Maths Curriculum

Age Range: 4-18

Maths at School 21 empowers all students to be and see themselves as successful mathematicians. It does this through placing mastery at the centre of their learning, focusing on strong conceptual understanding and fluency but also through utilising a love of learning through challenge, creativity and exploration.

Maths Curriculum Big Ideas

Equivalence	Any number, measure, object, numerical expression, algebraic expression or equation can be represented in a multitude of ways in the same form that all have the same value.
Proportionality	Two quantities can vary in a proportional relationship. This begins as a linear relationship but that can be extended to other relations.
Comparison	Numerical and algebraic forms can be compared by their relative size. This allows for equalities and inequalities.
Pattern	Relationships can be found in patterns. These relationships can then be generalised and tested. Pattern is the basis for much of mathematics, especially mathematical intuition.
Abstraction	Concrete and observable patterns and relationships can be abstracted. This is often through the power of algebraic representation. Algebra provides us with a language to talk about these abstracted ideas.
Chance	The likelihood of something occuring can be measured. It is described numerically using a number between 0 and 1.
Measurement	There are attributes of objects that can be quantified. Measurement allows us to do this quantifying.
Properties	Some numbers, shapes and other objects have properties that are always true. This allows us to develop rules, deduce further results and classify objects based on these properties.
Relations	Mathematical rules allow us to assign one set of numbers/objects to another set. This leads to a special set of relations called functions.
Proof	It is possible to logically prove something will always be the case, is sometimes the case or will never be the case.
Data	Information can be collected in a quantifiable form and this is called data. It can be analysed, represented in various forms and its distribution can be described using special numerical measures.
Representation	We can represent the same information in multiple forms. Each way allows for different interpretation to become apparent. Multiple representations of the same information allows for greater understanding to be drawn.
Operations	There are numerical and non-numerical operations that we can apply to numbers and algebraic forms. These can represent real world situations.
Base 10	The number system we use throughout mathematics is Base 10, which has some benefits and leads to some important understanding of the size of a number. That we use Base 10 makes it special, but it is not inevitable, other base systems also have important value currently and historically.
Logic	Mathematics is a hierarchical subject where logical deduction and reasoning allow us to draw results and conclusions from initial facts or axioms.

The School 21 approach

As a school we believe:

The mathematical learning should take place at depth throughout every stage of school.
That success will come through mastery and fluency. This will be achieved through suitable feedback and consolidation, rather than a focus on coverage. Coverage will come in time.
That conceptual understanding is the core aim of our curriculum.
That fundamental knowledge, skills and understandings allow students to access future learning.

We want students to become mathematicians that are able to:

Embrace challenge as a learning opportunity.
Feel that they are becoming successful mathematicians, and that success is not about “getting things right”.
Are able to explain the mathematics they are doing, what it means and how it can be applied.
Value mathematics as a process and discipline for understanding the world around us.
Take joy in the creativity of exploring Maths as an interconnected web of ideas.

We want students to feel supported regardless of their starting point, and that mathematics is a subject for them.

Subject Design Principles:

We focus on developing deep conceptual understanding. Where appropriate this is scaffolded using a progression of concrete to pictorial to abstract representation.
We focus on mastery of topics in the first instance and then interleave these topics throughout future topics highlighting and strengthening the interconnectedness of mathematics. Practice of a key skill comes before application. Opportunities for problem solving and creative thinking are built up to.
We teach in mixed attainment groupings. We offer support and stretch to meet all students’ needs. Support should enable students to access the work, not make the content easier. Stretch should develop greater depth of understanding and not move students on to the next part of content.
Collaboration between students is used, often with embedded Oracy, to support development of understanding. We communicate to students how concepts develop and are linked to the big ideas in our curriculum. Students can explain what they are learning, why it works and how it fits into the big ideas.
Assessment is embedded throughout lessons and units to react to and build on student’s developing knowledge and skills. Misconceptions are used to help deepen understanding.
We put emphasis on developing good mathematical literacy and use of mathematical language in an accurate manner that demonstrates understanding both in context and in the abstract.

Phase Specific Journey:

Phases 1 and 2	Developing a love of learning
Phase 1 Journey	Basic principles. Building number sense. Exploring the world around through numerical/mathematical kens. Beginning approaches to four operations.
Phase 2 Journey	Securing place value beyond 100. Building fluency with four operations. Laying foundational understanding of parts of a number (decimals, fractions), shape and measure

Phases 3 and 4	Developing passions and increasing independence
Phase 3 Journey	Finesse and fluency with key numerical skills that will be embedded in all future mathematics. First experiences with algebra.
Phase 4 Journey	Securing understanding of key concepts in number, ratio and proportion, geometry, data and algebra that will enable students to access higher level concepts and techniques.

Phases 5 and 6	Building choice, autonomy and empowered professionalism
Phase 5 Journey	Developing more abstract concepts that build on the secure understanding from phase 4. Another moment of finesse and fluency to be reached in our Apex point (GCSE exams). Becoming confident in a wide range of applications. For some, building readiness for making the jump to A Level, for others it is about building mathematical confidence in preparation for finishing their formal Maths education.
Phase 6 Journey	Building a secure foundation for the real world of academic mathematics, or to enable strong application in alternative degree or career routes. At the same time we explore the beauty of abstraction that moves from application into a way of thinking that goes beyond the everyday.

Progression Map

Primary

Secondary

Reception

Autumn term 1

Early mathematical experiences

Pattern and early number

Autumn term 2

Number within 6

Addition and subtraction within 6

Measures

Shape and sorting

Spring term 1

Numbers within 10

Calendar and time

Addition and subtraction within 10

Grouping and sharing

Spring term 2

Number patterns within 15

Doubling and halving

Shape and pattern

Summer term 1

Securing addition and subtraction facts

Number patterns within 20

Number patterns beyond 20

Summer term 2

Money

Measures

Exploration of patterns within number

Year 1

Autumn term 1

Numbers to 10

Addition and subtraction within 10

Shape and patterns

Autumn term 2

Numbers to 20

Addition and subtraction within 20

Spring term 1

Time

Exploring calculation strategies within 20

Numbers to 50

Spring term 2

Addition and subtraction within 20 (comparison)

Fractions

Measures (1): Length and mass

Summer term 1

Numbers 50 to 100 and beyond

Addition and subtraction (applying strategies)

Money

Summer term 2

Multiplication and division

Measures (2): Capacity and volume

Year 2

Autumn term 1

Numbers within 100

Addition and subtraction of 2-digit numbers

Addition and subtraction word problems

Autumn term 2

Measures: length

Graphs

Multiplication and division: 2, 5 and 10

Spring term 1

Time

Fractions

Addition and subtraction of 2-digit numbers (regrouping and adjusting)

Spring term 2

Money

Faces, shapes and patterns; lines and turns

Summer term 1

Number within 1000

Measures: Capacity and volume

Measures: Mass

Summer term 2

Exploring calculation strategies

Multiplication and division: 3 and 4

Year 3

Autumn term 1

Number sense and exploring calculation strategies

Place value

Graphs

Autumn term 2

Addition and subtraction

Length and perimeter

Spring term 1

Multiplication and division

Deriving multiplication and division facts

Spring term 2

Time

Fractions

Summer term 1

Angles and shape

Measures

Summer term 2

Securing multiplication and division

Exploring calculation strategies and place value

Year 4

Autumn term 1

Reasoning with 4-digit numbers

Addition and subtraction

Autumn term 2

Multiplication and division

Interpreting and presenting data

Spring term 1

Securing multiplication facts

Fractions

Time

Spring term 2

Decimals

Area and perimeter

Summer term 1

Solving measure and money problems

2D shape and symmetry

Summer term 2

3D shape

Position and direction

Reasoning with patterns and sequences

Year 5

Autumn term 1

Reasoning with large whole numbers

Problem solving with integer addition and subtraction

Line graphs and timetables

Autumn term 2

Multiplication and division

Perimeter and area

Spring term 1

Fractions and decimals

Angles

Spring term 2

Fractions and percentages

Transformations

Summer term 1

Converting units of measure

Calculating with whole numbers and decimals

Summer term 2

2D and 3D shape

Volume

Problem solving

Year 6

Autumn term 1

Integers & Decimals

Multiplication and division

Autumn term 2

Calculation problems

Fractions

Missing angles and lengths

Spring term 1

Coordinates and shape

Fractions

Decimals and measures

Spring term 2

Percentages and statistics

Proportion problems

Summer term 1

Summer term 2

Year 7

Autumn term 1

Number skills

Properties of Number

Autumn term 2

Properties of 2D shapes

Angles in 2D shapes

Spring term 1

Data Handling

Coordinates

Spring term 2

Fractions

Summer term 1

Introduction to Algebra

Formulae

Summer term 2

Circles

Year 8

Autumn term 1

Indices and Prime Factorisation

Negative Numbers

Autumn term 2

Ratio

Proportional Reasoning

Spring term 1

Transformations

Spring term 2

Solving Equations

Angles in Polygons

Summer term 1

Sequences

3D Shapes

Summer term 2

Inequalities

Probability

Year 9

Autumn term 1

Percentages

Extreme Numbers

Autumn term 2

Pythagoras

Angles on Parallel Lines

Right angled Trigonometry

Spring term 1

Straight Line Graphs

Spring term 2

Simultaneous Equations

Quadratic Equations

Summer term 1

Data Tables

Summer term 2

Probability

Year 10

Autumn term 1

Solving and Rearranging Equations

Volume and Surface Area

Autumn term 2

Algebraic Fractions

Further Probability

Spring term 1

Similar Shapes

Spring term 2

Algebraic Proportion

Statistical Diagrams

Summer term 1

Angle Rules and Circle Theorems

Summer term 2

Further Index Laws

Further Sequences

Year 11

Autumn term 1

Further Trigonometry

Surds and Indices

Autumn term 2

Sequences, Functions and Iteration

Congruency

Vectors

Spring term 1

Hard Quadratics and Proof

Further Graphs

Transformation of Graphs

Spring term 2

Constructions, Loci and Bearings

Summer term 1

Summer term 2

Year 12

Autumn term 1

Sequences and Series

Polynomials and Circles

Forces

Further Maths:

Introduction to Complex Numbers

Complex Roots of Polynomials

Series and Induction

Autumn term 2

Functions and Graphs

Radians and Trigonometric Functions

Forces

Moments

Further Maths:

Matrices and Transformation

Eigenvalues and Eigenvectors

Spring term 1

Exponentials and Logarithms

Kinematics with Constant Acceleration

Further Maths:

Vector Geometry

De Moivre’s Theorem

Group Theory

Spring term 2

Vectors

Kinematics with Constant Acceleration

Basics of Differentiation

Further Maths:

Work, Energy & Power

Summer term 1

Basics of Integration

Kinematics with Variable Acceleration

Further Maths:

Momentum & Impulse

Further Projectiles and Moments

Summer term 2

Proof

Kinematics with Variable Acceleration

Further Maths:

Polar Coordinates

Year 13

Autumn term 1

Functions

Further Trigonometric Functions

Further Differentiation Methods

Further Maths:

Recurrence Relations

Polar Coordinates

Circular Motion and Hooke’s Law

Autumn term 2

Further Integration Methods

Parametric and Differential Equations

Further Maths:

Hyperbolic Functions

Maclaurin Series

Applications of Integration

Differential Equations

Spring term 1

Raw Statistics and Sampling

Probability

Probability Distributions and Hypothesis Testing

Further Maths:

Multivariable Calculus

Centre of Mass

Applications of Differential Equations

Spring term 2

Summer term 1

Summer term 2

Maths Curriculum