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
Pupils 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 attainers
Pupils 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) / Tier 4
(mainly level 5) / Tier 5
(mainly level 6)
High attainers
Pupils who achieved level 5 at KS2 and will be entered for the level 6–8 test. / Tier 4
(mainly level 5) / Tier 5
(mainly level 6) / Tier 6
(mainly level 7)
Gifted and talented
Pupils who achieved a strong level 5 at KS2 and will be entered for the level 6–8 test. / Tier 5
(mainly level 6) / Tier 6
(mainly level 7) / Tier 7
(mainly level 8)

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
1 Place value
2 Adding and subtracting
3 Money problems
4 Properties of shapes
5 Tables, graphs and charts / R1.2 Revision unit 2
1 Sequences
2 Multiplying and dividing
3 Fractions
4 Measures
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
G2.4 Measures / 1 Converting units
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
1 Measures and measuring scales
2 Solving number problems
3 Sequences and patterns
4 Perimeter and area
5 Drawing and interpreting graphs
and charts / R2.2 Revision unit 2
1 Inverse operations
2 Equivalent fractions, decimals and percentages
3 Expressions and equations
4 Symmetry and reflection
5 Probability
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