Exploring maths and a condensed key stage 3



Exploring maths and a two-year key stage 3

Exploring maths is ideal for schools that want to cover the ks3 curriculum in two years. This guidance shows two different ways in which Exploring maths can be used.

Pupils in any year group who have completed Tier 4 or above successfully could be entered early for the Key Stage 3 test.

Approach 1

Exploring maths can be used to cover the key stage 3 curriculum in fewer lessons. Following this route would take 80 lessons per Tier.

Here are the lessons in Tiers 1 to 6 that cover the essential material for pupils taking this route.*

Any of the lessons that have been missed out could be used for consolidation or enrichment. Each Tier also has ten optional revision lessons that can be used at any time.

*Appendix 1 provides more detail by showing the lesson names in each unit.

|Tier 1 |

|Unit |Lessons |

|N1.1 Properties of numbers |1-3 |

|G1.1 Properties of shapes |1-3 |

|N1.2 Adding and subtracting |1-9 |

|A1.1 Patterns and sequences |1, 2, 3, 6, 7 |

|G1.2 Angles and symmetry |1, 2, 4 |

|N1.3 Multiplying and dividing |1-4 |

|S1.1 Graphs and charts 1 |1, 3 |

|N1.4 Mental calculations |1-7 |

|G1.3 Measures 1 |1-5 |

|N1.5 Fractions |1-2 |

|S1.2 Graphs and charts 2 |1-5 |

|N1.6 Money and decimals |1-5 |

|G1.4 Measures 2 |1-5 |

|N1.7 Numbers and measures |1-5 |

|G1.5 More properties of shapes |1, 2, 4, 5, 6 |

|N1.8 Multiplying and dividing 2 |1, 2, 4 |

|S1.3 Graphs and charts 3 |1, 3, 5 |

|G1.6 Measures 3 |1-6 |

| Tier 2 |

|Unit |Lessons |

|N2.1 Properties of numbers |1, 3 |

|N2.2 Whole numbers |1-3, 5, 6-8 |

|A2.1 Patterns and sequences |1-5 |

|N2.3 Fractions, decimals and percentages |1-6 |

|G2.1 Length, perimeter and area |1-4 |

|G2.2 Angles |1-3 |

|N2.4 Decimals |1-6 |

|A2.2 Sequences, functions and graphs |1, 2, 3, 5 |

|G2.3 Symmetry and reflection |1-3 |

|N2.5 Decimals and measures |1-6 |

|S2.3 Enquiry 1 |1-5 |

|G2.4 Measures |1-5 |

|N2.6 Fractions, percentages and direct proportion |2, 3, 5, 6 |

|S2.4 Probability 2 |1, 3 |

|G2.5 Properties of shapes |1-7 |

|A2.3 Expressions and equations |1-5 |

|S2.5 Enquiry 2 |1-5 |

|Tier 3 |

|Unit |Lessons |

|N3.1 Properties of numbers |1, 2, 4, 5 |

|A3.1 Sequences and patterns |1-5 |

|N3.2 Whole numbers and decimals |1-5 |

|G3.1 Area and perimeter |1-3 |

|N3.3 Fractions and percentages |1-7 |

|S3.1 Grouped data and simple statistics |1-3 |

|G3.2 Angles |1-3 |

|S3.2 Probability 1 |1-3 |

|N3.4 Decimals and measure |1-6 |

|A3.2 Equations and formulae |1-5 |

|S3.3 Enquiry 1 |1, 2, 5 |

|A3.3 Functions and graphs |2-5 |

|G3.3 Transformations |1-5 |

|N3.5 Percentages, ratio and proportion |1-4 |

|G3.4 Properties of shapes |1, 2, 5 |

|S3.4 Enquiry 2 |1-5 |

|G3.5 Constructions |1, 2, 3, 5, 6 |

|A3.4 Using algebra |1-7 |

|S3.5 Probability 2 |1-3 |

|Tier 4 |

|Unit |Lessons |

|N4.1 Properties of numbers |1-5 |

|G4.1 Angles and shapes |1, 2, 3, 5 |

|A4.1 Linear sequences |1, 2, 4 |

|N4.2 Whole numbers, decimals and fractions |1-5 |

|S4.1 Probability |1-4 |

|A4.2 Expressions and formulae |1, 2, 4 |

|G4.2 Measures and mensuration |1-5 |

|N4.3 Fractions, decimals and percentages |1-5 |

|S4.2 Enquiry 1 |1-6 |

|A4.3 Functions and graphs |1, 3, 4, 5 |

|N4.4 Proportional reasoning |1-4 |

|G4.3 Transformations |1-7 |

|A4.4 Equations and formulae |2, 3, 4, 5, 6 |

|S4.3 Enquiry 2 |1-7 |

|G4.4 Constructions |1, 2, 3, 6, 7 |

|A4.5 Using algebra |1-8 |

|Tier 5 |

|Unit |Lessons |

|N5.1 Powers and roots |1, 3 |

|A5.1 Sequences and graphs |1, 2, 4, 5, 6 |

|G5.1 Angles and constructions |1-8 |

|N5.2 Proportional reasoning |1-6 |

|S5.2 Enquiry 1 |1-6 |

|A5.2 Equations and formulae |1-6 |

|G5.2 Measures and mensuration |1-6 |

|N5.3 Calculations and calculators |1-6 |

|S5.2 Probability 1 |1-3 |

|A5.3 Functions and graphs |1, 2, 4, 5, 6 |

|G5.3 Transformations |2, 4, 6 |

|A5.4 Using algebra |1-3 |

|S5.3 Enquiry 2 |1-7 |

|G5.4 2D and 3D s hapes |1, 2, 4, 5, 7, 8 |

|A5.5 Equations, formulae and graphs |1, 3, 4, 5, 6, 7 |

|S5.4 Probability 2 |1-4 |

|Tier 6 |

|Unit |Lessons |

|N6.1 Powers and roots |1-3 |

|A6.1 Expressions and formulae |1-6 |

|N6.2 Proportional reasoning |1-6 |

|S6.1 Enquiry 1 |2-6 |

|G6.1 Geometrical reasoning |1-6 |

|A6.2 Linear graphs and inequalities |1,3, 4, 5 |

|G6.2 Trigonometry 1 |1-3 |

|A6.3 Algebraic expressions and equations |1, 3, 4, 5, 7 |

|G6.3 Transformations and loci |1-6 |

|N6.3 Decimals and accuracy |2-5 |

|S6.2 Probability 1 |1-5 |

|G6.4 Measures and mensuration |12, 3, 4, 6 |

|S6.3 Enquiry 2 |3-7 |

|G6.5 Trigonometry 2 |1, 2, 3, 5, 6, 7, 8 |

|A6.4 Using algebra |1-5 |

|S6.4 Probability 2 |1-4 |

|N6.4 Using and applying maths |3-4 |

Approach 2

If a school has made a substantial amount of extra teaching time available across the two years, teachers can use the materials with different groups as shown below.

Pupils would complete 1.5 Tiers in each year because they would be spending more time in maths lessons.

|ABILITY GROUP |FIRST YEAR (usually Y7) |SECOND YEAR (usually Y8) |

|Lower attainers |Tier 2 |Tier 3 |Tier 4 |

|Pupils who achieved a good level 3 or weak |(NC levels 3–4) |(both levels 4 and 5) |(mainly level 5) |

|level 4 at KS2 and will be entered for the | | | |

|level 4–6 test. | | | |

|Average attainers |Tier 3 |Tier 4 |Tier 5 |

|Pupils who achieved a secure level 4 at KS2 |(both levels 4 and 5) |(mainly level 5) |(mainly level 6) |

|and will be entered for the level 5–7 test. | | | |

|High attainers |Tier 4 |Tier 5 |Tier 6 |

|Pupils who achieved level 5 at KS2 and will be|(mainly level 5) |(mainly level 6) |(mainly level 7) |

|entered for the level 6–8 test. | | | |

|Gifted and talented |Tier 5 |Tier 6 |Tier 7 |

|Pupils who achieved a strong level 5 at KS2 |(mainly level 6) |(mainly level 7) |(mainly level 8) |

|and will be entered for the level 6–8 test. | | | |

Appendix 1 Exploring maths detailed two-year key stage 3 lesson pathway

|Tier 1 |

|Unit |Lessons |

|N1.1 Properties of numbers |1 Multiples of 10 |

| |2 Multiples of 2 or 5 |

| |3 Odd and even numbers |

|G1.1 Properties of shapes |1 Describing and recognising 2D shapes |

| |2 Describing and recognising 3D shapes |

| |3 Angles and lines |

|N1.2 Adding and subtracting |1 Place value, ordering and rounding |

| |2 Number facts to 20 |

| |3 Mental strategies |

| |4 More mental strategies |

| |5 Written methods: addition |

| |6 Written methods: subtraction |

| |7 Word problems |

| |8 Using a calculator |

| |9 Number investigations |

|A1.1 Patterns and sequences |1 Multiplication patterns |

| |2 Simple sequences |

| |3 More multiplication patterns |

| |6 Multiplying by 10 or 100 |

| |7 Multiplying bigger numbers |

|G1.2 Angles and symmetry |1 Symmetry |

| |2 More symmetry |

| |4 Angles |

|N1.3 Multiplying and dividing |1 Doubling and halving |

| |2 Sixes and eights |

| |3 Multiplication |

| |4 Division and remainders |

|S1.1 Graphs and charts 1 |1 Lists and tables |

| |3 Bar charts |

|N1.4 Mental calculations |1 Quick ways to add and subtract |

| |2 Adding and subtracting two-digit numbers |

| |3 Inverse operations |

| |4 Introducing thousands |

| |5 Multiplying and dividing by 10 or 100 |

| |6 Working out new facts |

| |7 Sevens and nines |

|G1.3 Measures 1 |1 Reading time |

| |2 A long time |

| |3 What measurements to use? |

| |4 The metric system |

| |5 Measuring length |

|N1.5 Fractions |1 Fractions of shapes |

| |2 Fractions of numbers |

Tier 1 cont.

|S1.2 Graphs and charts 2 |1 Tally charts and frequency diagrams |

| |2 Bar charts |

| |3 Pictograms |

| |4 Carroll diagrams |

| |5 Venn diagrams |

|N1.6 Money and decimals |1 Coins and notes |

| |2 Pounds and pence |

| |3 Money problems |

| |4 Tenths |

| |5 Tenths and hundredths |

|G1.4 Measures 2 |1 Clocks and timetables |

| |2 Seconds, minutes, hours, days and weeks |

| |3 Scales |

| |4 Mass |

| |5 Capacity |

|N1.7 Numbers and measures |1 Positive and negative numbers |

| |2 Reading scales |

| |3 Adding tenths |

| |4 Tenths and hundredths |

| |5 Metres, centimetres and millimetres |

|G1.5 More properties of shapes |1 Properties of polygons |

| |2 Making 2D shapes and patterns |

| |4 Angle |

| |5 Compass points |

| |6 Coordinates |

|N1.8 Multiplying and dividing 2 |1 Tables to 10 |

| |2 Multiplying by multiples of 10 |

| |4 Multiplication |

|S1.3 Graphs and charts 3 |1 Lists and tables |

| |3 Bar charts |

| |5 Interpreting pictograms |

|G1.6 Measures 3 |1 Clock, timetables and calendars |

| |2 Reading scales |

| |3 Standard metric units 1 |

| |4 Standard metric units 2 |

| |5 Perimeter |

| |6 Area |

|Optional Revision units for use at any point in Tier 1 |

|R1.1 Revision unit 1 |R1.2 Revision unit 2 |

|1 Place value |1 Sequences |

|2 Adding and subtracting |2 Multiplying and dividing |

|3 Money problems |3 Fractions |

|4 Properties of shapes |4 Measures |

|5 Tables, graphs and charts |5 Charts and graphs |

|Tier 2 |

|Unit |Lessons |

|N2.1 Properties of numbers |1 Square numbers |

| |3 Positive and negative integers |

|N2.2 Whole numbers |1 Place value, ordering and rounding |

| |2 Mental addition and subtraction |

| |3 Written methods |

| |5 Multiplying and dividing by 10, 100 and 1000 |

| |6 Multiplication tables |

| |7 Multiplication |

| |8 Division |

|A2.1 Patterns and sequences |1 Continuing sequences |

| |2 Sequences from rules |

| |3 Multiples |

| |4 Factors |

| |5 Investigating patterns |

|N2.3 Fractions, decimals and percentages |1 Fractions of shapes |

| |2 Equivalent fractions |

| |3 Fractions of quantities |

| |4 Decimal place value |

| |5 Tenths and hundredths |

| |6 Percentages of quantities |

|G2.1 Length, perimeter and area |1 Length |

| |2 Perimeter |

| |3 Finding areas by counting squares |

| |4 Area of rectangles |

|G2.2 Angles |1 Amounts of turn |

| |2 Measuring angles |

| |3 Drawing angles |

|N2.4 Decimals |1 Decimals and the number line |

| |2 Ordering decimals |

| |3 Rounding |

| |4 Decimals and money |

| |5 Adding and subtracting decimals |

| |6 Using a calculator |

|A2.2 Sequences, functions and graphs |1 Sequences |

| |2 Function machines |

| |3 Finding the rule |

| |5 Coordinates |

|G2.3 Symmetry and reflection |1 Reflection |

| |2 Symmetry |

| |3 Translation |

|N2.5 Decimals and measures |1 Metres, centimetres and millimetres |

| |2 Converting units of measurements |

| |3 Reading scales |

| |4 Time |

| |5 Remainders |

| |6 Word problems |

|S2.3 Enquiry 1 |1 Collecting and organising data |

| |2 Venn and Carroll diagrams |

| |3 Bar charts and pie charts |

| |4 Bar-line graphs |

| |5 Mode and range |

| |1 Converting units |

|G2.4 Measures |2 Reading scales |

| |3 Estimating and measuring |

| |4 Time intervals |

| |5 Timetables |

|N2.6 Fractions, percentages and direct proportion |2 Fractions, decimals and percentages |

| |3 Percentages of quantities |

| |5 Introducing ratio and proportion |

| |6 Scaling up and down |

|S2.4 Probability 2 |1 Probability scale |

| |3 Equally likely outcomes |

|G2.5 Properties of shapes |1 Parallel and perpendicular lines |

| |2 Properties of shapes |

| |3 Classifying shapes |

| |4 Angles |

| |5 Drawing 2D shapes on grids |

| |6 Making shapes and solids |

| |7 Nets |

|A2.3 Expressions and equations |1 Order of operations |

| |2 Using brackets |

| |3 Letters for numbers |

| |4 Collecting like terms |

| |5 Substitution |

|S2.5 Enquiry 2 |1 Collecting data |

| |2 Representing data |

| |3 Interpreting data |

| |4 Drawing conclusions and writing a report |

| |5 Line graphs |

|Optional Revision units for use at any point in Tier 2 |

|R2.1 Revision unit 1 |R2.2 Revision unit 2 |

|1 Measures and measuring scales |1 Inverse operations |

|2 Solving number problems |2 Equivalent fractions, decimals and percentages |

|3 Sequences and patterns |3 Expressions and equations |

|4 Perimeter and area |4 Symmetry and reflection |

|5 Drawing and interpreting graphs |5 Probability |

|and charts | |

|Tier 3 |

|Unit |Lessons |

|N3.1 Properties of numbers |1 Positive and negative integers |

| |2 Order of operations and brackets |

| |4 Multiples and tests of divisibility |

| |5 Factors, primes, HCF and LCM |

|A3.1 Sequences and patterns |1 Sequences and rules |

| |2 Find missing terms |

| |3 Sequences from patterns |

| |4 Using a letter symbol |

| |5 Finding a term from its position |

|N3.2 Whole numbers and decimals |1 Place value |

| |2 Ordering and rounding |

| |3 Mental calculations |

| |4 Written calculations |

| |5 Using a calculator |

|G3.1 Area and perimeter |1 Area and perimeter of rectangles |

| |2 Irregular shapes |

| |3 Surface area of cuboids |

|N3.3 Fractions and percentages |1 Fractions of shapes |

| |2 Equivalent fractions |

| |3 Changing fractions to decimals |

| |4 Equivalent fractions, decimals and % |

| |6 Fractions of whole-number quantities |

| |7 Percentages of whole-number quantities |

|S3.1 Grouped data and simple statistics |1 Constructing charts and tables |

| |2 Calculating statistics |

| |3 Interpreting graphs and diagrams |

|G3.2 Angles |1 Measuring and drawing angles |

| |2 Angles on a straight line |

| |3 Angles at a point |

|S3.2 Probability 1 |1 The probability scale |

| |2 Equally likely outcomes |

| |3 Probability experiments |

|N3.4 Decimals and measure |1 Estimating and converting measurements |

| |2 Reading scales |

| |4 Problems involving time |

| |5 Multiplication and division calculations |

| |6 Solving problems with a calculator |

|A3.2 Equations and formulae |1 Terms and expressions |

| |2 Multiplying terms in brackets |

| |3 Formulae |

| |4 Equations: addition and subtraction |

| |5 Equations: multiplication and division |

|S3.3 Enquiry 1 |1 Planning a project |

| |2 Collecting data 1 |

| |5 Interpreting charts and graphs |

|A3.3 Functions and graphs |2 Plotting points |

| |3 Straight-line graphs |

| |4 Plotting straight-line graphs |

| |5 Sequences |

|G3.3 Transformations |1 Line symmetry |

| |2 Reflections |

| |3 Rotation symmetry |

| |4 Rotations |

| |5 Translations |

|N3.5 Percentages, ratio and proportion |1 Equivalent fractions and percentages |

| |2 Finding percentages, including discounts |

| |3 Dividing a quantity in a given ratio |

| |4 Direct proportion |

|G3.4 Properties of shapes |1 Parallel and perpendicular lines |

| |2 Properties of shapes 1 |

| |5 Angle sum of a triangle |

|S3.4 Enquiry 2 |1 Collecting data |

| |2 Calculating statistics |

| |3 Using statistics |

| |4 Representing data |

| |5 Interpreting and discussing data |

|G3.5 Constructions |1 Drawing line segments and parallel lines |

| |2 Constructing shapes with right angles |

| |3 Acute, obtuse and reflex angles |

| |5 Nets of 3D shapes |

| |6 Properties of 3D shapes |

|A3.4 Using algebra |1 Working with expressions |

| |2 Functions and equations |

| |3 Solving equations |

| |4 Square and triangular numbers |

| |5 More sequences from patterns |

| |7 Interpreting real-life graphs 2 |

|S3.5 Probability 2 |1 Equally likely outcomes |

| |2 Experimental probability |

| |3 Comparing probabilities |

|Optional Revision units for use at any point in Tier 3 |

|R3.1 Revision unit 1 |R3.2 Revision unit 2 |

|1 Whole number and decimal |1 Solving word problems |

|calculations |2 Ratio |

|2 Fractions, decimals and |3 Sequences, functions and graphs |

|percentages |4 Area and perimeter |

|3 Expressions and equations |5 Symmetry and transformations |

|4 Charts, graphs and simple | |

|statistics | |

|5 Probability | |

|Tier 4 |

|Unit |Lessons |

|N4.1 Properties of numbers |1 Order of operations |

| |2 Adding and subtracting directed numbers |

| |3 Multiplying and dividing directed numbers |

| |4 Powers and roots |

| |5 Multiples, factors and primes |

|G4.1 Angles and shapes |1 Corresponding angles |

| |2 Alternate angles |

| |3 Angles in a triangle and quadrilateral |

| |5 Properties of quadrilaterals |

|A4.1 Linear sequences |1 Term-to-term rules |

| |2 Position-to-term rules |

| |4 Exploring patterns |

|N4.2 Whole numbers, decimals and fractions |1 Place value |

| |2 Ordering, adding and subtracting decimals |

| |3 Multiplication and division calculations |

| |4 Using a calculator |

| |5 Equivalent fractions and fractions of quantities |

|S4.1 Probability |1 Theoretical probability |

| |2 Events not happening |

| |3 The probability of two events |

| |4 Experimental probability |

|A4.2 Expressions and formulae |1 Simplifying expressions |

| |2 Using formulae |

| |4 Using algebraic expressions |

|G4.2 Measures and mensuration |1 Conversion between units |

| |2 Perimeter and area of triangles |

| |3 Perimeter and area of quadrilaterals |

| |4 Volume of cuboids |

| |5 Surface area of cuboids |

|N4.3 Fractions, decimals and percentages |1 Ordering fractions |

| |2 Calculations with fractions |

| |3 Multiplying and dividing decimals 1 |

| |4 Multiplying and dividing decimals 2 |

| |5 Calculating percentages |

|S4.2 Enquiry 1 |1 Specifying the problem and planning |

| |2 Processing data |

| |3 Representing data |

| |4 Analysing data sets |

| |5 Comparing groups |

| |6 Presenting results |

|A4.3 Functions and graphs |1 Plotting points |

| |3 Functions, equations and graphs |

| |4 Sketching graphs |

| |5 Interpreting equations of graphs |

|N4.4 Proportional reasoning |1 Dividing a quantity in a given ratio |

| |2 Solving ratio problems |

| |3 Scale drawings |

| |4 Direct proportion – the unitary method |

|G4.3 Transformations |1 Repeated transformations |

| |2 Using transformations to solve problems |

| |4 Scale factor |

| |5 Centre of enlargement |

| |7 Finding the midpoint |

|A4.4 Equations and formulae |2 Solving linear equations |

| |3 More linear equations |

| |4 Forming equations and formulae |

| |5 Equations with brackets |

| |6 Terms with x on both sides of the equation |

|S4.3 Enquiry 2 |1 Collecting continuous data |

| |2 Processing and representing continuous data |

| |3 Analysing and interpreting distributions |

| |4 Communicating findings |

| |5 Mean, median and range |

| |6 Comparing experimental and theoretical |

| |probability |

| |7 Line graphs for time series |

|G4.4 Constructions |1 Drawing arcs and circles |

| |2 Constructing midpoints and bisectors |

| |3 Constructing triangles on paper |

| |6 Scale drawings |

| |7 Using bearings |

|A4.5 Using algebra |1 Simplifying expressions |

| |2 Factorising expressions |

| |3 Solving linear equations |

| |4 Sketching linear graphs |

| |5 Drawing and interpreting linear graphs |

| |6 Interpreting graphs of real-life situations |

| |7 Word problems |

| |8 Geometrical problems |

|Optional Revision units for use at any point in Tier 4 |

|R4.1 Revision unit 1 |R4.2 Revision unit 2 |

|1 Place value |1 Percentages |

|2 Solving calculations problems |2 Ratio and proportion |

|3 Expressions and sequences |3 Equations and graphs |

|4 Perimeter, area and volume |4 Angles and transformations |

|5 Probability |5 Representing and interpreting data |

|Tier 5 |

|Unit |Lessons |

|N5.1 Powers and roots |1 Working with integer powers of numbers |

| |3 Prime factor decomposition |

|A5.1 Sequences and graphs |1 Generating sequences |

| |2 Making generalisations |

| |4 Sketching linear graphs |

| |5 Rearranging linear equations |

| |6 Graphs using real-life contexts |

|G5.1 Angles and constructions |1 Angles in polygons |

| |2 Regular polygons |

| |5 Polygons and parallel lines |

| |6 Constructions |

| |7 Constructing triangles |

| |8 Loci |

|N5.2 Proportional reasoning |1 Adding and subtracting fractions |

| |2 Multiplying fractions |

| |3 Dividing fractions |

| |4 Percentage change |

| |5 Ratio |

| |6 Direct proportion |

|S5.2 Enquiry 1 |1 Stem-and-leaf diagrams |

| |2 Starting investigation 1 |

| |3 Completing investigation 1 |

| |4 Data collection sheets |

| |5 Starting investigation 2 |

| |6 Completing investigation 2 |

|A5.2 Equations and formulae |1 Multiplying out brackets |

| |2 Factorising expressions |

| |3 Substituting into formulae |

| |4 Changing the subject of a formula |

| |5 Solving linear equations |

| |6 Trial and improvement |

|G5.2 Measures and mensuration |1 Perimeter and area |

| |2 Finding ( |

| |3 Area of a circle |

| |4 Solving circle problems and using ( |

| |5 Volume of prisms |

| |6 Surface area of prisms |

|N5.3 Calculations and calculators |1 Powers of 10 |

| |2 Rounding and approximation |

| |3 Mental calculations with decimals |

| |4 Written calculations with decimals |

| |5 Using a calculator |

| |6 Problems involving measures |

|S5.2 Probability 1 |1 Theoretical and experimental probability |

| |2 Mutually exclusive events |

| |3 Using experimental probability |

|A5.3 Functions and graphs |1 Generating linear graphs using ICT |

| |2 Sketching graphs |

| |4 Drawing accurate graphs |

| |5 Direct proportion |

| |6 Simple quadratic graphs using ICT |

|G5.3 Transformations |2 Combined transformations |

| |4 Enlargements |

| |6 Length, area and volume |

|A5.4 Using algebra |1 Using graphs to solve problems |

| |2 Using algebra in geometry problems |

| |3 Using algebra in investigations |

|S5.3 Enquiry 2 |1 Calculating statistics |

| |2 Line graphs for time series |

| |3 Scatter graphs |

| |4 Planning and collecting data |

| |5 Organising and presenting data |

| |6 Analysing and interpreting data |

| |7 Reporting and evaluating |

|G5.4 2D and 3D shapes |1 Exploring angles and lines |

| |2 Solving problems |

| |4 Drawing 3D objects |

| |5 Drawing plans and elevations |

| |7 Solving problems using surface area and |

| |volume |

| |8 Surface area and volume of prisms |

|A5.5 Equations, formulae and graphs |1 Factorising |

| |3 Working with formulae |

| |4 Forming equations |

| |5 Visualising graphs |

| |6 Interpreting graphs |

| |7 Matching graphs to real-life situations |

|S5.4 Probability 2 |1 Simple probability |

| |2 Equally likely outcomes with two events |

| |3 Mutually exclusive events |

| |4 Practical probability experiments |

|Optional Revision units for use at any point in Tier 5 |

|R5.1 Revision unit 1 |R5.2 Revision unit 2 |

|1 Efficient calculations |1 Ratio and proportion |

|2 Using percentages to compare |2 Solving number problems |

|proportions |3 Expressions, equations and formulae |

|3 Sequences, equations and |4 Circles and enlargements |

|graphs |5 Probability |

|4 Angles and polygons | |

|5 Constructing and interpreting | |

|diagrams | |

|Tier 6 |

|Unit |Lessons |

|N6.1 Powers and roots |1 Squares, cubes and roots |

| |2 Equivalent calculations using powers of 10 |

| |3 Standard form |

|A6.1 Expressions and formulae |1 Simplifying algebraic fractions |

| |2 Solving linear equations |

| |3 Expansion of brackets |

| |4 Factorising |

| |5 Identities |

| |6 Changing the subject of a formula |

|N6.2 Proportional reasoning |1 Fraction calculations |

| |3 Percentages and interest rates |

| |4 Reverse percentages |

| |5 Rate and speed |

| |6 Proportionality |

|S6.1 Enquiry 1 |2 Grouped data – frequency polygons |

| |3 Grouped data – average and range 1 |

| |4 Grouped data – average and range 2 |

| |5 Comparing sets of grouped data |

| |6 Scatter graphs and lines of best fit |

|G6.1 Geometrical reasoning |1 Isosceles triangle problems |

| |2 Evidence or proof? |

| |3 Congruent triangles |

| |4 Radii, chords and tangents |

| |5 Similar shapes |

| |6 Introducing Pythagoras’ rule |

|A6.2 Linear graphs and inequalities |1 Sketching and drawing linear graphs |

| |3 Properties of linear graphs |

| |4 Solving simultaneous equations 1 |

| |5 Solving simultaneous equations 2 |

|G6.2 Trigonometry 1 |1 Introducing trigonometry |

| |2 Using tangent |

| |3 Using sine and cosine |

|A6.3 Algebraic expressions and equations |1 Simultaneous equations 1 |

| |3 Expanding brackets 1 |

| |4 Expanding brackets 2 |

| |5 Factorising quadratic expressions |

| |7 Solving quadratic equations graphically |

|G6.3 Transformations and loci |1 How long is that line? |

| |2 Divide that line |

| |3 Enlargement |

| |4 Rotation |

| |5 Combinations of transformations |

| |6 Loci 1 |

Tier 6 cont.

|N6.3 Decimals and accuracy |2 Significant figures |

| |3 Using a calculator |

| |4 Back of an envelope calculations |

| |5 Measurement errors |

|S6.2 Probability 1 |1 Relative frequency |

| |2 Exploring relative frequency |

| |3 Combined events |

| |4 Tree diagrams and independent events |

| |5 Probability experiments |

|G6.4 Measures and mensuration |1 Arcs and circumference |

| |2 Sectors and area |

| |3 Right-prisms and cylinders |

| |4 Units of area and volume |

| |6 Plans and elevations |

|S6.3 Enquiry 2 |3 Drawing and interpreting frequency polygons |

| |4 Grouped data – estimating the mean |

| |5 Grouped data – average and range |

| |6 Scatter graphs and lines of best fit |

| |7 Lengths and angles 1 |

|G6.5 Trigonometry 2 |1 Using Pythagoras to find the hypotenuse |

| |2 Using Pythagoras’ rule to find a shorter side |

| |3 Triangles |

| |5 Using the trigonometry ratios |

| |6 Choosing between sine, cosine and tangent |

| |7 Finding lengths |

| |8 Tessellations |

|A6.4 Using algebra |1 Properties of linear graphs |

| |2 Parallel and perpendicular lines |

| |3 Generating quadratic graphs |

| |4 Generating cubic graphs |

| |5 Drawing quadratic graphs |

|S6.4 Probability 2 |1 Ice cream sales |

| |2 Right or left or …? |

| |3 Tree diagrams and probability |

| |4 Relative frequency and theoretical probability |

|N6.4 Using and applying maths |3 Investigating paper sizes |

| |4 Proof |

|Optional Revision units for use at any point in Tier 6 |

|R6.1 Revision unit 1 |R6.2 Revision unit 2 |

|1 Fractions and percentages |1 Decimals |

|2 Ratio and proportion |2 Sequences and graphs |

|3 Expressions and equations |3 Graphs and equations |

|4 Angles and triangles |4 2D and 3D shapes |

|5 Probability |5 Grouped frequency |

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