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)

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.

Primary

Maths

Key Stage 1

Key Stage 2

Key Stage 3

Key Stage 4

Secondary

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

Number: Addition and Subtraction

Number: Fractions

Number: Multiplication and division

Number: Place value

Probability

Ratio and Proportion

Statistics

In this unit pupils will review their knowledge from the EYFS with counting to and from 10. They will compare and order numbers to 10 practically and will consider the role of zero to represent nothing. In the future unit pupils will  consolidate counting to 20 and back. They will secure their understanding of the teens numbers and their understanding of these numbers in an ordinal context

Counting to and from 20

In prior learning, pupils will have learnt to count confidently and have developed a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. In this unit pupils will review their knowledge from the EYFS with counting to and from 10, comparing and ordering numbers to 10 and considering the role of zero.

Counting forwards and backwards within 10

Counting objects within ten

Counting different groups

Representing counting songs

Anything can be counted

Subitising numbers to five

Conservation

Using numerals

Introducing zero

Ordinal numbers

Ordering numbers to 10

More than and fewer than

One more with manipulatives and counting

One less with manipulatives and counting

Finding the missing numbers

Counting, recognising and comparing numbers 0 - 10

In this unit pupils will consolidate counting to 20 and back. They will secure their understanding of the teens numbers in a cardinal and an ordinal context. In the future unit pupils will extend their counting to counting the decade numbers and making representations using a variety of different manipulatives.

Counting in tens - decade numbers

In prior learning, pupils will have learnt to count confidently and have developed a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. In this unit pupils will consolidate counting to 20 and back and will secure their understanding of the teens numbers in a cardinal and an ordinal context.

Counting on

Counting back from 20

Counting forward to 20 and back from 20

Comparing numbers to 20

Ordering numbers 11- 20 practically

Comparing and ordering numbers 0-20 practically

Finding one more and one less using representations

Finding one more and one less with manipulatives and images

Finding the missing number from 0 to 20

In this unit pupils will extend their counting to counting the decade numbers and making representations using a variety of different manipulatives. In the future unit pupils will extend their learning by counting to 100. They will explore the pattern in counting and focus on the end of the decade and the start of the new decade numbers.

Pattern in counting from 20 to 100

In prior learning, pupils will have verbally counted beyond 20, recognising the pattern of the counting system. In this unit pupils will extend their counting o the decade numbers and represent them in different ways.

Counting forwards and backwards in 10s to 50

Counting forwards and backwards in 10s to 100

Composition of decade numbers to 100: making groups of 10

Count groups of 10 in decade numbers

Order and compare decade numbers on number tracks

In this unit pupils will extend their learning by counting to 100. They will explore the pattern in counting and focus on the end of the decade and the start of the new decade numbers.  In the future unit pupils will explore the counting sequence for counting to 100 and beyond and represent the numbers from 20-99 in different ways, including marking the position on a number line.

Counting and representing the numbers 20 to 99

In prior learning, pupils will have verbally counted beyond 20, recognising the pattern of the counting system. In this unit pupils will extend their learning by counting to 100 and exploring the pattern in counting.

Counting patterns within a decade

Crossing the tens boundary counting forwards

Crossing the tens boundary counting backwards

Crossing the tens boundary counting forwards and backwards

Find missing numbers between 20  and 100

In this unit pupils will explain that items can be compared using length and height, mass and volume/capacity. They will compare sets of objects using equality/inequality symbols. In the future unit pupils will combine 2 or more parts to make a whole. They will learn that addends can be represented in any order and that the = sign is used to show the whole and sum of the parts are equal.

Additive structures: addition

In prior learning, pupils will have had opportunities to use manipulatives to organise counting including using everyday manipulatives, tens frames and through measures. In this unit pupils will explain that items can be compared using length, mass and capacity and use the inequality symbols.

Explain that items can be compared using length and height

Explain that items can be compared using weight and mass

Explain that items can be compared using capacity

Count a set of objects

Solve problems by comparing sets of objects

Use equality and inequality symbols to compare sets of objects

Use equality and inequality symbols to compare the relative size of two numbers

Explain what a whole is

Explain that a whole can be split into parts

Explain that a whole can represent a group of objects

Identify a part of a whole group

Explain what a part-part-whole model is

Use a part-part-whole model to represent a whole partitioned into two parts

Use a part-part-whole model to represent partitioning into more than two parts

Solve problems using part-part-whole models with more than two parts

Comparing quantities - part part whole relationships

In this unit pupils will revisit how numbers are represented cardinally and ordinally. They will partition 1 - 5 in different ways and find a missing part. In the future unit pupils will represent numbers 6 - 10 by partitioning in different ways. They will learn what odd and even numbers are and how they can be partitioned. They will identify a missing part when a whole is partitioned into 2 parts

Composition of numbers 6 to 10

In prior learning, pupils will have explored the composition of numbers to 10 and be able to subitise up to 5. In this unit pupils will partition 1 to 5 in different ways and find a missing part.

Explain that numbers can represent how many objects there are in a set

Ordinal numbers show the position of an object in relation to another

Partition numbers one to five in different ways

Partition the numbers one to five in a systematic way

Find a missing part when one part and the whole is known

Solve problems finding a missing part when one part and the whole is known

Show one more and one less than a number using representations

Show one more and one less than a number using representations and describe this accurately

Use a bar model to represent a whole partitioned into two parts

Solve problems using a bar model to represent a whole partitioned into two parts

Composition of numbers 0 to 5

In this unit pupils will compose, copy, extend and develop repeating and radiating patterns. They will explore, discuss and compare 3D and 2D shapes. In the future unit pupils will  learn that polygons can be described, sorted, compared and named according to the number of sides and vertices. They will describe 3D shapes finding different ways to sort and compare them.

Shape: discuss and compare 2D and 3D shapes

In prior learning, pupils will have developed their spatial reasoning skills in the area of shape, space and measures. In this unit pupils will compose, copy, extend and develop radiating patterns and discuss and compare 2D and 3D shapes.

Composing pattern block images

Copy, extend and describe repeating patterns

Radiating patterns

Compose tangram images

Tetrominoes and pentominoes

Examine ways that cubes can be composed into different arrangements

Explore, recognise and compare three different 3D shapes

Explore, recognise and compare three more 3D shapes

Identify 2D shapes within 3D shapes

Recognise, describe and sort 3D shapes

Explore and recognise 2D shapes

Explore, discuss and compare 2D shapes

Explore, discuss and identify shapes that are and are not circles

Explore, discuss and identify shapes that are and are not triangles

Explore, discuss and identify shapes that are and are not rectangles

Recognise, compose, decompose and manipulate 2D and 3D shapes

In this unit pupils will represent numbers 6 - 10 by partitioning in different ways. They will learn what odd and even numbers are and how they can be partitioned. They will identify a missing part when a whole is partitioned into 2 parts. In the future unit pupils will explain 11-19 cardinally and ordinally. They will double and halve numbers 6-9. They will add and subtract within 20.

Composition of numbers 11 to 19

In prior learning, pupils will have explored the composition of numbers to 10 and be able to subitise up to 5. In this unit pupils will represent numbers 6 to 10 by partitioning in different ways and learn what odd and even numbers are and how they can be partitioned.

Count a set of objects and match the spoken number to the written numeral and number name

Represent the numbers 6 to 10 using a five and a bit structure

Compare two numbers and say which is greater than or less than the other

Identify the whole and parts of the numbers 6 to 10 using the five and a bit structure

Explore the numbers 6 to 10 using the parts and wholes on a number line

Explain where 6, 7, 8 and 9 lie on a number line

Estimate where 6, 7, 8 and 9 lie on an unmarked number line

Order and sort numbers into odd and even sets

Skip count in odds and evens

Explain what odd and even numbers are and the difference between them

Explain how even and odd numbers can be partitioned

Partition the numbers 6 and 7 in different ways

Partition the numbers 8 and 9 in different ways

Partition the numbers 6 to 10 in different ways

Identify a missing part when a whole is partitioned into two parts

In this unit pupils will combine 2 or more parts to make a whole. They will learn addends are represented in any order and the = sign shows the whole and sum of the parts are equal. In the future unit pupils will find missing addends. They will partition a whole into 2 parts representing first, then, now stories with subtraction equations. They will learn + and - are inverse operations.

Additive structures: addition and subtraction

In prior learning, pupils will have learnt to count confidently and have developed a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. In this unit pupils will combine two parts to make a whole, learn that addends are represented in any order and learn that the equals sign shows that the whole and the sum of the parts are equal.

KS1 & KS2 maths curriculum

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