Maths Curriculum Department

Maths Curriculum

Age Range: 4-18

Subject Vision Statement: 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.

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.

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.

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.