exploring maths and a condensed key stage...

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 1-3G1.1 Properties of shapes 1-3N1.2 Adding and subtracting 1-9A1.1 Patterns and sequences 1, 2, 3, 6, 7G1.2 Angles and symmetry 1, 2, 4N1.3 Multiplying and dividing 1-4S1.1 Graphs and charts 1 1, 3N1.4 Mental calculations 1-7 G1.3 Measures 1 1-5N1.5 Fractions 1-2S1.2 Graphs and charts 2 1-5N1.6 Money and decimals 1-5G1.4 Measures 2 1-5N1.7 Numbers and measures 1-5G1.5 More properties of shapes 1, 2, 4, 5, 6N1.8 Multiplying and dividing 2 1, 2, 4S1.3 Graphs and charts 3 1, 3, 5G1.6 Measures 3 1-6

Tier 2

Unit Lessons

N2.1 Properties of numbers 1, 3N2.2 Whole numbers 1-3, 5, 6-8A2.1 Patterns and sequences 1-5N2.3 Fractions, decimals and percentages 1-6G2.1 Length, perimeter and area 1-4G2.2 Angles 1-3N2.4 Decimals 1-6A2.2 Sequences, functions and graphs 1, 2, 3, 5G2.3 Symmetry and reflection 1-3Exploring maths 2yrks3 - 1 -

N2.5 Decimals and measures 1-6S2.3 Enquiry 1 1-5G2.4 Measures 1-5N2.6 Fractions, percentages and direct proportion 2, 3, 5, 6S2.4 Probability 2 1, 3G2.5 Properties of shapes 1-7A2.3 Expressions and equations 1-5S2.5 Enquiry 2 1-5

Tier 3

Unit Lessons

N3.1 Properties of numbers 1, 2, 4, 5A3.1 Sequences and patterns 1-5N3.2 Whole numbers and decimals 1-5G3.1 Area and perimeter 1-3N3.3 Fractions and percentages 1-7S3.1 Grouped data and simple statistics 1-3G3.2 Angles 1-3S3.2 Probability 1 1-3N3.4 Decimals and measure 1-6A3.2 Equations and formulae 1-5S3.3 Enquiry 1 1, 2, 5A3.3 Functions and graphs 2-5G3.3 Transformations 1-5N3.5 Percentages, ratio and proportion 1-4G3.4 Properties of shapes 1, 2, 5S3.4 Enquiry 2 1-5G3.5 Constructions 1, 2, 3, 5, 6A3.4 Using algebra 1-7S3.5 Probability 2 1-3

Tier 4

Unit Lessons

N4.1 Properties of numbers 1-5G4.1 Angles and shapes 1, 2, 3, 5A4.1 Linear sequences 1, 2, 4N4.2 Whole numbers, decimals and fractions 1-5S4.1 Probability 1-4A4.2 Expressions and formulae 1, 2, 4G4.2 Measures and mensuration 1-5N4.3 Fractions, decimals and percentages 1-5S4.2 Enquiry 1 1-6A4.3 Functions and graphs 1, 3, 4, 5N4.4 Proportional reasoning 1-4G4.3 Transformations 1-7A4.4 Equations and formulae 2, 3, 4, 5, 6S4.3 Enquiry 2 1-7G4.4 Constructions 1, 2, 3, 6, 7

Exploring maths 2yrks3 - 2 -

A4.5 Using algebra 1-8Tier 5

Unit Lessons

N5.1 Powers and roots 1, 3A5.1 Sequences and graphs 1, 2, 4, 5, 6G5.1 Angles and constructions 1-8N5.2 Proportional reasoning 1-6S5.2 Enquiry 1 1-6A5.2 Equations and formulae 1-6G5.2 Measures and mensuration 1-6N5.3 Calculations and calculators 1-6S5.2 Probability 1 1-3A5.3 Functions and graphs 1, 2, 4, 5, 6G5.3 Transformations 2, 4, 6A5.4 Using algebra 1-3S5.3 Enquiry 2 1-7G5.4 2D and 3D s hapes 1, 2, 4, 5, 7, 8A5.5 Equations, formulae and graphs 1, 3, 4, 5, 6, 7S5.4 Probability 2 1-4

Tier 6

Unit Lessons

N6.1 Powers and roots 1-3A6.1 Expressions and formulae 1-6N6.2 Proportional reasoning 1-6S6.1 Enquiry 1 2-6G6.1 Geometrical reasoning 1-6A6.2 Linear graphs and inequalities 1,3, 4, 5G6.2 Trigonometry 1 1-3A6.3 Algebraic expressions and equations 1, 3, 4, 5, 7G6.3 Transformations and loci 1-6N6.3 Decimals and accuracy 2-5S6.2 Probability 1 1-5G6.4 Measures and mensuration 12, 3, 4, 6S6.3 Enquiry 2 3-7G6.5 Trigonometry 2 1, 2, 3, 5, 6, 7, 8A6.4 Using algebra 1-5S6.4 Probability 2 1-4N6.4 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 attainersPupils who achieved a good level 3 or weak level 4 at KS2 and will be entered for the level 4–6 test.

Tier 2(NC levels 3–4)

Tier 3(both levels 4 and 5)

Tier 4(mainly level 5)

Average attainersPupils who achieved a secure level 4 at KS2 and will be entered for the level 5–7 test.

Tier 3(both levels 4 and 5)



High attainersPupils who achieved level 5 at KS2 and will be entered for the level 6–8 test.




Gifted and talentedPupils who achieved a strong level 5 at KS2 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 102 Multiples of 2 or 53 Odd and even numbers

G1.1 Properties of shapes 1 Describing and recognising 2D shapes2 Describing and recognising 3D shapes3 Angles and lines

N1.2 Adding and subtracting 1 Place value, ordering and rounding2 Number facts to 203 Mental strategies4 More mental strategies5 Written methods: addition6 Written methods: subtraction7 Word problems8 Using a calculator9 Number investigations

A1.1 Patterns and sequences 1 Multiplication patterns2 Simple sequences3 More multiplication patterns6 Multiplying by 10 or 1007 Multiplying bigger numbers

G1.2 Angles and symmetry 1 Symmetry2 More symmetry4 Angles

N1.3 Multiplying and dividing 1 Doubling and halving2 Sixes and eights3 Multiplication4 Division and remainders

S1.1 Graphs and charts 1 1 Lists and tables3 Bar charts

N1.4 Mental calculations 1 Quick ways to add and subtract2 Adding and subtracting two-digit numbers3 Inverse operations4 Introducing thousands5 Multiplying and dividing by 10 or 1006 Working out new facts7 Sevens and nines

G1.3 Measures 1 1 Reading time2 A long time3 What measurements to use?4 The metric system5 Measuring length

N1.5 Fractions 1 Fractions of shapes2 Fractions of numbers


Tier 1 cont.S1.2 Graphs and charts 2 1 Tally charts and frequency diagrams

2 Bar charts3 Pictograms4 Carroll diagrams5 Venn diagrams

N1.6 Money and decimals 1 Coins and notes2 Pounds and pence3 Money problems4 Tenths5 Tenths and hundredths

G1.4 Measures 2 1 Clocks and timetables2 Seconds, minutes, hours, days and weeks3 Scales4 Mass5 Capacity

N1.7 Numbers and measures 1 Positive and negative numbers2 Reading scales3 Adding tenths4 Tenths and hundredths5 Metres, centimetres and millimetres

G1.5 More properties of shapes 1 Properties of polygons2 Making 2D shapes and patterns4 Angle5 Compass points6 Coordinates

N1.8 Multiplying and dividing 2 1 Tables to 102 Multiplying by multiples of 104 Multiplication

S1.3 Graphs and charts 3 1 Lists and tables3 Bar charts5 Interpreting pictograms

G1.6 Measures 3 1 Clock, timetables and calendars2 Reading scales3 Standard metric units 14 Standard metric units 25 Perimeter6 Area

Optional Revision units for use at any point in Tier 1

R1.1 Revision unit 11 Place value2 Adding and subtracting3 Money problems4 Properties of shapes5 Tables, graphs and charts

R1.2 Revision unit 2 1 Sequences2 Multiplying and dividing3 Fractions4 Measures5 Charts and graphs


Tier 2

Unit Lessons

N2.1 Properties of numbers 1 Square numbers3 Positive and negative integers

N2.2 Whole numbers 1 Place value, ordering and rounding2 Mental addition and subtraction3 Written methods5 Multiplying and dividing by 10, 100 and 10006 Multiplication tables7 Multiplication8 Division

A2.1 Patterns and sequences 1 Continuing sequences2 Sequences from rules3 Multiples4 Factors5 Investigating patterns

N2.3 Fractions, decimals and percentages

1 Fractions of shapes2 Equivalent fractions3 Fractions of quantities4 Decimal place value5 Tenths and hundredths6 Percentages of quantities

G2.1 Length, perimeter and area 1 Length2 Perimeter3 Finding areas by counting squares4 Area of rectangles

G2.2 Angles 1 Amounts of turn2 Measuring angles3 Drawing angles

N2.4 Decimals 1 Decimals and the number line2 Ordering decimals3 Rounding4 Decimals and money5 Adding and subtracting decimals6 Using a calculator

A2.2 Sequences, functions and graphs

1 Sequences2 Function machines3 Finding the rule5 Coordinates

G2.3 Symmetry and reflection 1 Reflection2 Symmetry3 Translation

N2.5 Decimals and measures 1 Metres, centimetres and millimetres2 Converting units of measurements3 Reading scales4 Time5 Remainders6 Word problems


S2.3 Enquiry 1 1 Collecting and organising data2 Venn and Carroll diagrams3 Bar charts and pie charts4 Bar-line graphs5 Mode and range

G2.4 Measures1 Converting units2 Reading scales3 Estimating and measuring4 Time intervals5 Timetables

N2.6 Fractions, percentages and direct proportion

2 Fractions, decimals and percentages3 Percentages of quantities5 Introducing ratio and proportion6 Scaling up and down

S2.4 Probability 2 1 Probability scale3 Equally likely outcomes

G2.5 Properties of shapes 1 Parallel and perpendicular lines2 Properties of shapes3 Classifying shapes4 Angles5 Drawing 2D shapes on grids6 Making shapes and solids7 Nets

A2.3 Expressions and equations 1 Order of operations2 Using brackets3 Letters for numbers4 Collecting like terms5 Substitution

S2.5 Enquiry 2 1 Collecting data2 Representing data3 Interpreting data4 Drawing conclusions and writing a report5 Line graphs


R2.1 Revision unit 11 Measures and measuring scales2 Solving number problems3 Sequences and patterns4 Perimeter and area5 Drawing and interpreting graphs and charts

R2.2 Revision unit 21 Inverse operations2 Equivalent fractions, decimals and percentages3 Expressions and equations4 Symmetry and reflection5 Probability


Tier 3

Unit Lessons

N3.1 Properties of numbers 1 Positive and negative integers2 Order of operations and brackets4 Multiples and tests of divisibility5 Factors, primes, HCF and LCM

A3.1 Sequences and patterns 1 Sequences and rules2 Find missing terms3 Sequences from patterns4 Using a letter symbol5 Finding a term from its position

N3.2 Whole numbers and decimals

1 Place value2 Ordering and rounding3 Mental calculations4 Written calculations5 Using a calculator

G3.1 Area and perimeter 1 Area and perimeter of rectangles2 Irregular shapes3 Surface area of cuboids

N3.3 Fractions and percentages 1 Fractions of shapes2 Equivalent fractions3 Changing fractions to decimals4 Equivalent fractions, decimals and %6 Fractions of whole-number quantities7 Percentages of whole-number quantities

S3.1 Grouped data and simple statistics

1 Constructing charts and tables2 Calculating statistics3 Interpreting graphs and diagrams

G3.2 Angles 1 Measuring and drawing angles2 Angles on a straight line3 Angles at a point

S3.2 Probability 1 1 The probability scale2 Equally likely outcomes3 Probability experiments

N3.4 Decimals and measure 1 Estimating and converting measurements2 Reading scales4 Problems involving time5 Multiplication and division calculations6 Solving problems with a calculator


A3.2 Equations and formulae 1 Terms and expressions2 Multiplying terms in brackets3 Formulae4 Equations: addition and subtraction5 Equations: multiplication and division

S3.3 Enquiry 1 1 Planning a project2 Collecting data 15 Interpreting charts and graphs

A3.3 Functions and graphs 2 Plotting points3 Straight-line graphs4 Plotting straight-line graphs5 Sequences

G3.3 Transformations 1 Line symmetry2 Reflections3 Rotation symmetry4 Rotations5 Translations

N3.5 Percentages, ratio and proportion

1 Equivalent fractions and percentages2 Finding percentages, including discounts3 Dividing a quantity in a given ratio4 Direct proportion

G3.4 Properties of shapes 1 Parallel and perpendicular lines2 Properties of shapes 15 Angle sum of a triangle

S3.4 Enquiry 2 1 Collecting data2 Calculating statistics3 Using statistics4 Representing data5 Interpreting and discussing data

G3.5 Constructions 1 Drawing line segments and parallel lines2 Constructing shapes with right angles3 Acute, obtuse and reflex angles5 Nets of 3D shapes6 Properties of 3D shapes

A3.4 Using algebra 1 Working with expressions2 Functions and equations3 Solving equations4 Square and triangular numbers5 More sequences from patterns7 Interpreting real-life graphs 2

S3.5 Probability 2 1 Equally likely outcomes2 Experimental probability3 Comparing probabilities



R3.1 Revision unit 11 Whole number and decimal calculations2 Fractions, decimals and percentages3 Expressions and equations4 Charts, graphs and simple statistics5 Probability

R3.2 Revision unit 21 Solving word problems2 Ratio3 Sequences, functions and graphs4 Area and perimeter5 Symmetry and transformations


Tier 4

Unit Lessons

N4.1 Properties of numbers 1 Order of operations2 Adding and subtracting directed numbers3 Multiplying and dividing directed numbers4 Powers and roots5 Multiples, factors and primes

G4.1 Angles and shapes 1 Corresponding angles2 Alternate angles3 Angles in a triangle and quadrilateral5 Properties of quadrilaterals

A4.1 Linear sequences 1 Term-to-term rules2 Position-to-term rules4 Exploring patterns

N4.2 Whole numbers, decimals and fractions

1 Place value2 Ordering, adding and subtracting decimals3 Multiplication and division calculations4 Using a calculator5 Equivalent fractions and fractions of quantities

S4.1 Probability 1 Theoretical probability2 Events not happening3 The probability of two events4 Experimental probability

A4.2 Expressions and formulae 1 Simplifying expressions2 Using formulae4 Using algebraic expressions

G4.2 Measures and mensuration 1 Conversion between units2 Perimeter and area of triangles3 Perimeter and area of quadrilaterals4 Volume of cuboids5 Surface area of cuboids

N4.3 Fractions, decimals and percentages

1 Ordering fractions2 Calculations with fractions3 Multiplying and dividing decimals 14 Multiplying and dividing decimals 25 Calculating percentages

S4.2 Enquiry 1 1 Specifying the problem and planning2 Processing data3 Representing data4 Analysing data sets5 Comparing groups6 Presenting results


A4.3 Functions and graphs 1 Plotting points3 Functions, equations and graphs4 Sketching graphs5 Interpreting equations of graphs

N4.4 Proportional reasoning 1 Dividing a quantity in a given ratio2 Solving ratio problems3 Scale drawings4 Direct proportion – the unitary method

G4.3 Transformations 1 Repeated transformations2 Using transformations to solve problems4 Scale factor5 Centre of enlargement7 Finding the midpoint

A4.4 Equations and formulae 2 Solving linear equations3 More linear equations4 Forming equations and formulae5 Equations with brackets6 Terms with x on both sides of the equation

S4.3 Enquiry 2 1 Collecting continuous data2 Processing and representing continuous data3 Analysing and interpreting distributions4 Communicating findings5 Mean, median and range6 Comparing experimental and theoretical

probability7 Line graphs for time series

G4.4 Constructions 1 Drawing arcs and circles2 Constructing midpoints and bisectors3 Constructing triangles on paper6 Scale drawings7 Using bearings

A4.5 Using algebra 1 Simplifying expressions2 Factorising expressions3 Solving linear equations4 Sketching linear graphs5 Drawing and interpreting linear graphs6 Interpreting graphs of real-life situations7 Word problems8 Geometrical problems


R4.1 Revision unit 11 Place value2 Solving calculations problems3 Expressions and sequences4 Perimeter, area and volume5 Probability

R4.2 Revision unit 21 Percentages2 Ratio and proportion3 Equations and graphs4 Angles and transformations5 Representing and interpreting data


Tier 5

Unit Lessons

N5.1 Powers and roots 1 Working with integer powers of numbers3 Prime factor decomposition

A5.1 Sequences and graphs 1 Generating sequences2 Making generalisations4 Sketching linear graphs5 Rearranging linear equations6 Graphs using real-life contexts

G5.1 Angles and constructions 1 Angles in polygons2 Regular polygons5 Polygons and parallel lines6 Constructions7 Constructing triangles8 Loci

N5.2 Proportional reasoning 1 Adding and subtracting fractions2 Multiplying fractions3 Dividing fractions4 Percentage change5 Ratio6 Direct proportion

S5.2 Enquiry 1 1 Stem-and-leaf diagrams2 Starting investigation 13 Completing investigation 14 Data collection sheets5 Starting investigation 26 Completing investigation 2

A5.2 Equations and formulae 1 Multiplying out brackets2 Factorising expressions3 Substituting into formulae4 Changing the subject of a formula5 Solving linear equations6 Trial and improvement

G5.2 Measures and mensuration 1 Perimeter and area2 Finding p3 Area of a circle4 Solving circle problems and using p5 Volume of prisms6 Surface area of prisms

N5.3 Calculations and calculators 1 Powers of 102 Rounding and approximation3 Mental calculations with decimals4 Written calculations with decimals5 Using a calculator6 Problems involving measures

S5.2 Probability 1 1 Theoretical and experimental probability2 Mutually exclusive events3 Using experimental probability


A5.3 Functions and graphs 1 Generating linear graphs using ICT2 Sketching graphs4 Drawing accurate graphs5 Direct proportion6 Simple quadratic graphs using ICT

G5.3 Transformations 2 Combined transformations4 Enlargements6 Length, area and volume

A5.4 Using algebra 1 Using graphs to solve problems2 Using algebra in geometry problems3 Using algebra in investigations

S5.3 Enquiry 2 1 Calculating statistics2 Line graphs for time series3 Scatter graphs4 Planning and collecting data5 Organising and presenting data6 Analysing and interpreting data7 Reporting and evaluating

G5.4 2D and 3D shapes 1 Exploring angles and lines2 Solving problems4 Drawing 3D objects5 Drawing plans and elevations7 Solving problems using surface area and

volume8 Surface area and volume of prisms

A5.5 Equations, formulae and graphs

1 Factorising3 Working with formulae4 Forming equations5 Visualising graphs6 Interpreting graphs7 Matching graphs to real-life situations

S5.4 Probability 2 1 Simple probability2 Equally likely outcomes with two events3 Mutually exclusive events4 Practical probability experiments


R5.1 Revision unit 11 Efficient calculations2 Using percentages to compare

proportions3 Sequences, equations and

graphs4 Angles and polygons5 Constructing and interpreting

diagrams

R5.2 Revision unit 21 Ratio and proportion2 Solving number problems3 Expressions, equations and formulae4 Circles and enlargements5 Probability


Tier 6

Unit Lessons

N6.1 Powers and roots 1 Squares, cubes and roots2 Equivalent calculations using powers of 103 Standard form

A6.1 Expressions and formulae 1 Simplifying algebraic fractions2 Solving linear equations3 Expansion of brackets4 Factorising5 Identities6 Changing the subject of a formula

N6.2 Proportional reasoning 1 Fraction calculations3 Percentages and interest rates4 Reverse percentages5 Rate and speed6 Proportionality

S6.1 Enquiry 1 2 Grouped data – frequency polygons3 Grouped data – average and range 14 Grouped data – average and range 25 Comparing sets of grouped data6 Scatter graphs and lines of best fit

G6.1 Geometrical reasoning 1 Isosceles triangle problems2 Evidence or proof?3 Congruent triangles4 Radii, chords and tangents5 Similar shapes6 Introducing Pythagoras’ rule

A6.2 Linear graphs and inequalities

1 Sketching and drawing linear graphs3 Properties of linear graphs4 Solving simultaneous equations 15 Solving simultaneous equations 2

G6.2 Trigonometry 1 1 Introducing trigonometry2 Using tangent3 Using sine and cosine

A6.3 Algebraic expressions and equations

1 Simultaneous equations 13 Expanding brackets 14 Expanding brackets 25 Factorising quadratic expressions7 Solving quadratic equations graphically

G6.3 Transformations and loci 1 How long is that line?2 Divide that line3 Enlargement4 Rotation5 Combinations of transformations6 Loci 1


Tier 6 cont.N6.3 Decimals and accuracy 2 Significant figures

3 Using a calculator4 Back of an envelope calculations5 Measurement errors

S6.2 Probability 1 1 Relative frequency2 Exploring relative frequency3 Combined events4 Tree diagrams and independent events5 Probability experiments

G6.4 Measures and mensuration 1 Arcs and circumference2 Sectors and area3 Right-prisms and cylinders4 Units of area and volume6 Plans and elevations

S6.3 Enquiry 2 3 Drawing and interpreting frequency polygons4 Grouped data – estimating the mean5 Grouped data – average and range6 Scatter graphs and lines of best fit7 Lengths and angles 1

G6.5 Trigonometry 2 1 Using Pythagoras to find the hypotenuse2 Using Pythagoras’ rule to find a shorter side3 Triangles5 Using the trigonometry ratios6 Choosing between sine, cosine and tangent7 Finding lengths8 Tessellations

A6.4 Using algebra 1 Properties of linear graphs2 Parallel and perpendicular lines3 Generating quadratic graphs4 Generating cubic graphs5 Drawing quadratic graphs

S6.4 Probability 2 1 Ice cream sales2 Right or left or …?3 Tree diagrams and probability4 Relative frequency and theoretical probability

N6.4 Using and applying maths 3 Investigating paper sizes4 Proof


R6.1 Revision unit 11 Fractions and percentages2 Ratio and proportion3 Expressions and equations4 Angles and triangles5 Probability

R6.2 Revision unit 21 Decimals2 Sequences and graphs3 Graphs and equations4 2D and 3D shapes5 Grouped frequency


exploring maths and a condensed key stage...

Documents