KS3 & KS4 Maths
curriculum plan
Higher (KS4)
Contents
Our curriculum
Threads
Maths curriculum explainer
Year 7 units
Year 8 units
Year 9 units
Year 10 units
Year 11 units
Threads in maths
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Our curriculum
All of our curricula share the same set of principles that guide our curriculum design to ensure
our curricula are high-quality. They are:
Knowledge and vocabulary
rich
Lessons and units are knowledge and
vocabulary rich. Pupils will build on what
they already know to develop deep
knowledge and apply this knowledge in the
form of skills.
Sequenced and coherent
Careful sequencing and attention to building
coherence via vertical threads so that pupils
build on prior knowledge and make
meaningful connections.
Flexible
Our flexible curriculum enables schools to
tailor our content to their curriculum and
context.
Accessible
Creating an accessible curriculum that
addresses the needs of all pupils and meets
accessibility guidelines and requirements.
Diverse
We prioritise creating a diverse curriculum
by committing to diversity in teaching and
teachers, and the language, texts and media
we use, so all pupils feel positively
represented.
Evidence-informed
We take an evidence-informed approach
applying the science of learning and subjectspecific research.
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Threads
What are threads?
We use threads to signpost groups of units that link to one another, that together build a
common body of knowledge over time. We use the term thread, rather than vertical concepts,
themes or big ideas, because it helps us bring to mind the visual concept of a thread weaving
through the curriculum.
How to use threads
1. Familiarise yourself with all of the threads relating to the subject
2. Identify the unit you will be delivering
3. Review the threads associated with the unit
4. Audit where pupils have and will learn about these threads in your existing curriculum
sequence.
5. Ensure you understand how the thread relating to your new unit has been framed in prior
and future units
6. Review how the thread works within the unit you will be delivering
7. Teach and iterate your framing of the thread within the unit and across your curriculum
sequence
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Threads in subject

Algebra

Geometry and Measure

Number

Probability

Ratio and Proportion

Statistics
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Tools for using threads
Online curriculum
Our interactive tool enables you to
visualise how threads are
sequenced across our curriculum
plans.
Go to online curriculum
Threads in this document
The appendix displays the threads
and their related units.
Go to threads appendix
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Maths curriculum explainer
Aims and purpose
What are the aims and purpose of our curriculum?
This curriculum develops pupils’ understanding of mathematics over time so that they become
competent and confident in identifying and performing the mathematics they need both at
school and in their daily lives. We prepare pupils to become self-assured and resilient
mathematicians by developing their ability to select the most suitable tools to solve problems
across a range of topics and real-world scenarios.
Oak curriculum principles
What overarching curriculum principles inform the design of our
curriculum?
Knowledge and vocabulary rich
This principle recognises the important role that knowledge, and vocabulary as a particularly
important type of knowledge, plays in learning. We identify and map vocabulary across the
curriculum, both in terms of the introduction of new vocabulary and the necessary repetition of
vocabulary that has gone before. New vocabulary, called keywords, are signalled in bold in our
lesson materials to indicate their importance. Our curriculum develops pupils' knowledge and
understanding of mathematical concepts over time. For example, understanding of concepts
such as ‘factor’ and ‘equation’ evolves with increasing complexity as pupils move through the
key stages.
Sequenced and coherent
A careful and purposeful sequencing of our curriculum content underpins its design, ensuring
that pupils are able to build on and make links with existing knowledge. At its simplest this
means ensuring, for example, that pupils learn about the square and square root functions
before meeting Pythagoras’ Theorem. Attention is paid to vertical coherence in the curriculum
through the strategic mapping of mathematical concepts across the curriculum, allowing for their
incremental development over time. Curriculum content is intentionally revisited, for example, a
lesson on right-angled trigonometry may retrieve construction or circle theorem content, or a
lesson on ratios will use familiar models and tools to explicitly link to prior learning.
Evidence-informed
Our evidence-informed approach enables the rigorous application of research outcomes,
science of learning and impactful best practice both in education in general and at a subject
specific level. For example, the design of our resources reflects findings from Sweller’s cognitive
load theory and Mayer’s principles of multimedia learning whilst our lesson design draws on
Rosenshine’s principles of instruction. We also draw on findings from research organisations
such as the Education Endowment Foundation (EEF). At the subject level, our primary
mathematics curriculum is inspired by the NCETM Curriculum Prioritisation materials to develop
mastery of core concepts at an early age.
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Flexible
Our flexible approach enables schools to use our resources in a way that fits their context and
meets the varying needs of teachers and their pupils. Our curriculum can be used in its entirety
or units can be selected to complement existing curricula. Our resources are adaptable so that,
for example, teachers can change the mathematical model used to teach a concept to align with
their agreed department or school approach or adapt practice tasks to better reflect the prior
knowledge of their pupils. At key stage 4 our curriculum aligns with all exam board specifications
for GCSE Mathematics.
Diverse
Our commitment to breadth and diversity in content, language, texts and media can be seen in
our choices of real world contexts, mathematics history and application of mathematics plus the
use of a group of diverse school age characters. For example, we use real data sets when
analysing charts to make discussions and conjectures meaningful and grounded in recognisable
places, situations and events.
Accessible
Our curriculum is intentionally designed to facilitate high-quality teaching as a powerful lever to
support pupils with SEND. Aligned with EEF guidance, our resources have a focus on clear
explanations, modelling and frequent checks for understanding, with guided and independent
practice. Lessons are chunked into learning cycles and redundant images and information are
minimised to manage cognitive load. We have removed reference to year groups in our
resources so that they can be used when pupils are ready, regardless of their age. Our
resources are purposefully created to be accessible, for example by using accessible fonts,
colours with good contrast, and captions in our videos. We have used Equatio’s equation editor
to create digital, accessible written mathematics in our resources.
Oak subject principles
What subject specific principles inform the design of our curriculum?
Pairing procedural knowledge with conceptual understanding.
We introduce concepts and prompts to make pupils think hard about making sense of ideas,
while also focusing on efficient procedural methods to ensure calculations can be completed
easily and systematically. We often provide visual models to support understanding, then we
remove scaffolding as ideas progress and foundation knowledge becomes secure, in order to
aid development of mathematical fluency.
Aligning with the Concrete Pictorial Abstract approach to mathematics teaching and
learning.
We incorporate consistent visual models to explain mathematical ideas, and draw upon existing
knowledge directly through the models and tools used where underpinning concepts are the
same as those taught previously. We make use of pictorial representations of familiar concrete
manipulatives such as Dienes blocks, algebra tiles and double sided counters.
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Use an agreed set of models and representations which bridge mathematical concepts.
We have identified and used the smallest set of models and representations that underpin and
support the understanding of the greatest number of mathematical concepts. When pupils meet
familiar tools and approaches this signals explicit links between implicitly connected elements of
mathematics. For example, ratio tables are used to calculate the dimensions of similar shapes,
percentage changes, plotting coordinates and equivalent fractions which signposts the links
between them. For maximum impact, these models and representations are shared by both our
primary and secondary curricula.
Use of variation theory in practice tasks and modelling.
Modelling and practice makes use of variation to minimise the risk of pupils drawing incorrect
inferences which can cause misconceptions to develop. For example, varying the orientation of
shapes in geometry to ensure pupils understand that a horizontal base is not a ‘feature’ of a
particular type of shape, or that the ‘base’ of a triangle when calculating the area is not confined
to being a horizontal side. We also use minimally different examples in some tasks to draw
attention to singular changes and how they affect mathematical models and calculations.
National curriculum
How does our curriculum reflect the aims & purpose of the national
curriculum?
There are three main aims of the national curriculum for mathematics: fluency, reasoning and
problem solving. Our curriculum ensures that all pupils become fluent in the fundamentals of
mathematics. For example, small steps when teaching the knowledge and understanding of
counting, helps build fluency in simple addition and subtraction. Pupils are supported and
encouraged to reason mathematically by justifying decisions when choosing whether something
is true or false, providing the answer to a calculation or conjecturing when identifying patterns.
Lastly, our curriculum ensures pupils can solve problems through lessons at the end of each
unit that apply the knowledge they have learnt to new and sometimes unfamiliar contexts.
Curriculum delivery
What teaching time does our curriculum require?
Our curricula for key stages 1-3 are designed for 36 weeks of curriculum time across the school
year, leaving time for other activities both within and beyond the curriculum such as
assessments or school trips. At key stage 4, year 10 also has approximately 36 weeks of
curriculum time, but year 11 has only 24 weeks (around 2 terms) to recognise that schools will
not be teaching new content in the run up to the GCSE exams.
Our maths curriculum provides roughly a lesson a day for all key stages and year groups. Our
key stage 1 lessons are designed to be taught in approximately 40 minutes, and 50 minutes to
an hour in key stages 2, 3 and 4. We understand that exact time dedicated to mathematics can
vary greatly between schools due to differences in curriculum planning, resource allocation and
school-specific priorities. Therefore we fully expect and encourage teachers to adapt our
curriculum and resources to best suit their needs and available curriculum time. This is
particularly important where year groups may be streamed either through sets, or in key stage 4
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where pupils may be working both between and within the foundation and higher exam routes.
For example, a year 10 unit will typically include a few lessons revisiting knowledge taught
previously, and end with challenging problem solving activities. A teacher may decide that the
unit could be compressed to spend less time on earlier content, or more time developing it.
Curriculum coherence
What are 'threads'?
We use threads to signpost groups of units that link to one another, building a common body of
knowledge over time. We use the term thread, rather than vertical concepts, themes, or big
ideas, because it helps to bring to mind the visual concept of a thread weaving through the
curriculum.
Primary mathematics threads






Number
 addition and subtraction
 fractions
 multiplication and division
 place value
Algebra
Statistics
Probability
Ratio and proportion
Geometry and measure
Secondary mathematics threads






Number
Algebra
Statistics
Probability
Ratio and proportion
Geometry and measure
These threads are the distinct domains that appear in the national curriculum programme of
study. These domains have been used as threads because in each domain knowledge is built
over time, teachers of mathematics are very familiar with them and they are used by
examination boards. In primary, much of the curriculum is focussed on developing knowledge
and understanding of ‘number’. Therefore this thread has been further broken down into
‘addition and subtraction’, ‘fractions’, ‘multiplication and division’, and ‘place value’. Common
threads across our primary and secondary curricula can enable more effective transition,
helping pupils to bridge their knowledge and understanding from primary to secondary.
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Recommendations from subject specific reports
How does our curriculum address and enact recommendations from subject
specific reports (e.g. EEF guidance reports & Ofsted Research Review)?
Our curriculum addresses the EEF recommendations from 2018, which found a strong evidence
base for the use of manipulatives and visual models to support mathematical ideas. Our slides
typically draw upon visual representations of common manipulatives such as the Rekenrek,
multilink cubes, and counters, and we promote the use of physical versions of such tools in our
teacher tips. We focus on development of both procedural and conceptual mathematics by
making sense of concepts whilst developing efficacy through the use of algorithms and practice.
Subject-specific needs
How does our curriculum deal with elements that arise from the specific
needs of the subject?
Does the Oak curriculum embrace a mastery approach?
Our subject principles align to those of a mastery approach. The concrete-pictorial-abstract
approach is evident throughout, particularly as concepts are first introduced. Towards key stage
4, abstraction and efficacy are more frequently relied upon, however this is always with the
support of strong visual diagrams, tools and small steps to help pupils make sense of the
mathematics being used. We carefully build mathematical ideas using real-world situations and
recognisable narrative structures. We offer opportunities for pupils to think hard and discuss
concepts and problems together or with the teacher. We design activities for younger pupils to
explore ideas using manipulatives while also ensuring they recognise familiar tools used
consistently when learning topics underpinned by the same mathematical concept.
How are calculators introduced and used in the mathematics curriculum?
We have embedded calculator use throughout the secondary curriculum. It is introduced after
the understanding of what is happening is taught, and highlights that the calculator is a useful
tool for speeding up lengthy or repeated calculations. We make use of calculator functions such
as storing answers and displaying them in different formats to create unique activities that can
only be enabled by digital technology.
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Our curriculum partner
Mathematics in Education and Industry (MEI)
is an established charity and curriculum
development body. Their primary aims are to
raise the quality of maths education and
promote the relevance of maths education to
everyone. MEI are highly respected and are
well connected with other quality assured
organisations, including being a key partner in
the NCETM, and are well known in schools
for their excellent training and support
programmes.
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Year 7 units
View interactive sequence online
1
2
3
Place value
Properties of number:
factors, multiples,
squares and cubes
Arithmetic
procedures with
integers and decimals
4
5
6
Expressions and
equations
Plotting coordinates
Perimeter and area
7
8
9
Comparing and
ordering fractions
and decimals
(positive and
negative)
Arithmetic
procedures with
fractions
Understanding
multiplicative
relationships:
fractions and ratio
10
Transformations
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1. Place value
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of place value
in integers
2. Securing understanding of place value
in integers
3. Deepening understanding of place value
in integers
4. Exponential and fractional column
headings
5. Place value in decimals
6. Checking understanding of place value
in metric units
7. Securing understanding of place value
in metric units
8. Place value in imperial units
9. Checking understanding of ordering and
comparing numbers
10. Securing understanding of ordering and
comparing numbers
11. Problem solving with place value
Number
Unit description
In this unit pupils revisit, secure and develop
their understanding of place value with
integers, decimals, fractions, metric and
imperial units. This knowledge is then
extended to order and compare numbers of
increasing complexity.
Why this, why now?
We begin year 7 with checking, securing
and further development of place value in
order to prepare adequately for further work
on number in the following units for this
term.
Prior knowledge requirements



Understand value of digits in large and
decimal numbers
Multiply and divide by powers of 10
Convert between standard and decimal
forms
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2. Properties of number: factors, multiples, squares and
cubes
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of factors,
multiples, squares and cubes
2. Securing understanding of factors,
multiples, squares and cubes
3. Listing multiples
4. Divisibility tests for 2 and 3
5. Divisibility tests for 6 and 9
6. Divisibility tests for 5 and 10
7. Divisibility tests for 4 and 8
8. Square and cube numbers
9. Square and cube roots
10. Power notation
11. Powers and roots using a calculator
12. Listing factors
13. Checking understanding of prime
numbers
14. Expressing an integer as a product of its
prime factors
15. Calculating integers from their prime
factor expressions
16. Highest common factor
17. Lowest common multiple
18. HCF or LCM
19. Problem solving with factors, multiples,
squares and cubes
Number
Unit description
In this unit pupils develop their
understanding of factors and multiples, then
extend this knowledge to learn general
divisibility tests for integers and develop
strategies to determine the highest common
factor and lowest common multiple of two or
more integers.
Why this, why now?
This unit continues to develop proficiency in
handling and recognising different types of
numbers, as well as understanding their
mathematical structure in order to be more
efficient and fluent with mathematical
operations in the following unit.
Prior knowledge requirements



Identify and list factors and multiples
Recognise and calculate square and
cube numbers
Apply divisibility rules and prime
factorisation
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3. Arithmetic procedures with integers and decimals
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of arithmetic
procedures with integers and decimals
2. Securing understanding of arithmetic
procedures with integers and decimals
3. Checking and securing understanding of
negative numbers in context
4. Addition of positive and negative
integers
5. Subtraction of positive and negative
integers
6. Checking and securing understanding of
written addition and subtraction
strategies
7. Checking and securing understanding of
multiplication and division
8. Multiplication and division where only
one value is negative
9. Multiplication and division where two or
more values are negative
10. Simplifying multiplication and division
using multiples of 10
11. Multiplying with decimals
12. Dividing with decimals
13. Priority of operations with positive
integers
14. Priority of operations with positive and
negative integers and decimals
15. Using the associative, commutative and
distributive laws together
16. Using your calculator efficiently
17. Problem solving with integers and
decimals
Number
Unit description
In this unit pupils develop their ability and
efficacy with the four operations including
more complicated and challenging
calculations involving fractions, decimals
and negative numbers. This leads into an
exploration of the priority order of
operations.
Why this, why now?
This unit builds on knowledge established in
work on factors, multiples squares and
cubes, building on the understanding that
any positive integer can be expressed as a
product of its factors. This skill is used here
to explore multiplying and dividing with
decimals.
Prior knowledge requirements

Perform all four operations with whole
numbers
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

Add, subtract, multiply and divide
decimals
Apply integer rules (positive/negative) to
calculations
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4. Expressions and equations
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of expressions
and equations
2. Securing understanding of expressions
and equations
3. Representing a generalised number
4. Algebraic notation
5. Algebraic terminology
6. Representing an unknown or variable
7. Generalised algebraic statements
8. Substituting particular values
9. Like terms
10. Simplifying by collecting like terms
11. Multiplying an expression by a constant
12. Multiplying an expression by a term
13. Multiplying and simplifying with multiple
expressions
14. Simplifying before multiplying with
multiple expressions
15. Highest common factor with algebraic
terms
16. Factorising expressions
17. Problem solving with expressions and
equations
Algebra
Unit description
In this unit, pupils learn about generalisation
and formal algebraic manipulation
techniques such as substitution, collecting
like terms and factorising.
Why this, why now?
This unit is a natural extension of the
number work in the previous units. We are
now seeking to generalise patterns and
behaviours that were first seen in the
number units taught before, and pulling in
key skills such as factorisation and
multiplication of brackets as part of
algebraic manipulation.
Prior knowledge requirements



Simplify algebraic expressions
Solve linear equations and substitute
values
Rearrange and manipulate formulas
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5. Plotting coordinates
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of plotting
coordinates
2. Securing understanding of plotting
coordinates
3. Plotting non-integer coordinates
4. Plotting coordinates generated from a
rule
5. Plotting coordinates generated from a
rule using technology
6. Plotting a relationship
7. Problem solving with plotting
coordinates
Algebra
Unit description
In this unit pupils revisit and further develop
their understanding of the coordinate plane,
and learn how to plot non-integer
coordinates. Pupils then plot from an
equation both by hand and by using
technology.
Why this, why now?
Continuing from their recent work using
algebra, this unit introduces plotting from
algebraic equations and developing
generalisations from a set of coordinate
pairs.
Prior knowledge requirements



Understand and use axes in all four
quadrants
Plot and read coordinates accurately
Recognise and describe geometric
figures using coordinates
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6. Perimeter and area
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of perimeter
and area
2. Securing understanding of perimeter
and area
3. Finding the perimeter of polygons
4. Calculating missing lengths with
perimeter of polygons
5. Perimeter with composite rectilinear
shapes
6. Area of a triangle
7. Using the formula for the area of a
triangle
8. Area of composite rectilinear shapes
9. Calculating missing side lengths from
the area of composite rectilinear shapes
10. Area of a trapezium
11. Calculating missing side lengths from
the area of a trapezium
12. Problem solving with perimeter and area
Geometry and Measure
Unit description
In this unit pupils investigate how to
calculate the area and perimeter of
rectilinear shapes, and composite shapes
using rectangles and triangles. They will
also derive simple area formulae.
Why this, why now?
This unit requires some confidence in the
use of formulae and simple algebra, hence
it has been positioned after pupils have
done some work on algebraic manipulation
and number operations. This unit also
prepares pupils for further work on
geometry later in the year.
Prior knowledge requirements



Identify 2D shapes and their properties
Use and apply standard formulas for
area and perimeter
Calculate with units of length and area
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7. Comparing and ordering fractions and decimals (positive
and negative)
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
fractions
2. The identity property of multiplication
and division
3. Checking and securing converting
improper fractions to mixed numbers
4. Checking and securing converting mixed
numbers to improper fractions
5. Converting fractions to terminating
decimals
6. Converting fractions to recurring
decimals
7. Converting terminating decimals to
fractions
8. Simplifying fractions
9. Converting fractions with technology
10. Limitations of technology in calculations
11. Ordering negative integers
12. Ordering decimals
13. Ordering fractions by converting
14. Ordering fractions by way of a common
denominator
15. Ordering fractions in different ways
16. Ordering positive and negative fractions
and decimals
17. Between numbers
18. Problem solving with fractions and
decimals
Number
Unit description
This unit develops understanding and
manipulation of fractions, including
conversion between fractions to terminating
and recurring decimals. Pupils then learn
strategies to order fractions of increasing
complexity.
Why this, why now?
This unit builds upon work done in the
'arithmetic procedures with integers and
decimals' unit, supporting further
development of fluency in working with
decimals as well as fractions.
Prior knowledge requirements


Recognise and convert between
fractions and decimals
Understand number lines with negative
values
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
Compare values using place value and
visual representations
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8. Arithmetic procedures with fractions
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of addition and
subtraction with fractions
2. Securing understanding of addition and
subtraction with fractions
3. Checking understanding of multiplication
with fractions
4. Securing understanding of multiplication
with fractions
5. Deepening understanding of
multiplication with fractions
6. Checking and securing dividing a
fraction by a whole number
7. Dividing a whole number by a fraction
8. Dividing a fraction by a fraction
9. Priority of operations with positive and
negative integers, decimals and
fractions
10. Problem solving with arithmetic
procedures involving fractions
Number
Unit description
This unit revisits and secures fraction
operations and extends pupil understanding
to division of whole numbers by fractions
and division of fractions by fractions.
Why this, why now?
This unit continues from the previous one in
deepening pupil understanding of fractions
whilst also being explicitly linked to the
'arithmetic procedures with integers and
decimals' unit.
Prior knowledge requirements



Add, subtract, multiply and divide
fractions
Simplify fractions and find common
denominators
Convert between improper fractions and
mixed numbers
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9. Understanding multiplicative relationships: fractions and
ratio
Year 7
Go to unit resources
Threads
Lessons in unit


1. Checking understanding of multiplicative
relationships
2. Securing understanding of ratio as a
multiplicative relationship
3. Multiplicative relationships in context
4. Expressing multiplicative relationships
as ratios and fractions
5. Multiplicative relationships
6. Equivalent multiplicative relationships
7. Representing a multiplicative
relationship
8. Ratio language and notation
9. Checking and securing finding a fraction
of a given amount
10. Deepening understanding with fractions
of a given amount
11. Expressing one number as a fraction of
another
12. Dividing a quantity into a given ratio
13. Determining the whole
14. Determining the part
15. Describing exchange rates with ratio
16. Describing more conversions with ratio
17. Problem solving with fractions and ratios
Number
Ratio and Proportion
Unit description
This unit introduces the concept of
multiplicative relationsihps, and connects
fractions to the idea of ratios. Ratios are
then explored in depth and used to solve
contextual problems such as those involving
exchange rates and general conversions.
Why this, why now?
This unit finishes our work with fractions in
Year 7, relying upon pupil understanding of
multiplication of fractions, and explicitly
connecting fractions with ratios and general
multiplicative relationships.
Prior knowledge requirements



Convert between fractions and decimals
Use fractions to represent parts of a
whole
Apply ratios to compare and scale
quantities
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10. Transformations
Year 7
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of basic
transformations
2. Introduction to translation
3. Describing a translation
4. Translating objects
5. Introduction to rotations
6. Describing a rotation's direction and size
7. Understanding the centre of rotation
8. Rotating objects
9. Introduction to reflections
10. Describing a reflection
11. Reflecting objects
12. Introduction to enlargements
13. Describing an enlargement
14. Enlarging objects
15. Transformed objects
16. Investigating transformations with
Desmos
17. Investigating transformations with
GeoGebra
18. Problem solving with transformations
Geometry and Measure
Unit description
This unit introduces pupils to shape
tranformations: enlargements, rotations,
reflections and translations both by hand
and with technology.
Why this, why now?
This unit utilises prior knowledge with ratios
and percentages, applying general
multiplicative relationships to the
transformation of shapes, whilst also
drawing upon recently developed
knowledge of the coordinate plane.
Prior knowledge requirements



Identify and describe reflections,
rotations, translations and enlargements
Plot points and shapes in all four
quadrants
Use coordinates to represent
movements
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Year 8 units
View interactive sequence online
1
2
3
Estimation and
rounding
Sequences
Graphical
representations of
linear equations
4
5
6
Solving linear
equations
Understanding
multiplicative
relationships:
percentages and
proportionality
Graphical
representations of
data
7
8
9
Numerical summaries
of data
Perimeter, area and
volume
Geometrical
properties: polygons
10
Constructions
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1. Estimation and rounding
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of rounding
2. Securing understanding of rounding
3. Rounding to three decimal places
4. Rounding to any number of decimal
places
5. Rounding integers to one significant
figure
6. Rounding integers to significant figures
7. Rounding decimals to significant figures
8. Degrees of accuracy
9. Estimating numerical calculations
10. Checking by estimating
11. Truncating
12. Overestimating vs underestimating
13. Rounding errors
14. Inequality notation to express error
15. Using inequality notation for errors in
calculations
16. Problem solving with estimation and
rounding
Number
Unit description
This unit helps pupils understand rounding
to different decimal places, and significant
figures. Pupils will also learn how to truncate
numbers and understand the contexts in
which these skills are useful. The unit ends
will an exploration of rounding and inequality
errors.
Why this, why now?
Students up to this point have been working
with integer values and have had few
opportunities to work explicitly on
estimation. We are starting the year with
something that is familiar for students and
extend knowledge of estimation and
rounding to include more work on rounding
with decimals and significant figures.
Prior knowledge requirements



Round numbers to nearest 10, 100,
1000
Round decimals to 1 or 2 decimal places
Estimate calculations using compatible
numbers
Exported 04 September 2025
27
2. Sequences
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of sequences
2. Securing understanding of sequences
3. Formalising a sequence
4. Generating a sequence using a term-toterm rule
5. Generating a sequence using a positionto-term rule
6. Arithmetic sequences
7. Expressing an arithmetic sequence
8. Calculating any term
9. Finding the nth term
10. Representing sequences graphically
11. Justifying terms of a sequence
12. Problem solving with sequences
Algebra
Unit description
In this unit we develop knowledge of
sequences to be able to identify, determine,
and continue arithmetic sequences. We
finish the unit by looking at how sequences
may be reprsented graphically.
Why this, why now?
In this unit pupils are developing their
knowledge of plotting coordinates by
exploring the idea that a set of points can
satisfy a mathematical relationship. This unit
sets the foundation for working with
graphical representations of linear
equations.
Prior knowledge requirements



Recognise and continue number
patterns
Understand position-to-term rules
Use nth term to generate a sequence
Exported 04 September 2025
28
3. Graphical representations of linear equations
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
plotting coordinates
2. Checking and securing understanding of
plotting coordinates generated from a
rule
3. Checking and securing understanding of
plotting coordinates with technology
4. Checking and securing plotting a
relationship
5. Features of linear relationships
6. Defining features of linear relationships
7. Positive rate of change from a graph
8. Negative rate of change from a graph
9. Rate of change from a coordinate pair
10. The intercept point
11. The equation of a straight line
12. Finding the equation of the line y = mx +
c
13. Finding the equation of the line ay + bx
+c=0
14. Using dynamic software to explore linear
relationships
15. Problem solving with graphing linear
relationships
Algebra
Unit description
In this unti we develop understanding of
linear relationships and explore the key
features of a linear equation such as the
gradient, intercept and determining an
equation from coordinate pairs.
Why this, why now?
In this unit we continue to build on
knowledge developed in the previous work
on sequences and build confidence in how
a linear sequence produces a linear
relationship. We represent that graphically
along with development of understanding of
the equation of a line, positive, negative
relationships and the idea that a linear
sequence can produce an infinite set of
points.
Prior knowledge requirements



Rearrange equations into y = mx + c
form
Use tables of values to plot lines
Identify features of straight-line graphs
Exported 04 September 2025
29
4. Solving linear equations
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of algebraic
notation
2. Securing understanding of equality
3. Different types of equations
4. Equality in an equation
5. Solution to an equation
6. Many equations, one solution
7. Solving simple linear equations with an
additive step
8. Solving simple linear equations with a
multiplicative step
9. Preparing to solve two step linear
equations
10. Solving two step linear equations
11. Rearranging to solve linear equations
12. Solving complex linear equations
13. Brackets in equations
14. Solving linear equations where brackets
are used
15. Solving complex linear equations
involving brackets
16. Solving linear equations graphically
using technology
17. Problem solving with linear equations
Algebra
Unit description
In this unit pupils will learn how to find a
value that satisfies a linear relationship
when one value is known both with a single
step operation, and multiple step operations.
A variety of cases are explored including
using brackets and rearranging.
Why this, why now?
Further to graphing linear sequences in the
previous unit, pupils now learn to connect
understanding with solving linear equations
after demonstrating how for each point on a
linear graph there is a unique solution to the
equation of the line.
Prior knowledge requirements



Understand and apply inverse
operations
Simplify algebraic expressions
Solve one-step and two-step equations
Exported 04 September 2025
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5. Understanding multiplicative relationships: percentages
and proportionality
Year 8
Go to unit resources
Threads
Lessons in unit


1. Checking understanding of percentages
2. Securing understanding of percentages
3. Multiplicative relationships presented
graphically
4. Scaling diagrams for multiplicative
relationships
5. Expressing one number as a percentage
of another
6. Finding a percentage with a multiplier
7. Increase by a percentage
8. Decrease by a percentage
9. Finding the original amount after an
increase
10. Finding the original amount after a
decrease
11. Finding the percentage change
12. Multiplicative relationships and direct
proportion
13. Graphing direct proportion
14. Direct proportion in context
15. Inverse proportion in context
16. Problem solving with percentages and
proportionality
Number
Ratio and Proportion
Unit description
In this unit pupils explore multiplicative
relationships with percentages, direct and
inverse proportion.
Why this, why now?
Pupils build upon key stage 2 work with
finding percentages of amounts, then
extending their knowledge to percentage
change, connecting to previous learning
around decimals and fractions. Pupils then
explore a more general exploration of
multiplicative relationships.
Prior knowledge requirements



Convert between fractions, decimals,
and percentages
Understand ratio and scaling
Solve problems involving direct
proportion
Exported 04 September 2025
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6. Graphical representations of data
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of pictograms
and bar charts
2. Securing constructing pictograms
3. Securing constructing bar charts by
hand
4. Constructing bar charts by utilising
technology
5. Constructing pie charts
6. Constructing pie charts by utilising
technology
7. Interpreting pie charts
8. Constructing scatter graphs
9. Constructing scatter graphs by utilising
technology
10. Interpreting scatter graphs
11. Problem solving with graphical
representations of data
Statistics
Unit description
In this unit pupils will interpret and construct
a range of representations of data including
bar charts, pie charts and scatter graphs.
Why this, why now?
Pupils have prepared for this unit earlier in
the year by looking at graphical
representations of sequences. We build
upon that knowledge to show that data can
be represented in further ways as well as
how to construct and interpret those
representations.
Prior knowledge requirements



Draw and interpret bar charts, line
graphs and pie charts
Choose appropriate graphs for different
types of data
Understand and use frequency and
grouped data
Exported 04 September 2025
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7. Numerical summaries of data
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of the mean
2. Calculating the mean
3. Understanding the median
4. Calculating the median
5. Understanding the mode
6. Calculating the mode
7. Understanding and calculating the range
8. Summarising data
9. Changing a data point
10. Evaluating the range
11. Comparing statistical representations
12. Comparing summaries of data
13. Analysing different statistical
representations
14. Correlation
15. Statistical problems - data collection
16. Statistical problems - statistical
summaries
17. Statistical problems - data presentations
18. Statistical problems - drawing
conclusions
19. Problem solving with numerical
summaries of data
Statistics
Unit description
In this unit pupils explore the concept of
measures of central tendancy, developing
understanding of different types of average
and their relative benefits and drawbacks.
We then investigate other summaries of
data such as the range and data
comparison techniques.
Why this, why now?
Building on work pupils have undertaken on
averages in key stage 2, and linking to the
previous unit where we summarised data
graphically, pupils now explore representing
data numerically. Pupils focus on the
concept of measures of central tendency
and range. We also begin to look at
correlation as a relationship between data.
Prior knowledge requirements



Calculate mean, median, mode and
range
Organise data in frequency tables
Interpret results in context
Exported 04 September 2025
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8. Perimeter, area and volume
Year 8
Go to unit resources
Threads
Lessons in unit


1. Checking understanding of perimeter
2. Checking understanding of area
3. Multiplicative relationships in circles
4. Circumference of a circle
5. Area of a circle
6. Using the formula for the area of a circle
7. Area of composite shapes
8. Perimeter of composite shapes
9. Finding a length in composite shapes
10. Surface area of cuboids
11. Properties of prisms
12. Surface area of prisms
13. Surface area of cylinders
14. Volume of prisms
15. Volume of cylinders
16. Problem solving with perimeter, area
and volume
Geometry and Measure
Number
Unit description
In this unit pupils extend their knowledge of
shapes by exploring the properties of circles
and composite shapes before developing
understanding of 3-D shapes including
surface area and volume.
Why this, why now?
This unit is an extension of the perimeter
and area unit in year 7 (which focused on
polygons), and extends this knowledge to
focus on circles and circle based composite
shapes then extending to look at the
concept of prisms and volume.
Prior knowledge requirements



Use standard formulas for rectangles
and cuboids
Convert between units of measure
Calculate dimensions of composite
shapes
Exported 04 September 2025
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9. Geometrical properties: polygons
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of angles from
KS2
2. Securing understanding of angles from
KS2
3. Formalising understanding of triangles
from KS2
4. Formal angle notation
5. Corresponding angles
6. Alternate angles
7. Co-interior angles
8. Angles on parallel lines traversed by a
straight line
9. The sum of the interior angles of any
triangle
10. Using the sum of the interior angles of a
triangle
11. Interior angles of a polygon
12. Deriving the sum of interior angles in
multiple ways
13. Exterior angles of polygons
14. Interior and exterior angles of regular
polygons
15. Missing angles
16. Problem solving with polygons
Geometry and Measure
Unit description
In this unit pupils will investigate internal and
external angles of polygons and angles
made with a transveral and parallel lines.
Pupils will develop their ability to formally
prove properties of polygons to generalise.
Why this, why now?
This unit builds on knowledge developed
investigating angles and continues work
done in the previous unit investigating
polygons. Here pupils will develop
understanding of external and internal
angles of polygons and traversals through
parallel lines
Prior knowledge requirements



Identify and classify polygons by sides
and angles
Use angle rules (interior, exterior)
Calculate sum of angles and solve
problems using reasoning
Exported 04 September 2025
35
10. Constructions
Year 8
Go to unit resources
Threads
Lessons in unit

1. Checking compass skills
2. Securing the skill of using a pair of
compasses
3. Understanding constructing a circle
4. Constructing triangles
5. Constructing rhombi
6. Diagonals of a rhombus
7. Bisecting an angle
8. Perpendicular bisector of a line segment
9. Perpendicular to a given line through a
given point
10. Problem solving with constructions
Geometry and Measure
Unit description
In this unit we develop skills in using a pair
of compasses and ruler to construct various
accurate shapes and angles including
triangles, rhombi, perpendicular lines and
angle bisectors.
Why this, why now?
After studying polygons and circles in depth
in previous units, this year culminates in
learning to mathematically construct these
shapes using knowledge of the properties of
triangles, quadrilaterals and circles in order
to draw them accurately.
Prior knowledge requirements



Use ruler and compass for straight-edge
and arcs
Construct perpendiculars and bisectors
Interpret geometric conditions in
drawings
Exported 04 September 2025
36
Year 9 units
View interactive sequence online
1
2
3
Geometrical
properties: similarity
and Pythagoras'
theorem
Probability: possible
outcomes
Probability:
theoretical
probabilities
4
5
6
Non-linear
relationships
Expressions and
formulae
Trigonometry
7
8
9
Standard form
Graphical
representations
Maths and the
environment
10
11
12
Maths in the
workplace
Thinking critically
with maths
Calculator
functionality
Exported 04 September 2025
37
1. Geometrical properties: similarity and Pythagoras'
theorem
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of similarity
2. Checking understanding of congruence
3. Similarity in shapes
4. Congruence in shapes
5. Congruent, similar or neither
6. Rotational symmetry
7. Congruent triangles (SSS)
8. Congruent triangles (SAS)
9. Congruent triangles (ASA and AAS)
10. Congruent triangles (RHS)
11. Applying the criteria for congruence
12. Demonstrating Pythagoras' theorem
13. Further demonstrating of Pythagoras'
theorem
14. Length of the hypotenuse
15. Length of a shorter side
16. Determining which side
17. Pythagoras' theorem in context
18. Problem solving with similarity and
Pythagoras' theorem
Geometry and Measure
Unit description
This unit explores the concepts of
congruence and similarity, and ways to
prove or disprove similarity between shapes.
We then explore further properties of
triangles with Pythagoras' Theorem.
Why this, why now?
This unit builds on knowledge developed in
work on transformations, angles and
properties of triangles. Pupils explored the
effects of different transformations and
whether the transformed shape was
congruent or similar to the original shape.
This knowledge is built upon and applied to
new contexts as pupils formalise the criteria
for determining congruence in triangles and
study rotational symmetry. This unit also
prepares pupils for learning about
trigonometry to extend a right-angled
triangle in the unit circle to any other rightangled triangle.
Prior knowledge requirements



Recognise right-angled triangles
Apply Pythagoras' Theorem to find
missing lengths
Use ratios in similar shapes
Exported 04 September 2025
38
2. Probability: possible outcomes
Year 9
Go to unit resources
Threads
Lessons in unit

1. Equally likely outcomes
2. Non-equally likely outcomes
3. The scale of likelihoods
4. Experiments to determine how likely an
outcome is
5. Using lists to display outcomes for two
events
6. Using two-way tables to display
outcomes for two events
7. Using an outcome tree to display
outcomes for two events
8. Using a Venn diagram to display
outcomes for two events
9. Comparing representations of outcomes
for two events
10. Using lists to display outcomes for more
than two events
11. Using an outcome tree to display
outcomes for more than two events
12. Using a Venn diagram to display
outcomes for more than two events
13. Comparing representations of outcomes
for more than two events
14. Problem solving with possible outcomes
Probability
Unit description
This unit introduces and explores the
concept of liklihood as a relative measure,
and demonstrates multiple ways to
represent likelihood such as Venn diagrams,
tree diagrams and two-way tables.
Why this, why now?
This unit is the first introduction to probability
and likelihood. Pupils develop their
understanding of how likely something is,
looking at relative likelihoods and displaying
outcomes but without formalising
probability using measurable numerical
values at this stage. Pupils explore different
ways to display outcomes to gain a sense of
what it means to say something is likely or
unlikely in preparation for more calculative
methods and theoretical probability in the
next unit.
Prior knowledge requirements



Understand outcomes and sample
spaces
Use fractions and percentages to
represent probability
Recognise equally likely events and
basic probability rules
Exported 04 September 2025
39
3. Probability: theoretical probabilities
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking listing possible outcomes
2. The probability scale
3. Calculating theoretical probabilities from
lists (one event)
4. Calculating theoretical probabilities from
a table (one event)
5. Calculating theoretical probabilities from
probability tree diagrams (one event)
6. Calculating theoretical probabilities from
Venn diagrams (one event)
7. Comparing multiple representations to
calculate theoretical probabilities
8. Summing probabilities
9. Calculating theoretical probabilities from
two-way tables (two events)
10. Calculating theoretical probabilities from
Venn diagrams (two events)
11. Calculating theoretical probabilities from
probability trees (two events)
12. Comparing multiple representations to
calculate theoretical probabilities for
combined events
13. Problem solving with theoretical
probability
Probability
Unit description
In this unit we build upon the concept of
likelihood to work more mathematically with
more measurable probability using fraction
and decimal representations to both
interpret and calculate. We revisit and
develop ways to represent and compare
probabilities.
Why this, why now?
Further to developing the basic ideas and
foundations of probability, we move towards
more abstract measures of likelihood using
calculations to assign numerical values to
probability. We then revisit the visual models
of probability established in the previous
unit through the lens of representing and
utilising theoretical probability.
Prior knowledge requirements



Define probability as a ratio between
favourable and possible outcomes
Represent events using lists, tables or
diagrams
Calculate probabilities of single and
combined events
Exported 04 September 2025
40
4. Non-linear relationships
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of arithmetic
sequences
2. Securing understanding of arithmetic
sequences
3. Features of geometric sequences
4. Recognising geometric sequences
5. Representing geometric sequences
graphically
6. Features of special number sequences
7. Recognising special number sequences
8. Graphing special number sequences
using technology
9. Extrapolating a sequence
10. Problem solving with non-linear
relationships
Algebra
Unit description
In this unit we explore geometric and special
number sequences like the Fibonacci
sequence. We develop strategies to
recognise types of sequence and continue
them.
Why this, why now?
This unit builds from the sequences unit in
Year 8. We develop understanding of
sequences further to look at geometric and
other non-linear sequences and how they
appear graphically.
Prior knowledge requirements



Recognise non-linear patterns in graphs
and tables
Understand simple quadratic and
exponential relationships
Plot and interpret curves on coordinate
grids
Exported 04 September 2025
41
5. Expressions and formulae
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
the distributive law with algebraic terms
2. Checking and securing solving linear
equations
3. The product of two binomials
4. Difference of two squares
5. More complex binomial products
6. Additive relationships
7. Multiplicative relationships between
terms
8. Changing the subject with simple
formula
9. Changing the subject with more complex
formula
10. Changing the subject to suit the context
11. Evaluating expressions with and without
changing the subject
12. Problem solving with expressions and
formulae
Algebra
Unit description
This unit develops pupil understanding of
formulae and how to rearrange them. Pupils
will learn how to recognise and manipulate
binomials and learn to recognise the
difference of two squares.
Why this, why now?
This unit builds on solving linear equations
from year 7 where pupils learnt to rearrange
aan equation to find a specific value that
satisfied the equation. In expressions and
formulae, pupils use their understanding of
rearrangement to change the subject of a
formula. Pupils are then introduced binomial
equations in preparation for trigonometry.
Prior knowledge requirements



Simplify algebraic expressions
Use substitution in expressions and
formulas
Rearrange formulas involving one or
more steps
Exported 04 September 2025
42
6. Trigonometry
Year 9
Go to unit resources
Threads
Lessons in unit


1. Checking and securing understanding of
similar triangles
2. Checking and securing understanding of
Pythagoras' theorem
3. The unit circle
4. Scaling the right-angled triangle from the
unit circle
5. Sine and cosine ratios
6. Tangent ratio
7. Using the sine ratio
8. Using the cosine ratio
9. Using the tangent ratio
10. Choosing the right trigonometric ratio
11. Choosing an appropriate method for
finding lengths of a triangle
12. Problem solving with trigonometry
Geometry and Measure
Ratio and Proportion
Unit description
In this unit pupils learn how to recognise the
relationship between the unit circle and the
trigonometric ratios of sine, cosine and
tangent. Pupils then apply this knowledge to
solve trigonometric problems.
Why this, why now?
Pupils have recently learned about
geometrical properties of similarity and the
Pythagorean Theorem. This knowledge is
further developed to build on their
understanding of congruence and similarity
with right-angled triangles. In this unit,
similarity is used to extend a right-angled
triangle in the unit circle to any other rightangled triangle.
Prior knowledge requirements



Label sides in right-angled triangles
(opposite, adjacent, hypotenuse)
Use sine, cosine and tangent ratios
Rearrange and solve trigonometric
equations
Exported 04 September 2025
43
7. Standard form
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
multiples of 10
2. Checking and further securing
understanding of the commutative law
3. Multiples of 10 involving negative
exponents
4. Writing large numbers in standard form
5. Writing small numbers in standard form
6. Ordering numbers in standard form
7. Problem solving with standard form
Number
Unit description
In this unit pupils learn to recognise,
interpret and write in standard form. Pupils
then extend this knowledge so that they can
order numbers written in standard form.
Why this, why now?
This unit builds from arithmetic procedures
with integers and decimals. In the prior unit,
pupils learnt how to factorise multiples of 10
in order to simplify calculations. This
understanding is further developed in this
unit as values are converted to meet the
conditions for standard form.
Prior knowledge requirements



Understand place value and powers of
10
Convert between standard and ordinary
notation
Multiply and divide using powers of 10
Exported 04 September 2025
44
8. Graphical representations
Year 9
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
non-linear sequences
2. Extending thinking about sequences
3. Exploring the shapes of graphs using
technology
4. Equations and their graphs
5. Efficiently drawing linear graphs
6. Reading from graphs
7. Modelling with graphs
8. Graphically solving two linear graphs
that intersect
9. Problem solving with graphical
representations
Algebra
Unit description
In this unit pupils draw, interpret and utilise
linear graphs to solve problems. This
knowledge is further extended to look at
intersecting graphs.
Why this, why now?
This unit builds knowledge from previous
work on non-linear relationships. In that unit,
pupils considered geometric sequences and
how they might be represented graphically.
In this unit, pupils study the graphical
representation to link features of the graph
to its equation.
Prior knowledge requirements



Plot points and draw axes
Interpret bar charts, line graphs, and
scatter graphs
Select appropriate graphs for different
types of data
Exported 04 September 2025
45
9. Maths and the environment
Year 9
Go to unit resources
Threads
Lessons in unit
No threads
1. Solar power
2. Making a journey
3. Considering a route
4. Understanding weather data
5. Predicting the weather
6. Studying climate change
7. Studying local climate change
8. Making cities greener
9. Designing a green space
Unit description
-
Why this, why now?
-
Prior knowledge requirements



Interpret real-world contexts using
mathematical reasoning
Use units and conversions appropriately
Read and represent data using graphs
and tables
Exported 04 September 2025
46
10. Maths in the workplace
Year 9
Go to unit resources
Threads
Lessons in unit
No threads
1. Agricultural worker (animals)
2. Agricultural worker (crops)
3. Astrophysicist
4. Catering
5. Construction
6. Emergency response worker
7. Engineer
8. Event management
9. Graphic designer
10. Interior designer
11. Media - films and games
12. Medical professional
13. Operational researcher
14. Personal assistant
15. Programmer
16. Running a small business
17. Sales and marketing
18. Sports coaching
Unit description
-
Why this, why now?
-
Prior knowledge requirements



Read tables, charts, and schedules
Perform calculations with money and
units
Interpret job-based and practical
contexts using maths
Exported 04 September 2025
47
11. Thinking critically with maths
Year 9
Go to unit resources
Threads
Lessons in unit
No threads
1. Misleading data
2. Understanding advertising
3. Elections
4. Voting systems
5. Checking a claim
Unit description
-
Why this, why now?
-
Prior knowledge requirements



Interpret and evaluate information
logically
Justify reasoning using numerical and
graphical evidence
Identify assumptions and question
validity of arguments
Exported 04 September 2025
48
12. Calculator functionality
Year 9
Go to unit resources
Threads
Lessons in unit
No threads
1. Using the fx-83/85GT CW for number
2. Using the fx-83/85GT CW for statistics
3. Using the fx-991CW for number and
algebra
4. Using the fx-991CW for statistics
5. Using the fx-CG50 for number and
algebra
6. Using the fx-CG50 for statistics
Unit description
This unit teaches how to use scientific
calculators and expores their functionality
Why this, why now?
It is important to dedicate some time to
understanding the functionality of modern
scientific calculators so that they can be
used appropriately.
Prior knowledge requirements



Perform basic operations accurately
Use brackets, powers, roots and
memory functions
Interpret calculator display and rounding
appropriately
Exported 04 September 2025
49
Higher
Year 10 units
View interactive sequence online
1
2
3
Algebraic
manipulation
Simultaneous
equations: 2 variables
Percentages
4
5
6
Arithmetic
procedures: index
laws
Standard form
calculations
Surds
7
8
9
Sampling
Graphical
representations of
data: scatter graphs
and time series
Comparisons of
numerical summaries
of data
10
11
12
Rounding, estimation
and bounds
Ratio
Linear graphs
13
14
15
Non-linear graphs
2D and 3D shape:
compound shapes
Angles
16
17
18
Further
transformations
Similarity
Circle theorems
Exported 04 September 2025
50
19
20
21
Plans and elevations
Right-angled
trigonometry
Bearings
Exported 04 September 2025
51
1. Algebraic manipulation
Year 10
Go to unit resources
Threads
Lessons in unit

1. Further algebraic terminology
2. Checking and securing understanding of
factorising
3. Checking and securing understanding of
forming linear equations
4. Checking and securing understanding of
solving and interpreting linear equations
5. Checking and securing understanding of
changing the subject
6. Checking and securing understanding of
the product of two binomials
7. The product of three binomials
8. Factorising a quadratic expression
9. Factorising using the difference of two
squares
10. Factorising quadratics of the form ax^2 +
bx + c
11. Solving quadratic equations by
factorising
12. Solving quadratic equations by
factorising where rearrangement is
required
13. Solving quadratic equations by
completing the square
14. Solving complex quadratic equations by
completing the square
15. Solving quadratic equations by using the
formula
16. Advanced problem solving with
algebraic manipulation
Algebra
Unit description
In algebraic manipulation, pupils use apply
knowledge of the distributive law to find the
product of two binomaials in order to
factorise quadratics.
Why this, why now?
This unit is the foundation for a lot of the
generalisation done in this year, and is
placed at the start of the year accordingly.
Prior knowledge requirements



Collect like terms and use basic algebra
Expand and factorise expressions
Substitute values into algebraic formulas
Exported 04 September 2025
52
2. Simultaneous equations: 2 variables
Year 10
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
interpreting graphs
2. Forming simultaneous equations
3. Combining equations
4. Solving simultaneous equations by
elimination from a context
5. Solving algebraic simultaneous
equations by elimination
6. Solving more complex simultaneous
equations by elimination
7. Solving simultaneous linear equations
by substitution
8. Solving simultaneous linear equations
graphically
9. Solving a quadratic and linear pair of
simultaneous equations using
elimination
10. Solving a quadratic and linear pair of
simultaneous equations using
substitution
11. Solving a quadratic and linear pair of
simultaneous equations graphically
12. Solving simultaneous equations via any
method
13. Problem solving with linear and
quadratic simultaneous equations
Algebra
Unit description
In this unit pupils will learn to solve a pair of
simultaneous equations from different
starting points and cases using a variety of
strategies.
Why this, why now?
This unit builds from solving equations in
Year 8 and develops those skills further.
Prior knowledge requirements



Solve linear equations in one variable
Interpret solutions graphically
Substitute values into expressions
Exported 04 September 2025
53
3. Percentages
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
percentage increase
2. Checking and securing understanding of
percentage decrease
3. Percentage profit and loss
4. Simple and compound interest
5. Simple interest calculations
6. Simple interest calculations with
technology
7. Compound interest calculations
8. Compound interest calculations with
technology
9. Calculating compound interest rates
10. Changing compound interest rates
11. Advanced problem solving with
percentages
Ratio and Proportion
Unit description
In this unit pupils will learn how to perform
simple and compound interest calculations
using percentages.
Why this, why now?
This unit builds from percentage change and
because it utilises a formula it follows on
from more work on algebra.
Prior knowledge requirements



Convert between fractions, decimals,
and percentages
Find percentages of amounts (including
50%, 25%, 10%)
Use percentage increase/decrease in
context
Exported 04 September 2025
54
4. Arithmetic procedures: index laws
Year 10
Go to unit resources
Threads
Lessons in unit

1. Converting any recurring decimal to a
fraction
2. Checking and securing understanding of
prime factorisation
3. Checking and securing understanding of
LCM and HCF
4. Checking and securing understanding of
roots and integer indices
5. The laws of indices - multiplication
6. The laws of indices - division
7. The laws of indices - raising a power to
a power
8. The laws of indices - negative and zero
exponents
9. The laws of indices - fractional
exponents
10. Advanced problem solving with the laws
of indices
Number
Unit description
In this unit pupils learn how to manipulate
indices and perform calculations without
conversion by understanding index laws.
Why this, why now?
This unit builds on the index work covered in
the previous unit to formalise laws around
indices.
Prior knowledge requirements



Understand and apply powers and roots
Use rules for multiplying and dividing
powers
Apply zero, negative and fractional
indices
Exported 04 September 2025
55
5. Standard form calculations
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
writing large numbers in standard form
2. Checking and securing understanding of
writing small numbers in standard form
3. Adding numbers in standard form
4. Subtracting numbers in standard form
5. Multiplying numbers in standard form
6. Dividing numbers in standard form
7. Problem solving with standard form
calculations
Number
Unit description
In this unit pupils will learn how to add,
subtract, multiply and divide numbers written
in standard form.
Why this, why now?
This unit deepens pupil understanding of
index laws to now cover standard form.
Prior knowledge requirements



Understand powers of 10 and place
value
Convert numbers to and from standard
form
Perform calculations using
multiplication/division of powers of 10
Exported 04 September 2025
56
6. Surds
Year 10
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Threads
Lessons in unit

1. Accuracy of final answers
2. Identifying square factors to support
simplifying surds
3. Simplifying surds
4. Addition with surds
5. Multiplication of surds
6. Applying the underlying structure of
multiplication and division of surds
7. The distributive law with surds
8. The distributive law with two or more
binomials
9. Rationalising a single term denominator
10. Rationalising a two term denominator
11. Solving equations with surds
12. Problem solving with surds
Number
Unit description
In this unit pupils will learn how to recognise
surds, handle them in calculations and
rationalise fractions with surds as
denominators.
Why this, why now?
This unit continues to build knowledge
around the use of indices, looking deeper at
fractional indices and surds in general.
Prior knowledge requirements



Understand square and square root
notation
Simplify square roots of integers
Multiply and divide simple surds
Exported 04 September 2025
57
7. Sampling
Year 10
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Threads
Lessons in unit

1. Checking understanding of statistical
problems
2. The Statistical Enquiry Cycle
3. Types of data
4. Sampling methods
5. Stratified sampling
6. Capture/recapture sampling method
7. Sampling limitations
8. Data collection
9. Biased questioning
10. Advanced problem solving with sampling
Statistics
Unit description
In this unit pupils will learn how to sample,
and explore accuracy and limitations with
various sampling strategies and data
collection techniques.
Why this, why now?
This topic is placed here to benefit from
interleaving and builds from prior learning
around numerical summaries of data.
Prior knowledge requirements



Understand the concept of a population
and sample
Recognise bias and representativeness
Select and justify methods of sampling
Exported 04 September 2025
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8. Graphical representations of data: scatter graphs and
time series
Year 10
Go to unit resources
Threads
Lessons in unit

1. Checking understanding of scatter
graphs
2. Checking understanding of correlation
3. Estimating from scatter graphs
4. Interpolation versus extrapolation
5. Outliers in scatter graphs
6. Constructing time series graphs
7. Interpreting time series graphs
8. Problem solving with scatter graphs and
time series
Statistics
Unit description
In this unit pupils will learn how to interpret
and extract data from scatter graphs and
time series graphs.
Why this, why now?
This unit builds from data sampling to
deepen understanding of the ways in which
data can be interpreted and interrogated.
Prior knowledge requirements



Plot coordinates in all four quadrants
Interpret trends and patterns in data
Understand correlation and basic
statistical language
Exported 04 September 2025
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9. Comparisons of numerical summaries of data
Year 10
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Threads
Lessons in unit

1. Checking understanding of summary
statistics from a list
2. Checking understanding of summary
statistics from a frequency table
3. Calculating summary statistics from a
grouped frequency table
4. Calculating the mean from a grouped
frequency table
5. Weighted means
6. Constructing stem and leaf diagrams
7. Calculating summary statistics from
stem and leaf diagrams
8. Checking understanding of measures of
central tendency
9. Comparing data sets in context
10. Statistical summaries using technology
11. Comparing various representations of
data sets
12. Problem solving with comparisons of
numerical data
Statistics
Unit description
In this unit pupils will compare two different
data sets and compare different measures
of central tendancy when interpreting the
data. Pupils will learn to interrogate
frequency tables and stem and leaf
diagrams both with and without technology.
Why this, why now?
This unit benefits from the preceding units
on data collection and representations. It
furthers pupil understanding of data
representation and interrogation.
Prior knowledge requirements



Calculate mean, median, mode, and
range
Interpret and compare sets of data
Understand the purpose of each
statistical measure
Exported 04 September 2025
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10. Rounding, estimation and bounds
Year 10
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Threads
Lessons in unit

1. Upper and lower bounds
2. Upper and lower bounds in additive
calculations
3. Upper and lower bounds in multiplicative
calculations
4. Using upper and lower bounds
practically
5. Advanced problem solving with
rounding, estimation and bounds
Number
Unit description
This unit explores the impact of upper and
lower bounds on additive and multiplicative
calculations.
Why this, why now?
This unit builds upon ideas around data
accuracy and projection that are covered in
prior data units this year.
Prior knowledge requirements



Round whole numbers and decimals
appropriately
Estimate answers using compatible
numbers
Understand upper and lower bounds in
calculations
Exported 04 September 2025
61
11. Ratio
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
simplifying and unitising ratios
2. Checking and securing understanding of
equivalent ratios
3. Checking and securing understanding of
sharing in a ratio
4. Checking and securing understanding of
converting between ratios, percentages
and fractions
5. Checking and securing understanding of
real world ratios
6. Combining ratios
7. Changing ratios
8. Writing equations from ratios
9. Algebraic ratios
10. Problem solving with algebraic ratios
Ratio and Proportion
Unit description
In this unit pupils will learn how to combine
ratios, interpret algebraic ratios, and
investigate quantity changes and their effect
on ratios.
Why this, why now?
This unit builds on prior knowledge of simple
ratios but deepens understanding by
moving into new areas of practical
application and generalisation. .
Prior knowledge requirements



Use language of ratio and proportion
Divide quantities in a given ratio
Scale values up or down using ratios
Exported 04 September 2025
62
12. Linear graphs
Year 10
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Threads
Lessons in unit


1. Checking and securing understanding of
drawing vertical and horizontal graphs
2. Checking and securing understanding of
finding the equation of the line from the
graph
3. Checking and securing understanding of
finding the equation of the line from
coordinates
4. Parallel linear graphs
5. Perpendicular linear graphs
6. Identifying perpendicular linear graphs
7. Parallel and perpendicular lines on
coordinate axes
8. Ratios in line segments on coordinate
axes
9. Checking and understanding graphs
showing direct proportion
10. Graphs showing inverse proportion
11. Advanced problem solving with linear
graphs
Algebra
Ratio and Proportion
Unit description
In this unit pupils consider equations that
produce parallel or perpendicular graphs
and how their equations relate to each other.
Why this, why now?
This unit requires strong algebraic skills and
understanding of proof, as well as building
upon prior knowledge on ratio to work with
line segments.
Prior knowledge requirements



Plot coordinates in all four quadrants
Understand gradient and y-intercept in y
= mx + c
Interpret real-life contexts with linear
graphs
Exported 04 September 2025
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13. Non-linear graphs
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
drawing quadratic graphs
2. Key features of a quadratic graph
3. Drawing cubic graphs
4. Key features of a cubic graph
5. Drawing reciprocal graphs
6. Key features of a reciprocal graph
7. Drawing exponential graphs
8. Key features of an exponential graph
9. Drawing the graph for the equation of a
circle
10. Advanced problem solving with nonlinear graphs
Algebra
Unit description
In this unit graphical representations of nonlinear graphs are introduced and explored,
and their key features identified.
Why this, why now?
This unit builds upon the preceding unit to
incorporate non-linear graphs as well.
Prior knowledge requirements



Plot and interpret coordinates from
equations
Recognise linear and basic quadratic
forms
Understand symmetry and turning points
Exported 04 September 2025
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14. 2D and 3D shape: compound shapes
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
converting between metric and imperial
measures
2. Checking and securing understanding of
scales and conversion
3. Checking and securing understanding of
perimeter for compound shapes
4. Checking and securing understanding of
area for compound shapes
5. Perimeter and area in a contextual
setting
6. Calculating arc length
7. Area of a sector
8. Area of compound shapes
9. Shapes within shapes
10. Equations from complex shapes
11. Shapes on coordinate grids
12. Problem solving with complex 2D
shapes
Geometry and Measure
Unit description
In this unit, knowledge of circles and
polygons is drawn upon to find the arc
length and area of a circle sector and areas
of complex compound shapes.
Why this, why now?
This unit is a summation of KS3 work on
shape, but extends into parts of a circle and
more complicated compound shapes.
Prior knowledge requirements



Identify and name standard 2D and 3D
shapes
Calculate area, perimeter, and volume of
standard shapes
Break down complex shapes into known
components
Exported 04 September 2025
65
15. Angles
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
advanced angle facts
2. Checking and securing understanding
on chains of reasoning with angle facts
3. Checking and securing understanding of
polygons
4. Checking and securing understanding of
interior angles
5. Forming equations with angles
6. Problem solving with angles
Geometry and Measure
Unit description
In this unit pupils use their knowledge of
corresponding, alternate and co-interior
angles to reason through and solve more
complicated problems.
Why this, why now?
This unit builds upon the preceding unit on
shape and develops fluency of
understanding of angles.
Prior knowledge requirements



Identify types of angles (acute, obtuse,
right, reflex)
Understand angle facts (e.g. angles on a
line, around a point)
Use a protractor to measure and draw
angles
Exported 04 September 2025
66
16. Further transformations
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
congruence and similarity
2. Checking and securing understanding of
rotation
3. Checking and securing understanding of
translation
4. Checking and securing understanding of
reflection
5. Checking and securing understanding of
enlargement with positive integer scale
factors
6. Checking and securing understanding of
enlargement with positive fractional
scale factors
7. Enlargement using a negative scale
factor
8. Describing a negative enlargement
9. Multiple transformations
10. Identifying multiple transformations
11. Advanced problem solving with further
transformations
Geometry and Measure
Unit description
In this unit pupils apply their knowledge of
transformations to explore negative
enlargement factors and the application of
multiple transformations.
Why this, why now?
This unit extends knowledge of
transformations with combinations of
transformations. It purposefully follows
extended work on ratios as this is a key skill
in this unit.
Prior knowledge requirements



Identify translations, reflections and
rotations
Use vector notation for translations
Describe transformations using
appropriate language and coordinates
Exported 04 September 2025
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17. Similarity
Year 10
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Threads
Lessons in unit


1. Checking and securing understanding of
direct proportion in context
2. The effect of enlargement on the
perimeter of a shape
3. The effect of enlargement on the area of
a shape
4. Using the scale factor for enlarging an
area
5. The effect of enlargement on the volume
of a 3D shape
6. Using the scale factor for enlarging a
volume
7. Checking and securing understanding of
congruent triangles (SSS)
8. Checking and securing understanding of
congruent triangles (SAS)
9. Checking and securing understanding of
congruent triangles (ASA)
10. Checking and securing understanding of
congruent triangles (RHS)
11. Problem solving with advanced similarity
knowledge
Geometry and Measure
Ratio and Proportion
Unit description
In this unit, pupils investigate the effect of an
enlargement on the perimeter and area of a
2-D shape and the volume of a 3-D shape.
Why this, why now?
This unit builds upon work completed on
shape, ratio and transformations.
Prior knowledge requirements



Recognise congruent shapes
Understand scale factors and
enlargement
Use ratio to compare lengths, areas or
volumes
Exported 04 September 2025
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18. Circle theorems
Year 10
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Threads
Lessons in unit


1. Checking and securing understanding of
the parts of a circle
2. The angle at the centre of the circle is
twice the angle at any point on the
circumference
3. The angle in a semicircle is a right angle
4. The perpendicular from the centre of a
circle to a chord bisects the chord
5. The tangent at any point on a circle is
perpendicular to the radius at that point
6. The angles in the same segment are
equal
7. The alternate segment theorem
8. The opposite angles of a cyclic
quadrilateral sum to 180°
9. The tangents from an external point are
equal in length
10. Identifying which circle theorem to use
11. Problem solving with circle theorems
Algebra
Geometry and Measure
Unit description
In this unit, pupils will use their developed
mathematical reasoning skills to derive and
use various circle theorems.
Why this, why now?
This is an advanced unit investigating more
complex properties of circles, and as such
requires in depth knowledge and
understanding of shapes, shape properties,
proof, angles and ratios.
Prior knowledge requirements



Identify parts of a circle (radius,
diameter, chord, tangent)
Recognise angle facts in triangles and
quadrilaterals
Apply geometric reasoning and proof
techniques
Exported 04 September 2025
69
19. Plans and elevations
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
accurate drawings
2. Representing 3D shapes in 2D
3. Drawing the plan and elevations of a
solid
4. Drawing the solid from the plan and
elevations
5. Problem solving with plans and
elevations
Geometry and Measure
Unit description
In this unit, pupils will be considering a 3-D
shape from different viewpoints in order to
draw the side and front elevations as well as
the plan view.
Why this, why now?
This unit follows on from transformations
and further develops spatial awareness.
Prior knowledge requirements



Identify 2D shapes and 3D solids
Visualise 3D objects from 2D views
Draw front, side, and top elevations
Exported 04 September 2025
70
20. Right-angled trigonometry
Year 10
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Threads
Lessons in unit

1. Checking and further securing
understanding of Pythagoras' theorem
2. Using Pythagoras' theorem to justify a
right-angled triangle
3. Calculating the length of a line segment
4. Checking and securing understanding of
the unit circle
5. Checking and securing understanding of
sine ratio problems
6. Checking and securing understanding of
cosine problems
7. Checking and securing understanding of
tangent ratio problems
8. Calculate trigonometric ratios for 30°
and 60°
9. Calculate trigonometric ratios for 0°, 45°
and 90°
10. Applying trigonometric ratios in context
11. Applying Pythagoras' theorem in 3D
12. Applying trigonometric ratios in 3D
13. Advanced problem solving with rightangled trigonometry
Geometry and Measure
Unit description
In this unit, pupils are introduced to a variety
of situations where trigonometric ratios are
required, such as 3-D problems and
problems of elevation or depression.
Why this, why now?
This unit requires good understanding of
ratios, trigonometric ratios and manipulation
of formulae, as such it is positoned after
several units revisiting and building upon
these key skills.
Prior knowledge requirements



Identify opposite, adjacent and
hypotenuse
Use Pythagoras' Theorem
Understand ratios in similar triangles
Exported 04 September 2025
71
21. Bearings
Year 10
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Threads
Lessons in unit

1. Checking and securing understanding of
scaled drawings
2. Checking and securing understanding of
drawing accurate scaled diagrams
3. Following a bearing
4. Finding a bearing
5. Reverse bearings
6. Problem solving with bearings
Geometry and Measure
Unit description
In this unit, pupils apply their knowledge of
angles in order to calculate bearings and
solve angle problems within the context of
bearings.
Why this, why now?
This unit requires trigonometry, spatial
awareness and angle facts to be able to
calculate bearings and reverse bearings. As
such it is positioned after those units of
work.
Prior knowledge requirements



Measure angles accurately using a
protractor
Use a compass and draw angles from
North
Apply knowledge of angles on a straight
line and at a point
Exported 04 September 2025
72
Higher
Year 11 units
View interactive sequence online
1
2
3
Algebraic fractions
Non right-angled
trigonometry
2D and 3D shape:
surface area and
volume (pyramids,
spheres and cones)
4
5
6
Conditional
probability
Compound measures
Real-life graphs
7
8
9
Direct and inverse
proportion
Functions and proof
Further sequences
10
11
12
Iteration
Graphical
representations of
data: cumulative
frequency and
histograms
Inequalities
13
14
15
Vectors
Loci and construction
Transformations of
graphs
Exported 04 September 2025
73
1. Algebraic fractions
Year 11
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Threads
Lessons in unit

1. Checking and securing understanding of
solving with simple algebraic fractions
2. Simplifying algebraic fractions
3. Operations with algebraic fractions
4. Solving equations with algebraic
fractions
5. Checking and securing understanding of
changing the subject with simple
algebraic fractions
6. Changing the subject with multiple
algebraic fractions
7. Changing the subject where the variable
appears in multiple terms
8. Problem solving with advanced
algebraic fractions
Algebra
Unit description
In this unit, pupils apply skills in
manupulating and solving various equations
and formulae to algebraic fractions in order
to change the subject and manipulate them.
Why this, why now?
In this unit we are building on a solid
foundation of number and algebra skills to
extend into algebraic fractions which require
strong skills in algebraic manipulation.
Prior knowledge requirements



Simplify algebraic expressions
Apply fraction rules to algebraic terms
Factor and cancel common algebraic
factors
Exported 04 September 2025
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2. Non right-angled trigonometry
Year 11
Go to unit resources
Threads
Lessons in unit


1. Checking and securing understanding of
trigonometric ratios
2. Drawing the sine and cosine graphs
3. Drawing the tangent graph
4. Interpreting the trigonometric graphs
5. The area of any triangle
6. Calculating the area of any triangle
when the height is not known
7. The sine rule
8. The cosine rule
9. Using the sine and cosine rules
10. Considering the appropriate
trigonometric rule
11. Problem solving with non right-angled
trigonometry
Algebra
Geometry and Measure
Unit description
In this unit, pupils explore how to apply
knowledge in trigonometry to non rightangled triangles.
Why this, why now?
This unit continues work that pupils
completed at the end of Year 10, furthering
investigation into trigonometry to
incorporate non right-angled triangles.
Prior knowledge requirements



Use the sine, cosine and tangent ratios
in right-angled triangles
Apply Pythagoras' Theorem
Interpret the sine and cosine rules for
any triangle
Exported 04 September 2025
75
3. 2D and 3D shape: surface area and volume (pyramids,
spheres and cones)
Year 11
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Threads
Lessons in unit

1. Checking and securing understanding of
nets of solids
2. Checking and securing understanding of
volume of prisms
3. Checking and securing understanding of
surface area of cuboids
4. Checking and securing understanding of
surface area of other prisms
5. Checking and securing understanding of
volume of a cylinder
6. Checking and securing understanding of
surface area of a cylinder
7. The surface area of a pyramid
8. The volume of a pyramid
9. The surface area of a sphere
10. The volume of a sphere
11. The surface area of a cone
12. The volume of a cone
13. Surface area of composite solids
14. Volume of composite solids
15. Volume of a frustum of a cone
16. Surface area of a frustum of a cone
17. Forming equations involving complex
shape calculations
18. Advanced problem solving with further
surface area and volume
Geometry and Measure
Unit description
In this unit, pupils will further develop their
understanding of shapes by considering the
surface area and volume of pyramids,
spheres and cones.
Why this, why now?
This unit continues work on area and
volume from the Year 10, introducing more
complicated shapes including pyramids,
spheres and cones.
Prior knowledge requirements



Identify and name 2D and 3D shapes
Recall and use area and volume
formulas for simple solids
Apply formulas for curved surfaces and
composite shapes
Exported 04 September 2025
76
4. Conditional probability
Year 11
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Threads
Lessons in unit

1. Checking and securing displaying
outcomes
2. Checking and securing exhaustive
events
3. Probabilities involving algebra
4. Frequency trees
5. Checking and securing calculating
probabilities from tables
6. Checking and securing calculating
probabilities from diagrams
7. Experimental probability
8. Experimental vs theoretical probability
9. Set notation
10. Conditional probability in a two-way
table
11. Conditional probability in a Venn
diagram
12. Conditional probability in a tree diagram
13. Algebra in tree and Venn diagrams
14. Constructing three event Venn diagrams
15. Probabilities in three event Venn
diagrams
16. Comparing multiple representations to
calculate conditional probabilities
17. Combinations
18. Advanced problem solving with
conditional probability
Probability
Unit description
In this unit, pupils use their knowledge of
calculating theoretical probabilities and
extend it to calculate conditional
probabilities.
Why this, why now?
This unit is placed here to assist
interleaving, and draws upon prior
knowledge from the unit 'Probability:
theoretical probabilities' in Year 9 moving
into more complex models of probability.
Prior knowledge requirements



Interpret probability using tables and
tree diagrams
Understand dependent vs independent
events
Use multiplication and addition rules in
probability
Exported 04 September 2025
77
5. Compound measures
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and further securing
understanding of direct proportion in
context
2. Compound measures for speed
3. Compound measures for density
4. Compound measures for pressure
5. Converting between metric speed
measures
6. Converting between metric and imperial
speed measures
7. Converting between other compound
measures
8. Combining speeds
9. Combining densities
10. Advanced problem solving with
compound measures
Ratio and Proportion
Unit description
In this unit, pupils explore the multiplicative
relationship between different compound
meaures and units such as speed, rates of
pay, density and pressure.
Why this, why now?
This unit builds from knowledge developed
from work in ratio and conversion in Year
10.
Prior knowledge requirements



Use formulas involving speed, density,
and pressure
Convert between units of rate (e.g. km/h,
m/s)
Substitute into formulas and rearrange if
necessary
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6. Real-life graphs
Year 11
Go to unit resources
Threads
Lessons in unit


1. Checking and securing understanding of
reading from context-based graphs
2. Checking and securing understanding of
drawing distance-time graphs
3. Distance-time graphs
4. Speed-time graphs
5. Non-linear distance-time graphs
6. Interpreting and drawing real-life graphs
7. Interpreting and drawing more real-life
graphs
8. Calculating the rate of change
9. Estimating the gradient of a curve
10. Improving the estimate of the gradient of
a curve
11. Finding the equation of a radius of a
circle
12. Finding the equation of the tangent to a
circle
13. Calculating journeys from linear speedtime graphs
14. Estimating journeys from non-linear
graphs
15. Efficiently estimating journeys from nonlinear graphs
16. Advanced problem solving with real-life
graphs
Algebra
Ratio and Proportion
Unit description
In this unit pupils expand upon knowledge
developed in the linear graphs unit. Pupils
are introduced to rates of change and the
gradient of the tangent as a way of
estimating the gradient of a curve.
Why this, why now?
In the previous unit, pupils looked at
compound measures liike speed, and this
work is further developed to look at speed
distance time graphs, and links features of
graphs to practical interpretation.
Prior knowledge requirements



Interpret linear graphs and trends
Understand units and labels in context
(e.g. distance/time)
Use graphs to describe rates and
changes
Exported 04 September 2025
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7. Direct and inverse proportion
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
direct proportion graphs
2. Checking and securing understanding of
inverse proportion graphs
3. Abstract direct proportion
4. Finding the constant of proportionality
for direct proportion
5. Finding the constant of proportionality
for directly proportional relationships
6. Abstract inverse proportion
7. Finding the constant of proportionality
for inverse proportion
8. Proportion modelled algebraically
9. Problem solving with direct and inverse
proportion
Ratio and Proportion
Unit description
In this unit, pupils learn how to represent
direct and inverse proportion algebraically
as an extension of work done in the linear
graphs unit.
Why this, why now?
In this unit we continue work from linear
graphs, and link to the previous unit through
interpreting graphs which is utilised here
when discussing direct and inverse
proportion.
Prior knowledge requirements



Understand ratios and scaling
Use the unitary method to solve
proportional problems
Identify and apply proportional
relationships
Exported 04 September 2025
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8. Functions and proof
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
functions
2. Defining function notation
3. Finding the inverse of a function
4. Writing composite functions
5. Solving equations involving functions
6. Solving equations involving composite
functions
7. General algebraic forms for specific
number properties
8. Making conjectures about patterns and
relationships
9. Proving or disproving a statement
10. Writing a generalised statement about
specific number properties
11. Writing a proof
12. Logical arguments
13. Multiple approaches to logical
arguments
14. Problem solving with functions and proof
Algebra
Unit description
In this unit pupils will further develop their
understanding of algebraic notation and
graphs by learning about functions, their
inverses and composite functions.
Why this, why now?
This unit formalises what a function is, and
proof (including strategies to develop a
proof). It links with work done on algebraic
fractions earlier in the year.
Prior knowledge requirements



Understand mappings from inputs to
outputs
Use substitution in algebraic
expressions
Construct logical chains of reasoning
using algebra
Exported 04 September 2025
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9. Further sequences
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
special number sequences
2. Fibonacci and alternating sequences
3. Checking and securing rules for
generating arithmetic sequences
4. Identifying values in an arithmetic
sequence
5. Reasoning about values in an arithmetic
sequence
6. Conditions in arithmetic sequences
7. Arithmetic sequences and their graphs
8. Introducing quadratic sequences
9. Quadratic sequences
10. Checking and securing understanding of
geometric sequences
11. Sequence notation
12. Advanced problem solving with further
sequences
Algebra
Unit description
In this unit, pupils consider different types of
sequences such as Fibonacci and oscillating
sequences. They then consolidate their
knowledge of different types of sequences
by solving contextual problems.
Why this, why now?
This unit builds knowledge of all types of
sequences covered so far, and links
explicitly to theoretical problems and
graphical representations.
Prior knowledge requirements



Generate terms from nth-term
expressions
Identify linear, quadratic and geometric
sequences
Use recursive rules to build sequences
Exported 04 September 2025
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10. Iteration
Year 11
Go to unit resources
Threads
Lessons in unit

In this unit, pupils continue to explore
composite functions and develop
understanding of iteration, building on their
work on functions and proof.
1. Checking and securing understanding of
compound interest calculations
2. Building on composite functions
3. Evaluating iterative formulas
4. Approximating solutions to equations
5. Signs of a solution
6. Problem solving with iteration
Why this, why now?
Prior knowledge requirements
This unit builds on function notation and
compound functions to more efficiently
represent and understand repeated
applications.


Algebra
Unit description

Understand function machines and
input-output
Substitute into simple expressions
Recognise convergence in repeated
processes
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11. Graphical representations of data: cumulative
frequency and histograms
Year 11
Go to unit resources
Threads
Lessons in unit

1. Constructing a cumulative frequency
graph
2. Interpreting a cumulative frequency
graph
3. Constructing box plots
4. Comparing box plots
5. Interquartile range
6. Histograms with equal bar width
7. Histograms with unequal bar width
8. Moving between tables and histograms
9. Summary statistics from histograms
10. Constructing histograms and box plots
using technology
11. Problem solving with cumulative
frequency and histograms
Statistics
Unit description
In this unit, pupils consider cumulative
frequency graphs and histograms, and
compare these with other known graphical
representations.
Why this, why now?
This unit continues work on representing
and interpreting data and incorporates
knowledge developed in Year 10 on
comparisons of data. Here we also develop
the use of technology to better understand
and interrogate data.
Prior knowledge requirements



Interpret grouped data tables
Plot and interpret frequency and
cumulative frequency graphs
Understand class intervals and scale in
histograms
Exported 04 September 2025
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12. Inequalities
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
simultaneous equations
2. Non-solutions to simultaneous linear
equations
3. Inequalities on number lines
4. Solving simple linear inequalities
5. Solving more complicated linear
inequalities
6. Linear inequalities in context
7. A single solution set
8. Solution set notation
9. Solving a linear inequality graphically
10. Solving a set of linear inequalities
graphically
11. Relating graphical solutions to algebraic
solutions for inequalities
12. Solving quadratic inequalities in one
variable graphically
13. Solving quadratic inequalities
algebraically
14. Advanced problem solving with linear
inequalities
Algebra
Unit description
In this unit, pupils extend their
understanding of inequalities and consider a
range of contextual inequalities and ways to
find and represent their solutions.
Why this, why now?
This unit requires strong knowledge of
number, manipulation of number, and
number generalisation through algebraic
skills. Here we further develop that
understanding and investigate similar
themes through inequalities rather than
equations.
Prior knowledge requirements



Solve linear equations
Represent inequalities on number lines
Interpret inequality symbols and
solutions
Exported 04 September 2025
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13. Vectors
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
translations
2. Column vectors
3. Parallel vectors
4. Addition with vectors
5. Subtraction with vectors
6. Multiplication with vectors
7. Fluency in arithmetic procedures with
vectors
8. Algebraic vector notation
9. Parallel vectors in algebraic vector
notation
10. The sum and difference with algebraic
vector notation
11. Fluency in arithmetic procedures with
algebraic vector notation
12. Calculating the magnitude of a vector
13. Dividing vectors into ratios
14. Geometric proofs with vectors
15. Advanced problem solving with vectors
Geometry and Measure
Unit description
In this unit, pupil understanding of vectors is
deepened with pupils exploring column
vector notation and arithmetic procedures.
Why this, why now?
This unit requires confidence in different
notation and types of notation as well as
strong geometric reasoning and number
skills. As such it is placed here as units
covering those skills have been completed.
Prior knowledge requirements



Understand direction and magnitude
Add and subtract vectors using
diagrams or components
Represent vectors algebraically in 2D
Exported 04 September 2025
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14. Loci and construction
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
constructing the perpendicular bisector
of a line segment
2. Checking and securing understanding of
constructing a perpendicular to a given
line through a point
3. Checking and securing understanding of
bisecting an angle
4. Constructing angles of 90° and 45°
5. Constructing a triangle given three side
lengths using compasses
6. Constructing a triangle given two side
lengths and the angle between them
using a compass
7. Constructing a triangle given two angles
and the side length between them
8. Constructing a right-angled triangle
given the length of the hypotenuse and
one other side length
9. Constructing a triangle given two side
lengths and an angle not between them
10. Constructing loci
11. Applying constructions to loci problems
12. Solving loci problems in context
13. Advanced problem solving with loci and
constructions
Geometry and Measure
Unit description
In this unit, pupils construct triangles and
construct diagrams following specific
restrictions using their knowledge of loci and
their work on constructions.
Why this, why now?
This unit follows from vectors where pupils
revisited and enhanced their understanding
of shape and space. We link that knowledge
to this unit as well as building from proof
and trigonometry to construct accurate and
specific shapes and diagrams.
Prior knowledge requirements



Use compass and straightedge
accurately
Understand perpendicular and angle
bisectors
Apply basic properties of geometric
figures
Exported 04 September 2025
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15. Transformations of graphs
Year 11
Go to unit resources
Threads
Lessons in unit

1. Checking and securing understanding of
function notation
2. Checking and securing understanding of
moving between function notation and
the definition
3. Transforming graphs: y = f(x) + a
4. Transforming graphs: y = f(x + a)
5. Transforming graphs: y = −f(x)
6. Transforming graphs: y = f(−x)
7. Transforming graphs: y = af(x)
8. Transforming graphs: y = f(ax)
9. Transforming graphs: combinations of
transformations
10. Problem solving with graph
transformations
Algebra
Unit description
In this unit pupils learn how to perform
transformations on functions both
algebraically and visually.
Why this, why now?
This unit explores the structure of
transforming graphs and as such it is
positioned after function notation which is
essential knowledge building towards this
unit.
Prior knowledge requirements



Understand horizontal and vertical shifts
Know equations of standard graphs
(e.g., y = x_, y = √x)
Interpret effect of operations on graph
shape and position
Exported 04 September 2025
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Threads in maths
See how to use threads
Algebra
Geometry and Measure
Number
Probability
Ratio and Proportion
Statistics
Exported 04 September 2025
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Thread, 'Algebra'
Year 7


Unit 4, 'Expressions and equations'
Unit 5, 'Plotting coordinates'
Year 8



Unit 2, 'Sequences'
Unit 3, 'Graphical representations of linear equations'
Unit 4, 'Solving linear equations'
Year 9



Unit 4, 'Non-linear relationships'
Unit 5, 'Expressions and formulae'
Unit 8, 'Graphical representations'
Year 10





Unit 1, 'Algebraic manipulation'
Unit 2, 'Simultaneous equations: 2 variables'
Unit 12, 'Linear graphs'
Unit 13, 'Non-linear graphs'
Unit 18, 'Circle theorems'
Year 11








Unit 1, 'Algebraic fractions'
Unit 2, 'Non right-angled trigonometry'
Unit 6, 'Real-life graphs'
Unit 8, 'Functions and proof'
Unit 9, 'Further sequences'
Unit 10, 'Iteration'
Unit 12, 'Inequalities'
Unit 15, 'Transformations of graphs'
Exported 04 September 2025
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Thread, 'Geometry and Measure'
Year 7


Unit 6, 'Perimeter and area'
Unit 10, 'Transformations'
Year 8



Unit 8, 'Perimeter, area and volume'
Unit 9, 'Geometrical properties: polygons'
Unit 10, 'Constructions'
Year 9


Unit 1, 'Geometrical properties: similarity and Pythagoras' theorem'
Unit 6, 'Trigonometry'
Year 10








Unit 14, '2D and 3D shape: compound shapes'
Unit 15, 'Angles'
Unit 16, 'Further transformations'
Unit 17, 'Similarity'
Unit 18, 'Circle theorems'
Unit 19, 'Plans and elevations'
Unit 20, 'Right-angled trigonometry'
Unit 21, 'Bearings'
Year 11




Unit 2, 'Non right-angled trigonometry'
Unit 3, '2D and 3D shape: surface area and volume (pyramids, spheres and cones)'
Unit 13, 'Vectors'
Unit 14, 'Loci and construction'
Exported 04 September 2025
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Thread, 'Number'
Year 7






Unit 1, 'Place value'
Unit 2, 'Properties of number: factors, multiples, squares and cubes'
Unit 3, 'Arithmetic procedures with integers and decimals'
Unit 7, 'Comparing and ordering fractions and decimals (positive and negative)'
Unit 8, 'Arithmetic procedures with fractions'
Unit 9, 'Understanding multiplicative relationships: fractions and ratio'
Year 8



Unit 1, 'Estimation and rounding'
Unit 5, 'Understanding multiplicative relationships: percentages and proportionality'
Unit 8, 'Perimeter, area and volume'
Year 9

Unit 7, 'Standard form'
Year 10




Unit 4, 'Arithmetic procedures: index laws'
Unit 5, 'Standard form calculations'
Unit 6, 'Surds'
Unit 10, 'Rounding, estimation and bounds'
Exported 04 September 2025
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Thread, 'Probability'
Year 9


Unit 2, 'Probability: possible outcomes'
Unit 3, 'Probability: theoretical probabilities'
Year 11

Unit 4, 'Conditional probability'
Exported 04 September 2025
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Thread, 'Ratio and Proportion'
Year 7

Unit 9, 'Understanding multiplicative relationships: fractions and ratio'
Year 8

Unit 5, 'Understanding multiplicative relationships: percentages and proportionality'
Year 9

Unit 6, 'Trigonometry'
Year 10




Unit 3, 'Percentages'
Unit 11, 'Ratio'
Unit 12, 'Linear graphs'
Unit 17, 'Similarity'
Year 11



Unit 5, 'Compound measures'
Unit 6, 'Real-life graphs'
Unit 7, 'Direct and inverse proportion'
Exported 04 September 2025
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Thread, 'Statistics'
Year 8


Unit 6, 'Graphical representations of data'
Unit 7, 'Numerical summaries of data'
Year 10



Unit 7, 'Sampling'
Unit 8, 'Graphical representations of data: scatter graphs and time series'
Unit 9, 'Comparisons of numerical summaries of data'
Year 11

Unit 11, 'Graphical representations of data: cumulative frequency and histograms'
Exported 04 September 2025
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© Oak National Academy 2024.
Produced in partnership with Mathematics Education Innovation (MEI).
Licensed on the Open Government Licence v3.0 , except where otherwise stated.
See Oak terms and conditions .
Exported 04 September 2025
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