Units and Real Life Graphs

•Understand and manipulate units and compound units.

•Understand and know the difference between scalar and vector quantities.

•Draw and interpret real-life graphs.

•Calculate the gradient of a straight line and know what this represents on a real-life graph.

•Calculate the area under a straight line and know what this represents on a real-life graph.

##### Proportion

•Understand direct proportion and its link to equivalent ratios.

•Solve problems involving direct and inverse proportion, understand a graphical representation of something in direct proportion.

•Compare lengths, areas and volumes using ratio notation; make links to similarity and scale factors.

• Use a multiplier when solving problems involving direct proportion or proportional increase/decrease.

•Use and convert compound units e.g. speed, rates of pay, unit pricing using decimal quantities where appropriate.

• Form and interpret equations that describe direct and inverse proportion.

• Understand that x is inversely proportional to y is equivalent to x is proportional to 1/y.

##### Pythagoras’ Theorem

• Identify and label different parts of a triangle including the hypotenuse and use conventional notation for this.

• Recall and use the formula a²+b²=c²to find the hypotenuse right angled triangle.

• Recall and use the formula a²+b²=c² to find one of the shorter side lengths of a right-angled triangle.

• Be able to use the formula a²+b²=c²to show whether a triangle is right-angled or not.

• Use Pythagoras’ theorem in context or to solve other geometrical problems - for example to find the distance between two coordinates.

##### Fractions Decimals and Percentages

• Understand and find a reciprocal.

• Perform all four operations with decimals.

• Perform all four operations with fractions.

• Convert between improper fractions and mixed numbers.

• Find a fraction of a quantity.

• Convert fluently between fractions, decimals, and percentages.

• Find a percentage of a quantity.

• Increase or decrease a quantity by a given percentage.

• Calculate a repeated percentage change.

• Calculate a change in quantity as a percentage change.

• Calculate reverse percentages

##### Linear and Quadratic Functions

• Generate and plot coordinates for any linear function.

• Recognise that y=mx+c corresponds to a linear graph and know how the parts of this equation determine the line.

• Calculate the gradient of a straight-line segment using dy/dx.

• Be able to find the equation of any straight line. • Recognise and plot simple quadratic functions

##### Probability

• Compare the probabilities of events by comparing sizes of fractions, decimals, and percentages.

• Use theoretical models to include outcomes using dice, spinners, and coins.

• Record outcomes of probability experiments in tables.

• Compare experimental data and theoretical probabilities.

• Compare relative frequencies from samples of different sizes.

• Find the probability of an event happening using relative frequency.

•Estimate the number of times an event will occur, given the probability and the number of trials - both for experimental and theoretical probabilities.

• Use two way tables and frequency trees to record information and calculate probabilities.

##### Circle Theorems

• Identify alternate and corresponding angles and know they are equal.

• Use knowledge of alternate and corresponding angles to calculate missing angles in geometrical diagrams.

• Use the fact that angles in a triangle total 180° to work out the total of the angles in any polygon.

• Establish the size of an interior angle and an exterior angle in a regular polygon.

• Know the total of the exterior angles in any polygon.

• Identify when a circle theorem can be used to find missing angles in a geometrical problem.

• Apply and prove the standard circle theorems concerning angles, radii, tangents and chords.

•Know when to use circle theorems to prove geometrical problem.

##### Linear and Quadratic functions

• Generate and plot coordinates for any linear function.

• Solve an equation in the form y=mx+c graphically or otherwise.

• Recognise that y=mx+c corresponds to a linear graph and know how the parts of this equation determine the line.

• Be able to find the equation of any straight line.

• Understand the gradients of parallel and perpendicular lines.

• Draw a quadratic graph including graphs with a negative coefficient of x2.

• Find approximate solutions to quadratic equations using a graph.

• Deduce roots of quadratic functions algebraically.

• Be able to use a quadratic graph to find roots and turning points (minimum and maximum points).

##### Surface Area and Volume

• Know and understand units for volume, area, and length.

• Calculate the volume of any prism.

• Calculate the volume of spheres, pyramids, and cones- including frustums.

• Calculate the surface area of any prism.

• Calculate the surface area of spheres, pyramids, and cones.

• Find the surface area and volume of composite solids.

• Solve problems involving area/volume of enlarged shapes.

##### Conditional Probability

• Compare relative frequencies from samples of different sizes.

• Find the probability of an event happening using relative frequency.

• Estimate the number of times an event will occur, given the probability and the number of trials - both for experimental and theoretical probabilities.

•Combine probabilities by multiplying them together for simple experiments.

•Draw a probability tree diagram based on given information, and use this to find probability and expected number of outcomes

•Understand conditional probabilities and decide if two events are independent - knowing the difference between selection with and without replacement.

•Calculate the probability of independent and dependent combined events.

•Use a two-way table or tree diagram to calculate conditional probability.

• Know how to place elements in Venn diagrams with 2 sets, according to their properties.

• Understand the notation for intersection and union, and which regions these statements apply to in a Venn diagram.

• Use set notation to find probabilities from a Venn diagram.

• Calculate conditional probabilities from a Venn diagram.

##### Simplifying algebraic Fractions

• Manipulate any expression by simplifying (including with indices), expanding brackets or factorising.

• Simplify and algebraic fraction such as 12x3y4/24xy2 by cancelling common factors.

• Simplify an algebraic fraction where one or both numerator/denominators need factorising in order to find the common factors.

• Calculate with algebraic fractions.

• Solve fractional equations, both linear and quadratic.

##### Financial Awareness

• Be able to understand the real-life cost of renting a property.

• Understand what a mortgage is and what interest rates mean.

• Understand how a student loan works, on be able to work out what sort of support they can get at university

• Work out the cost of financing a car. Students will understand the different payment options available to them.

## Year 11

##### Foundation

##### Higher

##### Fractions Decimals and Percentages

• Perform all four operations with decimals.

• Perform all four operations with fractions.

• Convert between improper fractions and mixed numbers.

• Find a fraction of a quantity.

• Convert fluently between fractions, decimals, and percentages.

• Find a percentage of a quantity.

• Increase or decrease a quantity by a given percentage. • Calculate a repeated percentage change.

• Calculate a change in quantity as a percentage change.

• Calculate simple reverse percentage changes.

• Calculate compound percentage change.

##### Probability Trees and Venn Diagrams

• Combine probabilities by multiplying them together for simple experiments.

• Draw and use tree diagrams to calculate the probability of two independent events.

• Draw and use tree diagrams to calculate the probability of two dependent events.

• Know how to place elements in Venn diagrams with 2 sets, according to their properties.

• Understand the notation for intersection and union, and which regions these statements apply to in a Venn diagram.

• Use set notation to find probabilities from a Venn diagram.

##### Powers. Roots and Standard form

• Use indices correctly in the hierarchy of operations including with brackets, with and without a calculator.

• Recall and use the index laws of multiplication, division and powers of powers.

• Interpret and compare numbers in standard form a x 10n 1≤a<10 and n is a positive of negative integer.

• Calculate with numbers in standard form.

• Interpret a calculator display in standard form and know how to enter numbers in standard form.

• Recall and use square numbers and square roots up to 15 squared.

• Simplify expressions in the form √y x √y or (√y)2. • Simplify expressions involving surds such as x√a + y√a.

• Expand and Simplify expressions involving surds and brackets such as a(√x + b).

##### Sequences

• Generate a sequence given an nth term and find an nth term of a given sequence.

• Recognise, use and continue non-linear sequences such as Fibonacci chains, cube numbers and triangular numbers.

• Recognise and continue simple geometric progressions such as 2n.

##### Arcs and Sectors

• Know and recognise the parts of circle.

• Know and apply the formulae for area of a circle and circumference of a circle.

• Calculate the perimeter of composite shapes that include sections of a circle.

• Calculate the area of composite shapes that include sections of a circle.

• Know how to find arc length.

• Calculate the angle of a sector when radius is given.

• Know how to find the area of a sector.

• Know how to solve problems involving arc length and area of sectors.

• Know the formula for finding the volume of a cylinder. • Calculate the volume of a cylinder.

##### Simultaneous Equations and Inequalities

• Generate and plot coordinates and draw the graph of any linear function.

• Recognise that y=mx+c corresponds to a linear graph and know how the parts of this equation determine the line.

• Solve any linear equation including those with brackets or where the unknown appears as a denominator.

• Solve linear equations where the unknown appears twice.

• Use elimination to solve a pair of simultaneous equations, including those where one or both equations need to be multiplied.

• Form a pair of simultaneous equations from a worded question, or from a geometric diagram.

• Plot a pair of simultaneous equations on a set of axes and know that the point of intersection is the solution for that pair of equations.

• Know the symbols < ≤ > ≥ = ≡

• Represent inequalities on a number line.

• Solve an inequality.

##### Ratio

•Understand the link between ratio and fractions and be able to use fractions to solve ratio problems.

•Use ratio notation, including reduction to simplest form.

•Divide a given quantity into two parts in a given part: part or part: whole ratio; apply ratio to real contexts and problems.

• Write three part or two-part ratios by combining two other ratios e.g. Find A: C given A: B and B: A.

•Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

• Relate ratios to linear functions

##### Formulae

• Know the hierarchy of operations and be able to use this to form expressions and formulae.

• Substitute numerical values into scientific formulae.

• Understand and use standard mathematical formulae.

• Rearrange formulae to change the subject.

• Change the subject of a formula with brackets or when the subject appears twice.

• Translate simple situations or procedures into algebraic formulae.

##### Similarity and Congruence

•Be able to identify congruent shapes, and to show that two shapes are congruent.

•Be able to produce a congruent shape by reflecting, rotating, or translating a shape and understand why it is congruent.

•Be able to produce similar shapes by enlargement – including with a fractional scale factor and explain why these shapes are similar.

•Solve problems involving similar shapes where the scale factor is known or can be found.

•Compare lengths using ratio notation.

•Use and convert units of metric units of length, area and volume e.g. cm2 to m2

•Apply the concepts of congruence and similarity, including the relationships between lengths of similar objects.

##### Ratio and Proportion

•Understand the link between ratio and fractions and be able to use fractions to solve ratio problems.

•Use and convert standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate.

•Use ratio notation, including reduction to simplest form.

•Divide a given quantity into two parts in a given part: part or part: whole ratio; apply ratio to real contexts and problems.

•Express a multiplicative relationship between two quantities as a ratio or a fraction.

•Understand direct proportion and its link to equivalent ratios.

•Solve problems involving direct and inverse proportion, understand a graphical representation of something in direct proportion.

•Compare lengths, areas and volumes using ratio notation; make links to similarity and scale factors.

• Understand that x is inversely proportional to y is equivalent to x is proportional to 1/y

• Interpret equations that describe inverse and direct proportion

##### Constructions and Loci

• Use the angle facts for points, lines, parallel and intersecting lines, and regular polygons.

• Know what similar and congruent mean.

• Construct congruent triangles using ASA, SAS, SSS & RHS.

• Prove two tringles are congruent using the rules ASA, SAS, SSS or RHS.

• Apply congruence, similarity, and triangle constructions to solve problems.

• Know the difference between congruent and similar shapes.

• Construct both angle, line and point to line bisections.

• Construct a locus of a points from a fixed point, line or shape.

• Apply bisections and loci to solve problems.

##### Quadratics

• Expand single brackets/factorise linear expressions.

• Expand double brackets (using grid method) to produce a quadratic expression/equation.

• Solve a quadratic equation of the form x² + bx + c by factorising.

• Solve a quadratic equation of the form ax² + bx + c by factorising.

• Draw a quadratic graph including graphs with a negative coefficient of x².

• Find approximate solutions to quadratic equations using a graph.

• Deduce roots of quadratic functions algebraically.

• Be able to use a quadratic graph to find roots and turning points (minimum and maximum points).

• Solve problems that involve solving a quadratic (by factorising) equation in context.

##### Pythagoras Recap and Trigonometry

• Recall and use the formula a²+b²=c² to find the hypotenuse right angled triangle and one of the shorter side lengths of a right-angled triangle.

• Use Pythagoras’ theorem in context or to solve other geometrical problems - for example to find the distance between two coordinates.

• Choose an appropriate trigonometric ratio that can be used in a given situation.

• Understand that sine, cosine and tangent are functions of an angle.

• Know the trigonometric ratios, sinθ = opp/hyp, cosθ = adj/hyp, tanθ = opp/adj.

• Set up and solve a trigonometric equation to find a missing side in a right-angled triangle.

• Set up and solve a trigonometric equation to find a missing angle in a right-angled triangle.

##### Averages

• Find the mean, median and mode from a list of data.

• Know when to use each average and why.

• Use the mean to find a missing number in a set of data

• Understand the range as a measure of spread (or consistency)

• Make comparisons using averages or the range

• Estimate the range from a grouped and ungrouped frequency table

• Find the mode and median from a frequency table.

• Find the mean from a frequency table.

• Find the interval that contains the modal group median from grouped data.

• Find the estimated mean from grouped frequency data.

• Find any average from a range of graphs and diagrams.

##### Vectors

• Describe vectors as 2D translations.

• Add and subtract column vectors and multiply column vectors by a scalar.

• Add and subtract diagrammatic vectors and multiply diagrammatic vectors by a scalar.

• Recognise that when one vector is a scalar multiple of another then the lines will be parallel.

##### Other Graphs

• Recognise, sketch and interpret graphs of linear and quadratic functions.

• Recognise, sketch and interpret graphs of cubic functions, the reciprocal function y = 1/x.

• Plot and interpret graphs in real contexts to find approximate solutions to problems.

##### Accuracy and Bounds

• Write down the maximum or minimum figure for a value rounded to a given accuracy (including writing error intervals).

• Combine upper or lower bounds appropriately to achieve an overall maximum or minimum for a situation.

• Work with practical problems involving bounds including in statistics. For example, finding the midpoint of a class interval, such as 10 < t ⩽ 20, in order to estimate a mean.

• Use bounds to calculate a value to an appropriate degree of accuracy.

##### Surds, Indices and Standard Form (Recap)

• Understand and use index notation including finding (or estimating) values of calculations involving square roots, positive, negative, and fractional indices.

• Use indices correctly in the hierarchy of operations including with brackets.

• Recall and use the index laws of multiplication, division, and powers of powers.

• Recall and use laws of fractional and negative indices.

• Use a calculator for all operations including powers, roots, and brackets.

• Interpret and compare numbers in standard form a x 10n, where 1≤a<10 and n is a positive or negative integer.

• Calculate with numbers in standard form.

• Interpret a calculator display in standard form and know how to enter numbers in standard form.

• Be aware of the concept of an irrational number and understand that the use of surds allows us to maintain accuracy.

• Understand surd notation, including interpreting calculator display given in surd form.

• Be able to simplify a surd such as √12 = √(4 × 3) = √4 × √3 = 2√3.

• Simplify expressions involving surds such as 4√3 + √75.

• Manipulate expressions involving surds, including expanding double brackets with surds.

• Rationalise the denominator of an expression.

• Know the exact values of sinɵ, cosɵ and tanɵ when ɵ=0, 30, 45 and 60. Know that sin90° = 1 and cos90° = 0.

##### Cumulative Frequency, Box plots and Histograms

• Work out the cumulative frequency from a grouped frequency table.

• Draw a cumulative frequency graph/curve from a grouped frequency table.

• Use a cumulative frequency graphs/curves to estimate the median.

• Use a cumulative frequency graphs/curves to estimate the interquartile range.

• Draw a box plot.

• Interpret a box plot and know that each section represents 25% of the data.

• Compare two data sets from cumulative frequency graphs/curves and box plots and make reasoned conclusions.

• Construct histograms for grouped data with equal and unequal class intervals.

• Interpret histograms for grouped data with equal and unequal class intervals.

• Use histograms to solve problems that draw on other topic in maths.

• Use histograms to work backwards to find missing frequency’s in a grouped frequency table.

##### Quadratic Equations

• Expand and simplify double and triple brackets.

• Factorise all forms of quadratic expression including recognising the difference of two squares.

• Solve a quadratic equation of the form x² + bx + c by factorising.

• Solve a quadratic equation of the form ax² + bx + c by factorising.

• Identify when a quadratic equation cannot be solved by factorising.

• Recall the quadratic formula and use it to solve a quadratic equation that is equal to zero.

• Complete the square of a quadratic expression with leading coefficient = 1.

• Complete the square of a quadratic expression with leading coefficient >1.

• Solve a quadratic equation equal to zero by completing the square.

• Solve a quadratic equation that is not equal to zero by factorising/completing the square/using the formula.

• Solve problems that involve solving a quadratic equation in context.

##### FDP – Reverse and Compound Percentages

• Complete the four operations with fractions.

• Complete the four operations with decimals.

• Convert and compare fractions, decimals and percentages including those greater than 1.

• Find a percentage of an amount and increase and decrease by a given percentage.

• Express a change in quantity as a percentage change and calculate reverse percentage and fraction changes.

• Calculate over a range of time periods using compound percentage change with indices.

• Use FDP skills to solve a range of functional problems including reverse compound interest calculations.

• Apply the idea of compound interest to solve exponential growth and decay problems in various contexts.

##### Graphs

• Solve quadratics graphically and know how to find the roots of a quadratic by factorising.

• Solve simultaneous equations graphically.

• Know how to find the turning point of a quadratic by completing the square.

• Be able to sketch a quadratic graph by finding its roots and turning point. • Shade a region given by one or more inequalities. • Solve a quadratic inequality. • Draw a cubic graph.

##### Constructions and Loci

• Construct congruent triangles using ASA, SAS, SSS & RHS.

• Construct both angle, line and point to line bisections.

• Construct a locus for a given set of conditions.

• Apply bisections and loci to problems.

##### Sine and Cosine Rule

• Prior knowledge: Use Pythagoras' theorem and trigonometry in 2 dimensions.

• Use Pythagoras’ theorem to find lengths in three dimensional figures.

• Use trigonometry to find the angle between a line and a plane.

• Solve practical problems involving lengths and angles in three dimensional figures.

• Know the labelling conventions for non-right-angled triangles.

• Know the sine rule and use if to find a missing length or angle in a non - right angled triangle.

• Know the cosine rule and use if to find a missing length or angle in a non - right angled triangle.

• Identify when the sine/cosine rule is needed to solve a problem and which of the two is needed.

• Solve problems involving bearings and the Sine/Cosine rule.

• Know how to find the area of a triangle using 0.5abSinC.

• Solve problems in 2D and 3D using all forms of trigonometry.

##### Ratio and Proportion

• Express the division of a quantity into two or three parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations).

• Identify and work with fractions in ratio problems.

• Understand and use proportion as equality of ratios.

• Use a multiplier when solving problems involving direct proportion or proportional increase/decrease.

• Form and interpret equations that describe direct and inverse proportion.

• Understand that x is inversely proportional to y is equivalent to x is proportional to 1/y.

• Recognise and interpret graphs that illustrate simple and complex direct and inverse proportional relationships.

• Solve complex problems using algebra to interpret ratio problems

##### Functions

• Understand the meaning of a function

• Know the notation for composite functions

• Find the inverse of a given function

• Solve problems involving inverse functions

• Solve problems involving composite functions

##### Real Life graphs

•Draw and interpret real-life graphs.

•Calculate the gradient of a straight line and know what this represents on a real-life graph.

•Calculate the area under a straight line and know what this represents on a real-life graph.

•Know how to estimate the instantaneous rate of change from a 'real life graph' by drawing a tangent.

• Know how to use the trapezium rule to estimate the area underneath a curve and understand what it means in various contexts.

•Know how to find speed, average speed, acceleration, distance, average acceleration from real life graphs.

##### Iteration and simultaneous Equations

• Understand the process of interval bisection to locate an approximate solution for a complex equation and use interval bisection to locate an approximate solution for a complex equation

• Rearrange an equation to form an iterative formula

• Use an iterative formula to find approximate solutions to equations

• Solve two linear simultaneous equations in two variables by elimination (multiplication of both equations required)

• Understand the concept of solving simultaneous equations by substitution and solve one linear and one quadratic simultaneous equation in two variables by substitution

• Decide whether to use elimination or substitution to solve a pair of simultaneous equations

• Derive and solve two simultaneous equations in complex cases

• Interpret the solution to a pair of simultaneous equations

##### Vectors

• Use diagrammatic representation of vectors.

• Know and use different notations for vectors.

• Add and subtract vectors.

• Multiply a vector by a scalar.

• Understand how to create and present a proof involving vectors.

• Make deductions about situations involving vectors that are multiples of other vectors.

• Make deductions about situations involving vectors expressed using ratios.

• Make deductions about situations involving vectors and parallel lines.

• Prove that three points are colinear.

• Solve multi step problems involving vectors.

##### Other Graphs

• Plot the graph of an exponential function, y = k^x, for positive values of k

• Understand that trigonometric values can be found for angles of any size

• Plot the graphs of the trigonometric functions, y = sin x, y = cos x and y = tan x

• Know the key features of exponential and trigonometric graphs

• Know the effects of transforming the graph y = f(x): f(x), f(ax), af(x), f(x) + a, f(x + a), y = f(-x) and y = -f(x)

• Solve problems involving the transformation of graphs

• Recognise and use the equation of a circle with centre at the origin

• Find the equation of a tangent to a circle at a given point.