Mathematics

Algebraic Manipulation

Data and averages

Factors, multiples and primes

Algebraic expressions

Indices

Negative numbers

2D-shapes

Sequences

Algebraic notation

Equality and Equivalence

Representing Data

Percentages

Fractions, Decimals and percentages

Numbers

Place value

Ratio

Calculations, BIDMAS and using a calculator

Substitution

Place value and ordering 1 – 3

FDP equivalence 1 – 3

Sequences

Ratio and Proportion

Angles

Solving equations and inequalities

Time

Estimation and approximation

Using measures and scales

Addition and subtraction 1 & 2

Multiplication and division 1& 2

Fractions and percentages

Calculations and BIDMAS

Indices

Similarity and congruency

Fractions

Percentages

Averages

Angles

Directed numbers 1 & 2

Addition and subtraction of fractions 1 – 3

Trigonometry

Construction & loci

Solving equations

Quadratics

Angles

Sequences

Plotting graphs

Area and perimeter

Constructing, measuring and using geometric notation 1 & 2

Developing geometric reasoning 1 & 2

Volume & Surface Area

Transformations

Probability

Inequalities

Simultaneous Equations

Vectors

Circles

Probability

Transformations

Collecting & Representing Data

3D Shapes

Volume & Surface Area

Money

Developing number sense 1 & 2

Sets and probability 1 & 2

Prime numbers and proof 1 & 2

Will be able to estimate the size of everyday objects,

know suitable units to use to estimate or measure length, mass and capacity,

work out time intervals. Know the definitions of expressions, equations, formulae., functions, inequalities and terms. Form simple algebraic expressions and formulae. Complete a tally chart,

construct and complete grouped frequency tables,

interpret two-way tables. find averages from a list.

Secure students:

Will be able to plan journeys using timetables,

convert between metric units of measure,

convert between imperial units of measure,

calculate with speed, distance and time,

construct and interpret distance-time graphs,

construct and interpret simple velocity-time graphs,

calculate with mass, density and volume,

calculate with pressure, force and area,

calculate with exchange rates. Form an expression to show the area and perimeter of simple shapes. Use arithmetic operations with algebra. Collect like terms. Multiply a single term over a bracket and factorise a linear expression. use function machines. expand and simplify over two linear brackets. can expand a double bracket. factorise a quadratic expression where the coefficient of x2 is 1. Find a missing piece of data given the mean,

construct and complete frequency trees,

compare the mean, median, mode and range as appropriate of two distributions,

understand which measure of average is most appropriate and consider outliers.

Find averages from a bar chart and stem and leaf diagrams,

find averages from frequency tables.

Excelling students:

Will be able to understand that area under a velocity-time graph is acceleration,

understand that area under a speed-time graph is distance covered,

can convert between compound and area units,

can convert between units of measure including compound units from algebraic contexts. factorise an expression using the difference of two squares. form quadratic expressions. form an expression to show the area and perimeter of complex shapes. rearrange formulae including fractions and powers to make a different variable the subject. expand more than two brackets. n factorise a quadratic expression where the coefficient of x2 is greater than 1. simplify and manipulate algebraic expressions including algebraic fractions. Complete and interpret a table for time series data,

understand and use sampling methods including understanding their limitations,

complete a cumulative frequency table,

find quartiles and interquartile range,

estimate averages from a histogram,

understand the capture-recapture method.

Will be able to round to decimal places and significant figures. Construct, interpret and compare bar charts, vertical line graphs

Pictograms. Convert between fractions, decimals and percentages

find percentages of amounts without a calculator

find percentages of amounts with a calculator. Use fraction notation to describe parts of shapes

convert between fractions, decimals and percentages

simplify and find equivalent fractions. Order negative integers,

use negative numbers in context and

calculate with negative numbers.

Secure students:

Will be able to estimate an answer before calculating and truncate a number to a given degree of accuracy. Construct, interpret and compare frequency polygons, pie charts, stem and leaf diagrams and scatter graphs. Increase/decrease an amount by a percentage,

write one number as a percentage of another,

calculate the percentage change e.g. profit/loss. Find a fraction of an amount,

calculate with decimals,

recognise common recurring decimals as fractions,

multiply and divide numbers by powers of ten,

order fractions and decimals and

calculate with fractions and mixed numbers. Give the square root of a number,

identify factors and multiples,

identify the HCF and LCM,

square, cube and triangle numbers.

Excelling students:

Will be able to use inequality notation to specify simple error intervals for rounding and truncation. Interpolate and extrapolate apparent trends and understand the dangers of doing so.

Find the equation of a line of best fit and interpret in context. Construct, interpret and compare cumulative frequency diagrams, histograms and box plots. Use multipliers to find a percentage of an amount and to increase and decrease by a percentage,

find the original amount after a percentage change,

use percentages to find the simple interest over a number of years

find the compound interest over a number of years. Find reciprocals

understand the effect of multiplying and dividing by a number between 0 and 1,

write one number as a fraction of another,

simplify and manipulate algebraic expressions including algebraic fractions,

convert between recurring decimals and fractions. Tests of divisibility,

do prime factor decomposition including using product notation,

use prime factor decomposition to find the HCF or LCM.

Will be able to substitute into an expression and

use function machines. Find terms in sequences

generate sequences given term to term or an nth term. Write and simplify ratios (including different units),

calculate equivalent ratios. Identify types of angles and use standard conventions for labelling sides and angles of triangles,

find missing angles on a straight line and around a point,

identify vertically opposite angles,

derive and use the sum of angles in a triangle.

Secure students:

Will be able to substitute positive and negative numbers into expressions and formulae, including scientific expressions

substitute into functions. Recognise and use triangular, square, cube and simple arithmetic progressions.

Calculate the nth term of a linear sequence. Write a ratio as a fraction,

express a relationship between two quantities as a ratio or fraction,

share and amount in a ratio,

solve ratio problems given in contexts (eg conversion, scaling, mixing and concentrations),

understand proportion as equality of a ratio,

draw using scales,

calculate best buys and value for money,

convert between different currencies. Find missing angles in parallel lines,

find interior and exterior angles in quadrilaterals and other polygons,

find out how many sides a polygon has given interior angles,

find and use bearings.

Excelling students:

Will be able to use prime factor decomposition to decide whether a number is square etc. Interpret the reverse process as the inverse function,

interpret the succession of two functions as the composite function and

find composite and inverse functions. Recognise and use Fibonacci, quadratic and simple geometric progressions (rⁿ where n is an integer and r is a rational number >0).

Find the nth term of a quadratic sequence. Relate ratios to linear functions,

use unitary ratios to compare amounts

solve ratio problems given one of the shares and NOT the total,

interpret equations which describe direct and inverse proportion,

recognise and interpret graphs that illustrate direct and inverse proportion,

compare lengths, areas and volumes using ratio notation and scale factors.

Construct and use equations which describe direct and inverse proportion and

find unknown sides using the relationship between length, area and volume scale factors in similar shapes. Use circle theorems,

prove circle theorems and form geometric proofs.

Will be able to name and identify properties of 2D & 3D shapes,

recognise parallel and perpendicular lines,

identify and construct nets. Use a calculator efficiently. Calculate basic square and cube numbers,

estimate the value of a square root,

multiply and divide by powers of 10. Identify congruent shapes by comparing sides and angles,

identify similar shapes.

Secure students:

Will be able to find the area and perimeter of 2D shapes including compound shapes by counting squares or using formulae,

identify and apply circle vocabulary including: centre, radius, chord, diameter, circumference.

Calculate missing side lengths given areas and perimeters, including circles,

identify and apply circle vocabulary including: tangent, arc, sector and segment,

find the area and circumference of a circle. Insert brackets & operations into a calculation to make it true,

use one calculation to find the answer to another. Recognise and use index notation

evaluate simple indices (e.g. 2⁴, 3³),

understand that anything raised to the power of 0 is equal to 1,

evaluate and calculate with numbers written in standard form,

calculate with roots and with integer indices,

use index laws to evaluate algebraic and numerical expressions (multiplication, division and brackets). Find the scale factor for similar shapes,

find unknown sides and angles using similarity.

Excelling students:

Will be able to find the area and perimeter of sectors, including arc length,

find the area of compound shapes including sectors,

construct and interpret plans & elevations,

calculate exactly with multiples of π,

find the area and perimeter of segments,

find the area of compound shapes including segments. Understand the difference between subtracting a squared number and squaring a negative number. Evaluate negative indices,

rationalise denominators,

simplify surds,

simplify and manipulate expressions including surds (including algebraic expressions),

evaluate fractional indices,

recognise geometric progressions (rⁿ where n is an integer and r is a surd),

calculate exactly with surds. Compare lengths, areas and volumes using ratio notation and scale factors including trigonometric ratios,

obtain simple proofs by applying angle facts, triangle congruence, similarity and properties of quadrilaterals (prove two triangles are congruent or similar),

prove two triangles are congruent.

Will be able to use Pythagoras’ theorem to find unknown sides of a triangle.​ Use trigonometric ratios to find any side or angle in a right- angled triangle. use a ruler and a compass to construct:  angles,

use correct notation for labelling lines, angles and triangles. solve one step equations,

solve one step equations including negatives. Expand two brackets.

Secure students:

Will be able to find the area of an isosceles triangle using Pythagoras’ Theorem.​

Use Pythagoras’ Theorem to find the distance between two points. Sketch trigonometric graphs and know the exact values,

calculate trigonometric ratios in surd form. Know that the perpendicular distance from a point to a line is the shortest distance to the line,

use a ruler and a compass to construct the midpoint and perpendicular bisector of a line segment,

use a ruler and a compass to construct the bisector of an angle,

use a ruler and a compass to construct the perpendicular from a point to a line,

use a ruler and a compass to construct the perpendicular from a point on a line. solve two step equations,

solve two step equations including negatives and brackets,

solve equations with unknowns on both sides and brackets. Plot quadratic graphs,

factorise a quadratic expression and solve when the coefficient of  is ,

solve quadratic equations by factorisation,

use quadratic graphs to estimate the solution to an equation.

Excelling students:

Will be able to use Pythagoras’ Theorem in 3D shapes. Recognise, sketch and interpret trigonometric functions  for angles of any size,

find angle solutions using trigonometric graphs between 0≤θ≤360° (in degrees only),

solve trigonometric equations with solutions between 0≤θ≤360°.

Find the missing angle between a line and a plane,

use sine rule to find missing sides & angles,

use cosine rule to find missing sides & angles,

use the area of a triangle using . Solve loci problems

construct SAS, ASA and SSS triangles, including equilateral triangles from a sketch or written description. solve equations involving fractions,

form and solve equations, interpreting the solution,

find approximate solutions to equations numerically using iteration. Identify roots, intercepts and turning points of quadratic functions graphically,

factorise a quadratic expression and solve, when the coefficient of  is greater than 1,

solve quadratic equations by completing the square and using the formula, including those that require rearrangement and those where coefficient of  is greater than ,

identify turning points by completing the square.

Will be able to plot and read coordinates in all 4 quadrants,

find the coordinates of points identified by geometrical information in 2D. Find the volume by counting cubes,

find the volume and surface area of cubes, cuboids & prisms. Describe & complete a translation using 2D vectors,

describe & complete a rotation. Place events on a probability scale,

use words to describe probability,

calculate simple probabilities. Use inequality symbols,

represent and evaluate inequalities on a number line.

Solve a pair of linear simultaneous equations.

Calculate with vectors including addition and subtraction and multiplication by a scalar.

Secure students:

Will be able to find midpoints and end points,

plot a graph of a linear functions,

identify the gradient and y intercept from graphs and equations e.g. ,

recognise, sketch and interpret linear graphs. Find the volume of cylinders,

link volume to capacity,

find the surface area of cylinders,

find the surface area of simple compound 3D shapes,

find the volume and surface area of pyramids including cones. Describe & complete a reflection,

describe & complete a positive integer enlargement. Find the probability of an event not occurring,

list outcomes from events,

use a sample space to calculate probabilities,

find probabilities from two-way tables,

that exhaustive probability sums to one,

record, describe and analyse the frequency of probability experiments using tables and frequency trees. Solve linear inequalities including unknowns on both sides, brackets, fractions and where it is necessary to multiply or divide by a negative number,

draw and shade inequalities on a graph. Form and solve simultaneous equations. Use diagrammatic and column representations of vectors.

Excelling students:

Will be able to identify parallel lines by comparing gradients,

find the equation of a straight line given the gradient and a point,

find the equation of a straight line given two points,

identify perpendicular lines by comparing gradients,

calculate and estimate gradients of graphs and areas under graphs and interpret results. Find the volume and surface area of spheres,

find missing lengths of a prism given the volume,

find the volume and surface area of more complex 3D shapes. Know that translations, rotations and reflections preserve length and angle, mapping objects to congruent images,

know that enlargements preserve angle but not length and produce similar,

can describe & complete fractional enlargements. Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events,

relate relative expected frequencies to theoretical probability,

enumerate sets and combinations of sets systematically using tables, grids & Venn diagrams

complete and use a Venn diagram,

construct and interpret a tree diagram with replacement,

use the ‘and’ & ‘or’ rule to calculate probabilities. Solve inequalities in two variables,

solve quadratic inequalities in one variable,

solve inequalities using set notation,

use inequalities and regions to solve real life problems. Graphically solve simultaneous equations,

solve simultaneous equations where one equation is quadratic or the equation of a circle. Prove two vectors are parallel or perpendicular,

use vectors to construct geometric arguments and proofs.

Median

Factor

Volume

Estimate

Profit

Pictograms

Loss

Fractions

Multiple

Simplify

Ratio

Simplify

Substitute

Interior Angles

Sequence

Area

Perimeter

Parallel

Powers

Square Root

Midpoint

Solve

Product

Gradient

Surface Area

Reflection

Rotate

Outcome

Simultaneous

Scale Factor

— = part of departmental termly list and Frayer model display

Frequency

Expand

Velocity

Significant Figure

Stem and Leaf

Factorise

Inequalities

Equivalent

Square Root

Quadratic Expression

Truncate

Depreciation

Reciprocals

Error Interval

Upper Bound

Correlation

Multiplier

Recurring

Integer

Compound Interest

Proportion

Equivalent

Unitary Ratio

Function Machine

Integer

Alternate Angles

Polygons

Bearings

Linear Sequence

Nth Term

Compound Shape

Trapezium

Quadrilateral

Diameter

Inverse

Standard Form

Index Notation

Cube Numbers

Congruent

Scale Factor

Hypotenuse

Adjacent

Perpendicular

Line Segment

Inequality

Variable

Factorise

Roots

Quadratic Equation

Quadratic Graph

Linear Equation

Linear Graph

Volume

Capacity

Congruent

Vector

Translate

Venn Diagram

Column Vectors

Transformation

These units are taught now because it has number at their heart and as a result has a large proportion of time spent reinforcing number to build competency.

These units are taught now because it develops on from number and gives the pupils opportunities to build competency in solving problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

These units are taught now so that students can transfer number and problem solving skills and will learn how to use mathematics in unfamiliar circumstances including problem solving and reasoning to ensure mastery and fluency across the curriculum.

Students will have the opportunity to demonstrate aspects of the learning model through identifying the strategies needed to solve mathematical problems, working with others to solve more complex problems and being able to discuss and justify techniques and methods used. They will be encouraged to review progress as they work, check and evaluate solutions and modify their approach if necessary. Students will be given opportunities to evaluate their strengths and limitations and to set realistic targets. Students will develop their ability to visualise and illustrate a maths problem and make connections between representations. In the course of learning mathematics and solving mathematical problems students will develop resilience and optimism.

Staff seek to inspire and motivate their students and the subject is presented in a wide variety of ways including those using technology such as computers and interactive whiteboards. Students will also use a scientific calculator to perform calculations involving powers, roots and Pi.

Learning will take place through well-structured, differentiated lessons delivered at an appropriate pace using challenge and assessment for learning. Engaging starters to provide social, cultural and educational opportunities for learning. Lessons are scaffolded to promote challenge and differentiation by outcome, as neither the English Language or English Literature terminal exams are tiered. All our Schemes of Learning provide modelling of reading and writing examples to develop appropriate exam-related skills.

Students will be given a Baseline assessment when they first join the school which will determine their approximate working at grade. They will then be given a levelled assessment each half term.

Links to Literacy will include the spelling and definitions of new words associated with mathematics. Students’ work will be checked for spelling, punctuation and grammar. Awareness of terminology in functional skills exam questions. Students will be given an understanding of how things work in real life eg. understanding ten pin bowling scores, in preparation for functional skills exams.

Following Whole School Literacy Policy as displayed in all classrooms and:

• Use capital letters and full-stops correctly.
• Use commas and apostrophes correctly.
• Spell regular words correctly.
• Use homophones correctly.
• Use a wider range of vocabulary.
• Use semi colons and colons.
• Use clear sentences.

Social – Development of problem solving skills and reasoning skills and team work. Being able to justify methods and ideas. Communicating with others and explaining concepts to each other. Making sense of the data available in the modern world around them.

Moral – Use and interpretation of data that is becoming more prevalent in society. Maths in real life contexts such as finance and implications

Cultural – Islamic geometric patterns and discussing mathematics in cultural symbols and patterns (Rangoli patterns, symmetry, tessellations and Islamic geometric patterns). exchange rates for foreign travel, links to mathematicians such as Fibonacci and discussion on ratio and proportion in the real world e.g. Golden ratio. Encouragement of various approaches to mathematics influenced by different cultures, discussions on the cultural and historical roots of maths

Spiritual – sense of wonder in the exactness of maths as well as a sense of personal achievement in solving problems.

Progress data in the inside cover of exercise books as well as SIMS Tracking System and regular subject data analysis.

Estimation

Collecting Data and Averages

Measures

Fractions, Decimals and Percentages

Representing data

Percentages

Substitution

Ratio and Proportion

Sequences

Solving equations

Pythagoras

Indices

Quadratics

Calculations and BIDMAS

Area and perimeter

Similarity & congruency

Transformations

Inequalities

Simultaneous Equations

Constructions & Loci

Volume & Surface Area

Vectors

Will be able to know the definitions of expressions, equations, formulae., functions, inequalities and terms. Form simple algebraic expressions and formulae. Round to decimal places and significant figures. Complete a tally chart,

construct and complete grouped frequency tables, interpret two-way tables. find averages from a list. Estimate the size of everyday objects,

know suitable units to use to estimate or measure length, mass and capacity,work out time intervals.

Secure students:

Will be able to form an expression to show the area and perimeter of simple shapes. Use arithmetic operations with algebra. Collect like terms. Multiply a single term over a bracket and factorise a linear expression. use function machines. expand and simplify over two linear brackets. can expand a double bracket. factorise a quadratic expression where the coefficient of x2 is 1. Estimate an answer before calculating and truncate a number to a given degree of accuracy. Find a missing piece of data given the mean,

construct and complete frequency trees, compare the mean, median, mode and range as appropriate of two distributions, understand which measure of average is most appropriate and consider outliers. Find averages from a bar chart and stem and leaf diagrams, find averages from frequency tables. plan journeys using timetables,

convert between metric units of measure, convert between imperial units of measure, calculate with speed, distance and time, construct and interpret distance-time graphs, construct and interpret simple velocity-time graphs, calculate with mass, density and volume, calculate with pressure, force and area, calculate with exchange rates.

Excelling students:

Will be able to factorise an expression using the difference of two squares. form quadratic expressions. form an expression to show the area and perimeter of complex shapes. rearrange formulae including fractions and powers to make a different variable the subject. expand more than two brackets. n factorise a quadratic expression where the coefficient of x2 is greater than 1. simplify and manipulate algebraic expressions including algebraic fractions. use inequality notation to specify simple error intervals for rounding and truncation. Interpolate and extrapolate apparent trends and understand the dangers of doing so. Complete and interpret a table for time series data,

understand and use sampling methods including understanding their limitations, complete a cumulative frequency table, find quartiles and interquartile range, estimate averages from a histogram, understand the capture-recapture method. understand that area under a velocity-time graph is acceleration,

understand that area under a speed-time graph is distance covered, can convert between compound and area units, can convert between units of measure including compound units from algebraic contexts.

Will be able to Order negative integers,

use negative numbers in context and calculate with negative numbers. Convert between fractions, decimals and percentages

find percentages of amounts without a calculator, find percentages of amounts with a calculator. Use fraction notation to describe parts of shapes, convert between fractions, decimals and percentages, simplify and find equivalent fractions. Construct, interpret and compare bar charts, vertical line graphs and pictograms. find percentages of amounts without a calculator

find percentages of amounts with a calculator. Will be able to substitute into an expression and

use function machines.

Secure students:

Will be able to find a fraction of an amount,

calculate with decimals, recognise common recurring decimals as fractions, multiply and divide numbers by powers of ten, order fractions and decimals and calculate with fractions and mixed numbers. Give the square root of a number, identify factors and multiples, identify the HCF and LCM, square, cube and triangle numbers. Construct, interpret and compare frequency polygons, pie charts, stem and leaf diagrams and scatter graphs. Increase/decrease an amount by a percentage,

write one number as a percentage of another, calculate the percentage change e.g. profit/loss. Substitute positive and negative numbers into expressions and formulae, including scientific expressions

substitute into functions.

Excelling students:

.

Will be able to do tests of divisibility,

do prime factor decomposition including using product notation, use prime factor decomposition to find the HCF or LCM. Use multipliers to find a percentage of an amount and to increase and decrease by a percentage,

find the original amount after a percentage change, use percentages to find the simple interest over a number of years. find the compound interest over a number of years. Find reciprocals understand the effect of multiplying and dividing by a number between 0 and 1, write one number as a fraction of another, simplify and manipulate algebraic expressions including algebraic fractions, convert between recurring decimals and fractions. Find the equation of a line of best fit and interpret in context. Construct, interpret and compare cumulative frequency diagrams, histograms and box plots. use prime factor decomposition to decide whether a number is square etc. Interpret the reverse process as the inverse function,

interpret the succession of two functions as the composite function and find composite and inverse functions.

Will be able to Identify types of angles and use standard conventions for labelling sides and angles of triangles,

find missing angles on a straight line and around a point, identify vertically opposite angles, derive and use the sum of angles in a triangle. Write and simplify ratios (including different units),

calculate equivalent ratios. Find terms in sequences

generate sequences given term to term or an nth term. solve one step equations,

solve one step equations including negatives. Expand two brackets.

Secure students:

Will be able to find missing angles in parallel lines,

find interior and exterior angles in quadrilaterals and other polygons, find out how many sides a polygon has given interior angles, find and use bearings. Write a ratio as a fraction,

express a relationship between two quantities as a ratio or fraction, share and amount in a ratio, solve ratio problems given in contexts (eg conversion, scaling, mixing and concentrations), understand proportion as equality of a ratio, draw using scales, calculate best buys and value for money, convert between different currencies. Recognise and use triangular, square, cube and simple arithmetic progressions.

Calculate the nth term of a linear sequence. Solve two step equations,

solve two step equations including negatives and brackets, solve equations with unknowns on both sides and brackets.

Excelling students:

Will be able to use circle theorems,

prove circle theorems and form geometric proofs. Relate ratios to linear functions,

use unitary ratios to compare amounts solve ratio problems given one of the shares and NOT the total, interpret equations which describe direct and inverse proportion, recognise and interpret graphs that illustrate direct and inverse proportion, compare lengths, areas and volumes using ratio notation and scale factors. Recognise and use Fibonacci, quadratic and simple geometric progressions (rⁿ where n is an integer and r is a rational number >0).

Find the nth term of a quadratic sequence. solve equations involving fractions,

form and solve equations, interpreting the solution, find approximate solutions to equations numerically using iteration.

Will be able to use trigonometric ratios to find any side or angle in a right- angled triangle. Use Pythagoras’ theorem to find unknown sides of a triangle.​ Calculate basic square and cube numbers,

estimate the value of a square root, multiply and divide by powers of 10.

Secure students:

Will be able to find the area of an isosceles triangle using Pythagoras’ Theorem.​ Use Pythagoras’ Theorem to find the distance between two points. Sketch trigonometric graphs and know the exact values, Calculate trigonometric ratios in surd form. Insert brackets & operations into a calculation to make it true,

use one calculation to find the answer to another. Recognise and use index notation evaluate simple indices (e.g. 2⁴, 3³), understand that anything raised to the power of 0 is equal to 1, evaluate and calculate with numbers written in standard form, calculate with roots and with integer indices, use index laws to evaluate algebraic and numerical expressions (multiplication, division and brackets).

Excelling students:

Will be able to Recognise, sketch and interpret trigonometric functions  for angles of any size,

find angle solutions using trigonometric graphs between 0≤θ≤360° (in degrees only), solve trigonometric equations with solutions between 0≤θ≤360°. Find the missing angle between a line and a plane, use sine rule to find missing sides & angles, use cosine rule to find missing sides & angles, use the area of a triangle using . Use Pythagoras’ Theorem in 3D shapes. Understand the difference between subtracting a squared number and squaring a negative number. Evaluate negative indices,

rationalise denominators, simplify surds, simplify and manipulate expressions including surds (including algebraic expressions), evaluate fractional indices, recognise geometric progressions (rⁿ where n is an integer and r is a surd), calculate exactly with surds.

Will be able to place events on a probability scale, use words to describe probability,

calculate simple probabilities. Use inequality symbols. Expand two brackets.

Use a calculator efficiently. Name and identify properties of 2D & 3D shapes,

recognise parallel and perpendicular lines, identify and construct nets. Identify congruent shapes by comparing sides and angles,

identify similar shapes.

Secure students:

Will be able to find the probability of an event not occurring,

list outcomes from events, use a sample space to calculate probabilities, find probabilities from two-way tables, that exhaustive probability sums to one, record, describe and analyse the frequency of probability experiments using tables and frequency trees. Plot quadratic graphs,

factorise a quadratic expression and solve when the coefficient of  is , solve quadratic equations by factorisation, use quadratic graphs to estimate the solution to an equation. Insert brackets & operations into a calculation to make it true,

use one calculation to find the answer to another. Find the area and perimeter of 2D shapes including compound shapes by counting squares or using formulae,

identify and apply circle vocabulary including: centre, radius, chord, diameter, circumference. Calculate missing side lengths given areas and perimeters, including circles, identify and apply circle vocabulary including: tangent, arc, sector and segment, find the area and circumference of a circle. Find the scale factor for similar shapes,

find unknown sides and angles using similarity.

Excelling students:

Will be able to apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events,

relate relative expected frequencies to theoretical probability, enumerate sets and combinations of sets systematically using tables, grids & Venn diagrams complete and use a Venn diagram, construct and interpret a tree diagram with replacement, use the ‘and’ & ‘or’ rule to calculate probabilities. Identify roots, intercepts and turning points of quadratic functions graphically,

factorise a quadratic expression and solve, when the coefficient of  is greater than 1, solve quadratic equations by completing the square and using the formula, including those that require rearrangement and those where coefficient of  is greater than , identify turning points by completing the square. Understand the difference between subtracting a squared number and squaring a negative number. find the area and perimeter of sectors, including arc length,

find the area of compound shapes including sectors, construct and interpret plans & elevations, calculate exactly with multiples of π, find the area and perimeter of segments, find the area of compound shapes including segments. Compare lengths, areas and volumes using ratio notation and scale factors including trigonometric ratios,

obtain simple proofs by applying angle facts, triangle congruence, similarity and properties of quadrilaterals (prove two triangles are congruent or similar), prove two triangles are congruent.

Will be able to plot and read coordinates in all 4 quadrants,

find the coordinates of points identified by geometrical information in 2D. Describe & complete a translation using 2D vectors,

describe & complete a rotation. Use inequality symbols,

represent and evaluate inequalities on a number line. Solve a pair of linear simultaneous equations.

Use a ruler and a compass to construct:  angles, use correct notation for labelling lines, angles and triangles. Find the volume by counting cubes,

find the volume and surface area of cubes, cuboids & prisms.  Calculate with vectors including addition and subtraction and multiplication by a scalar.

.

Secure students:

Will be able to find midpoints and end points, plot a graph of a linear functions, identify the gradient and y intercept from graphs and equations e.g. , recognise, sketch and interpret linear graphs. Describe & complete a reflection,

describe & complete a positive integer enlargement. Draw and shade inequalities on a graph. Form and solve simultaneous equations. Know that the perpendicular distance from a point to a line is the shortest distance to the line, use a ruler and a compass to construct the midpoint and perpendicular bisector of a line segment, use a ruler and a compass to construct the bisector of an angle, use a ruler and a compass to construct the perpendicular from a point to a line, use a ruler and a compass to construct the perpendicular from a point on a line. Find the volume of cylinders,

link volume to capacity, find the surface area of cylinders, find the surface area of simple compound 3D shapes, find the volume and surface area of pyramids including cones. Use diagrammatic and column representations of vectors.

Excelling students:

Will be able to identify parallel lines by comparing gradients,

find the equation of a straight line given the gradient and a point, find the equation of a straight line given two points, identify perpendicular lines by comparing gradients, calculate and estimate gradients of graphs and areas under graphs and interpret results. Know that translations, rotations and reflections preserve length and angle, mapping objects to congruent images,

know that enlargements preserve angle but not length and produce similar, can describe & complete fractional enlargements. Solve inequalities in two variables,

solve quadratic inequalities in one variable, solve inequalities using set notation, use inequalities and regions to solve real life problems. Graphically solve simultaneous equations,

solve simultaneous equations where one equation is quadratic or the equation of a circle. Solve loci problems

construct SAS, ASA and SSS triangles, including equilateral triangles from a sketch or written description. Find the volume and surface area of spheres,

find missing lengths of a prism given the volume,

find the volume and surface area of more complex 3D shapes. Prove two vectors are parallel or perpendicular,

use vectors to construct geometric arguments and proofs.

Mean

Square Numbers

Mass

Estimate

Simple Interest

Tally Chart

Percentage

Improper Fractions

Multiple

Formulae

Sequence

Ratio

Proportion

Equivalent

Simplify

Interior Angles

Parallel Lines

Square Root

Quadrilateral

Polygon

Area

Perimeter

Radius

Powers

Operations

Expand

Probability

Reflection

Surface Area

Volume

— = part of departmental termly list and Frayer model display

Frequency

Factorise

Velocity

Significant Figure

Stem and Leaf

Factorise

Inequalities

Equivalent

Square Root

Quadratic Expression

Truncate

Depreciation

Reciprocals

Error Interval

Upper Bound

Correlation

Multiplier

Recurring

Integer

Compound Interest

Nth Term

Linear Sequence

Fibonacci Sequence

Unitary Ratios

Direct Proportion

Inverse Proportion

Corresponding Angles

Alternate Angles

Opposite Angles

Unknown Variables

Hypotenuse

Adjacent

Isosceles Triangle

Trigonometry

Pythagoras Theorem

Index Notation

Standard Form

Indices

Negative Indices

Fractional Indices

Compound shapes

Trapezium

Diameter

Chord

Inverse

Congruent

Quadratic Graphs

Intercept

Venn Diagram

Tree Diagram

Linear Graph

Gradient

Vector

Translate

Inequalities

Coefficient

Unknown Variables

Construct

Perpendicular

Capacity

These units are taught now because it has number at their heart and as a result has a large proportion of time spent reinforcing number to build competency.

These units are taught now because it develops on from number and gives the pupils opportunities to build competency in solving problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

These units are taught now so that students can transfer number and problem solving skills and will learn how to use mathematics in unfamiliar circumstances including problem solving and reasoning to ensure mastery and fluency across the curriculum.

Term 1

Term 2

Directed numbers/FDP

Charts & Graphs

Algebra Expanding & Factorising

Solving Equations

Probability

Ratio/HCF/LCM

Inequalities & Bounds

Rearranging Formulae

Simultaneous equations

Area and perimeter

Pythagoras Theorem

Indices and St. Form

Volume/SA/Plans/ Nets

Conversion rates/graphs

Plotting lines and curves

Calculator Skills

Constructions/ Transformations & Vectors

Angles

Sequences

Trigonometry

Exam techniques.

Targeted assistance sessions.

Analysis of Mock papers and previous assessments.

Exam techniques.

Targeted assistance sessions.

Analysis of Mock papers and previous assessments.

Knowledge/ Skills to be developed and enhanced

Developing students:

Students will be able to round to decimal places and significant figures. Order negative integers,

use negative numbers in context and calculate with negative numbers. Convert between fractions, decimals and percentages. Complete a tally chart, construct and complete grouped frequency tables, interpret two-way tables. find averages from a list. Construct, interpret and compare bar charts, vertical line graphs and pictograms. Know the definitions of expressions, equations, formulae., functions, inequalities and terms. Form simple algebraic expressions and formulae. solve one step equations, solve one step equations including negatives. Expand two brackets.

Secure students:

Students will be able to Estimate an answer before calculating and truncate a number to a given degree of accuracy. find a fraction of an amount, calculate with decimals, recognise common recurring decimals as fractions, multiply and divide numbers by powers of ten, order fractions and decimals and calculate with fractions and mixed numbers. Give the square root of a number, identify factors and multiples, identify the HCF and LCM, square, cube and triangle numbers. Construct, interpret and compare frequency polygons, pie charts, stem and leaf diagrams and scatter graphs. form an expression to show the area and perimeter of simple shapes. Use arithmetic operations with algebra. Collect like terms. Multiply a single term over a bracket and factorise a linear expression. use function machines. expand and simplify over two linear brackets. can expand a double bracket. factorise a quadratic expression where the coefficient of x2 is 1. Solve two step equations, solve two step equations including negatives and brackets, solve equations with unknowns on both sides and brackets.

Excelling students:

Students will be able to use inequality notation to specify simple error intervals for rounding and truncation. Use multipliers to find a percentage of an amount and to increase and decrease by a percentage, find the original amount after a percentage change, use percentages to find the simple interest over a number of years. find the compound interest over a number of years. Find reciprocals understand the effect of multiplying and dividing by a number between 0 and 1, write one number as a fraction of another, simplify and manipulate algebraic expressions including algebraic fractions, convert between recurring decimals and fractions. Find the equation of a line of best fit and interpret in context. Construct, interpret and compare cumulative frequency diagrams, histograms and box plots. factorise an expression using the difference of two squares. form quadratic expressions. form an expression to show the area and perimeter of complex shapes. rearrange formulae including fractions and powers to make a different variable the subject. expand more than two brackets. n factorise a quadratic expression where the coefficient of x2 is greater than 1. simplify and manipulate algebraic expressions including algebraic fractions. solve equations involving fractions,

form and solve equations, interpreting the solution, find approximate solutions to equations numerically using iteration.

Developing students:

.

Students will be able to construct, interpret and compare bar charts, vertical line graphs and pictograms. Complete a tally chart,

construct and complete grouped frequency tables, interpret two-way tables. find averages from a list. Place events on a probability scale, use words to describe probability, calculate simple probabilities. Use inequality symbols. Write and simplify ratios (including different units), calculate equivalent ratios. Use inequality symbols, represent and evaluate inequalities on a number line. Rearrange simple formulae involving 1 or 2 steps. Solve a pair of linear simultaneous equations. Calculate the area and perimeter of simple shapes Eg, square, rectangles, triangles and parallelograms. Use Pythagoras’ theorem to find unknown sides of a triangle.​

Secure students:

Students will be able to Construct, interpret and compare frequency polygons, pie charts, stem and leaf diagrams and scatter graphs. Find a missing piece of data given the mean, construct and complete frequency trees, compare the mean, median, mode and range as appropriate of two distributions, understand which measure of average is most appropriate and consider outliers. Find averages from a bar chart and stem and leaf diagrams, find averages from frequency tables. Find the probability of an event not occurring,

list outcomes from events, use a sample space to calculate probabilities, find probabilities from two-way tables, that exhaustive probability sums to one, record, describe and analyse the frequency of probability experiments using tables and frequency trees. Write a ratio as a fraction, express a relationship between two quantities as a ratio or fraction, share and amount in a ratio, solve ratio problems given in contexts (eg conversion, scaling, mixing and concentrations), understand proportion as equality of a ratio, draw using scales, calculate best buys and value for money, convert between different currencies. Estimate an answer before calculating and truncate a number to a given degree of accuracy. Draw and shade inequalities on a graph. simplify and manipulate algebraic expressions including algebraic fractions. Form and solve simultaneous equations. Calculate missing side lengths given areas and perimeters, including circles, identify and apply circle vocabulary including: tangent, arc, sector and segment, find the area and circumference of a circle. find the area of an isosceles triangle using Pythagoras’ Theorem.​ Use Pythagoras’ Theorem to find the distance between two points.

Excelling students:

Students will be able to construct, interpret and compare cumulative frequency diagrams, histograms and box plots. complete a cumulative frequency table, find quartiles and interquartile range, estimate averages from a histogram, understand the capture-recapture method. apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events, relate relative expected frequencies to theoretical probability, enumerate sets and combinations of sets systematically using tables, grids & Venn diagrams complete and use a Venn diagram, construct and interpret a tree diagram with replacement, use the ‘and’ & ‘or’ rule to calculate probabilities. Relate ratios to linear functions,

use unitary ratios to compare amounts solve ratio problems given one of the shares and NOT the total, interpret equations which describe direct and inverse proportion, recognise and interpret graphs that illustrate direct and inverse proportion, compare lengths, areas and volumes using ratio notation and scale factors. solve quadratic inequalities in one variable, solve inequalities using set notation, use inequalities and regions to solve real life problems. Graphically solve simultaneous equations,

solve simultaneous equations where one equation is quadratic or the equation of a circle. find the area and perimeter of sectors, including arc length,

find the area of compound shapes including sectors, construct and interpret plans & elevations, calculate exactly with multiples of π, find the area and perimeter of segments, find the area of compound shapes including segments. Use Pythagoras’ Theorem in 3D shapes.

Developing students:

Students will be able to identify and apply circle vocabulary including: centre, radius, chord, diameter, circumference. Calculate basic square and cube numbers,

estimate the value of a square root, multiply and divide by powers of 10. Find the volume by counting cubes,

find the volume and surface area of cubes, cuboids & prisms. Estimate the size of everyday objects,

know suitable units to use to estimate or measure length, mass and capacity,work out time intervals. Plot and read coordinates in all 4 quadrants, find the coordinates of points identified by geometrical information in 2D.

Secure students:

Students will be able to calculate missing side lengths given areas and perimeters, including circles, identify and apply circle vocabulary including: tangent, arc, sector and segment, find the area and circumference of a circle. Recognise and use index notation evaluate simple indices (e.g. 2⁴, 3³), understand that anything raised to the power of 0 is equal to 1, evaluate and calculate with numbers written in standard form, calculate with roots and with integer indices, use index laws to evaluate algebraic and numerical expressions (multiplication, division and brackets). Find the volume of cylinders,

link volume to capacity, find the surface area of cylinders, find the surface area of simple compound 3D shapes, find the volume and surface area of pyramids including cones. Find midpoints and end points, plot a graph of a linear functions, identify the gradient and y intercept from graphs and equations e.g. , recognise, sketch and interpret linear graphs.

Excelling students:

Students will be able to find the area and perimeter of sectors, including arc length. Evaluate negative indices, rationalise denominators, simplify surds, simplify and manipulate expressions including surds (including algebraic expressions), evaluate fractional indices, recognise geometric progressions (rⁿ where n is an integer and r is a surd), calculate exactly with surds. Find the volume and surface area of spheres, find missing lengths of a prism given the volume, find the volume and surface area of more complex 3D shapes. To identify parallel lines by comparing gradients,

find the equation of a straight line given the gradient and a point, find the equation of a straight line given two points, identify perpendicular lines by comparing gradients, calculate and estimate gradients of graphs and areas under graphs and interpret results.

Developing students:

Students will be able to estimate the size of everyday objects,

know suitable units to use to estimate or measure length, mass and capacity, work out time intervals. Use a calculator efficiently. Use a ruler and a compass to construct:  angles, use correct notation for labelling lines, angles and triangles. Describe & complete a translation using 2D vectors, describe & complete a rotation. Calculate with vectors including addition and subtraction and multiplication by a scalar. Identify types of angles and use standard conventions for labelling sides and angles of triangles, find missing angles on a straight line and around a point, identify vertically opposite angles, derive and use the sum of angles in a triangle. Find terms in sequences, generate sequences given term to term or an nth term. use trigonometric ratios to find any side or angle in a right- angled triangle.

Secure students:

Students will be able to convert between metric units of measure, convert between imperial units of measure, calculate with speed, distance and time, construct and interpret distance-time graphs, construct and interpret simple velocity-time graphs, calculate with mass, density and volume, calculate with pressure, force and area, calculate with exchange rates. Know that the perpendicular distance from a point to a line is the shortest distance to the line, use a ruler and a compass to construct the midpoint and perpendicular bisector of a line segment, use a ruler and a compass to construct the bisector of an angle, use a ruler and a compass to construct the perpendicular from a point to a line, use a ruler and a compass to construct the perpendicular from a point on a line. Describe & complete a reflection,

describe & complete a positive integer enlargement. Use diagrammatic and column representations of vectors. find missing angles in parallel lines,

find interior and exterior angles in quadrilaterals and other polygons, find out how many sides a polygon has given interior angles, find and use bearings. Recognise and use triangular, square, cube and simple arithmetic progressions. Calculate the nth term of a linear sequence. Sketch trigonometric graphs and know the exact values, Calculate trigonometric ratios in surd form.

Excelling students:

Students will be able to understand that area under a velocity-time graph is acceleration,

understand that area under a speed-time graph is distance covered, can convert between compound and area units, can convert between units of measure including compound units from algebraic contexts. Solve loci problems

construct SAS, ASA and SSS triangles, including equilateral triangles from a sketch or written description. Know that translations, rotations and reflections preserve length and angle, mapping objects to congruent images,

know that enlargements preserve angle but not length and produce similar, can describe & complete fractional enlargements. Prove two vectors are parallel or perpendicular, use vectors to construct geometric arguments and proofs. Use circle theorems,

prove circle theorems and form geometric proofs. Recognise and use Fibonacci, quadratic and simple geometric progressions (rⁿ where n is an integer and r is a rational number >0).

Find the nth term of a quadratic sequence. Recognise, sketch and interpret trigonometric functions  for angles of any size, find angle solutions using trigonometric graphs between 0≤θ≤360° (in degrees only), solve trigonometric equations with solutions between 0≤θ≤360°. Find the missing angle between a line and a plane, use sine rule to find missing sides & angles, use cosine rule to find missing sides & angles, use the area of a triangle using .

Catering – Recipes

Bricklaying. Gardening – laying turf.

Mode

Directed Numbers

Frequency Polygons

Inverse

Probability

Frequency Tables

Proportion

Mixed Number

Hypotenuse

Simultaneous Equations

Radius

Cube Numbers

Volume

Translate

Conversion Graphs

Estimate

Gradients

Time Intervals

Construct

Reflection

Solve

Expand

Simplify

Justify

Sketch

Calculate

Measure

Show

Prove

Product

— = part of departmental termly list and Frayer model display

Factorise

Significant Figure

Recurring

Correlation

Variables

Reciprocals

Cumulative Frequency

Coefficient

Linear Equations

Compound Interest

Stem and Leaf

Venn Diagrams

Unitary Ratios

Inequality Symbols

Inverse Function

Truncate

Compound Shapes

Perpendicular Lines

Isosceles Triangle

Error Intervals

Diameter

Tangent

Index Notation

Standard Form

Capacity

Front/Side Elevations

Density

Velocity

Nets of 3D shapes

Negative indices

Index Number

Midpoint

Vectors

Congruent

Vertex

Arc Length

Polygons

Linear Sequence

Nth Term

Adjacent

Quadratic

Interquartile

Integer

HCF/LCM

Function Machine

Inverse Proportion

Bearings

Chord

Scalene Triangle

Cosine

Segment

Sector

Scale Factor

Trigonometric Ratios

Intercepts

Cubic Graphs

Cylinder

Compound Area

Algebraic Fractions

Cumulative Graph

These units are taught now because it has number at their heart and as a result has a large proportion of time spent reinforcing number to build competency.

These units are taught now because it develops on from number and gives the pupils opportunities to build competency in solving problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

These units are revisited now so that students feel confident with these topics in preparation for the final exams.

Students will have the opportunity to demonstrate aspects of the learning model through identifying the strategies needed to solve mathematical problems, working with others to solve more complex problems and being able to discuss and justify techniques and methods used. They will be encouraged to review progress as they work, check and evaluate solutions and modify their approach if necessary. Students will be given opportunities to evaluate their strengths and limitations and to set realistic targets. Students will develop their ability to visualise and illustrate a maths problem and make connections between representations. In the course of learning mathematics and solving mathematical problems students will develop resilience and optimism.

Staff seek to inspire and motivate their students and the subject is presented in a wide variety of ways including those using technology such as computers and interactive whiteboards. Students will also use a scientific calculator to perform calculations involving powers, roots and Pi.

Learning will take place through well-structured, differentiated lessons delivered at an appropriate pace using challenge and assessment for learning. Engaging starters to provide social, cultural and educational opportunities for learning. Lessons are scaffolded to promote challenge and differentiation by outcome, as neither the English Language or English Literature terminal exams are tiered. All our Schemes of Learning provide modelling of reading and writing examples to develop appropriate exam-related skills.

Students will be given a Baseline assessment when they first join the school which will determine their approximate working at grade. They will then be given a levelled assessment each half term.

Links to Literacy will include the spelling and definitions of new words associated with mathematics. Students’ work will be checked for spelling, punctuation and grammar. Awareness of terminology in functional skills exam questions. Students will be given an understanding of how things work in real life eg. understanding ten pin bowling scores, in preparation for functional skills exams.

Following Whole School Literacy Policy as displayed in all classrooms and:

• Use capital letters and full-stops correctly.
• Use commas and apostrophes correctly.
• Spell regular words correctly.
• Use homophones correctly.
• Use a wider range of vocabulary.
• Use semi colons and colons.
• Use clear sentences.

Social – Development of problem solving skills and reasoning skills and team work. Being able to justify methods and ideas. Communicating with others and explaining concepts to each other. Making sense of the data available in the modern world around them.

Moral – Use and interpretation of data that is becoming more prevalent in society. Maths in real life contexts such as finance and implications

Cultural – Islamic geometric patterns and discussing mathematics in cultural symbols and patterns (Rangoli patterns, symmetry, tessellations and Islamic geometric patterns). exchange rates for foreign travel, links to mathematicians such as Fibonacci and discussion on ratio and proportion in the real world e.g. Golden ratio. Encouragement of various approaches to mathematics influenced by different cultures, discussions on the cultural and historical roots of maths

Spiritual – sense of wonder in the exactness of maths as well as a sense of personal achievement in solving problems.

Progress data in the inside cover of exercise books as well as SIMS Tracking System and regular subject data analysis.