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.

What overarching curriculum principles inform the design of our curriculum?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

Mathematics Education Innovation (MEI)

Secondary maths curriculum explainer video 

Secondary

Maths

Key Stage 1

Key Stage 2

Key Stage 3

Key Stage 4

Primary

Art and design

Core

GCSE

Citizenship

Computing

Cooking and nutrition

Design and technology

Edexcel

Eduqas

English

French

Edexcel B

Geography

German

History

Music

Physical education

Science

Spanish

Religious education

Algebra

Geometry and Measure

Number

Probability

Ratio and Proportion

Statistics

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

Simultaneous equations: 2 variables

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Expressions and formulae

In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.

Checking and securing understanding of simplifying

Checking and securing understanding of substitution

Further algebraic terminology

Checking and securing understanding of expanding a single bracket

Checking and securing understanding of factorising

Checking and securing understanding of forming linear equations

Checking and securing understanding of solving and interpreting linear equations

Checking and securing understanding of changing the subject

Checking and securing understanding of the product of two binomials

Factorising a quadratic expression

Factorising using the difference of two squares

Solving quadratic equations by factorising

Problem solving with algebraic manipulation

Algebraic manipulation

The product of three binomials

Factorising quadratics of the form ax^2 + bx + c

Solving quadratic equations by factorising where rearrangement is required

Solving quadratic equations by completing the square

Solving quadratic equations by using the formula

Advanced problem solving with algebraic manipulation

In the future unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

Inequalities

In the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Combining equations

Solving simultaneous equations by elimination from a context

Solving algebraic simultaneous equations by elimination

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving simultaneous equations via any method

Problem solving with simultaneous equations

Solving a quadratic and linear pair of simultaneous equations using elimination

Solving a quadratic and linear pair of simultaneous equations using substitution

Solving a quadratic and linear pair of simultaneous equations graphically

Problem solving with linear and quadratic simultaneous equations

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. This unit ensures pupils have had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

Ratio

In the prior unit, pupils developed the skills to calculate a given percentage of an amount. In this unit, these skills are extended to performing simple and compound interest calculations.

Understanding multiplicative relationships: percentages and proportionality

In this unit pupils will learn how to perform simple and compound interest calculations using percentages.

Checking and securing understanding of finding a percentage

Checking and securing understanding of percentage increase

Checking and securing understanding of percentage decrease

Percentage profit and loss

Simple and compound interest

Simple interest calculations

Simple interest calculations with technology

Compound interest calculations

Compound interest calculations with technology

Problem solving with percentages

Percentages

Calculating compound interest rates

Changing compound interest rates

Advanced problem solving with percentages

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

Standard form calculations

The conditions for standard form mean that pupils have explored how different powers of 10 can be written in the prior unit. In this unit, this understanding is generalised and the index laws formalised.

Standard form

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Converting any recurring decimal to a fraction

Checking and securing understanding of prime factorisation

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

The laws of indices - fractional exponents

Advanced problem solving with the laws of indices

Arithmetic procedures: index laws

Checking and securing understanding of converting between fractions and decimals

Checking and securing understanding of calculating with fractions and decimals

Checking and securing understanding of calculations involving negative numbers

Problem solving with the laws of indices

In the prior unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

In this unit pupils will learn how to add, subtract, multiply and divide numbers written in standard form.

Checking and securing understanding of writing large numbers in standard form

Checking and securing understanding of writing small numbers in standard form

Adding numbers in standard form

Subtracting numbers in standard form

Multiplying numbers in standard form

Dividing numbers in standard form

Problem solving with standard form calculations

In the prior unit, pupils explored the concept of square root, including calculating this on their calculators. In this unit, pupils work with surds and the notion that a surd is both an operation and the result of that operation.

Properties of number: factors, multiples, squares and cubes

In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.

Accuracy of final answers

Surds

Identifying square factors to support simplifying surds

Simplifying surds

Addition with surds

Multiplication of surds

Applying the underlying structure of multiplication and division of surds

The distributive law with surds

The distributive law with two or more binomials

Rationalising a single term denominator

Rationalising a two term denominator

Solving equations with surds

Problem solving with surds

In this unit, pupils are given the opportunity to assess how valid a sample may be and what the averages might tell us. In the future unit, pupils extend their knowledge of averages to stem and leaf diagrams as well as comparing two data sets.

Comparisons of numerical summaries of data

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

Numerical summaries of data

In this unit pupils will learn how to sample, and explore accuracy and limitations with various sampling strategies and data collection techniques.

Checking understanding of statistical problems

The Statistical Enquiry Cycle

Types of data

Sampling methods

Stratified sampling

Capture/recapture sampling method

Sampling limitations

Data collection

Biased questioning

Advanced problem solving with sampling

Sampling

Problem solving with sampling

In the prior unit, pupils explored different graphs and charts as a way of presenting data visually. Pupils were introduced to scatter graphs and learnt how to construct them. In this unit, this understanding is extended to using a line of best fit to allow interpolation.

Graphical representations of data

In this unit pupils will learn how to interpret and extract data from scatter graphs and time series graphs.

KS3 & KS4 maths curriculum

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