Maths

“Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.”

– Deepak Chopra

Curriculum intent

Mathematics and the understanding of its concepts is a key fundamental life skill.  We want to instil a belief that everyone can have success in mathematics. All students are encouraged by the belief that by working hard at mathematics they can succeed and that making mistakes is to be seen not as a failure but as a valuable opportunity for new learning. We want to develop students’ love for learning mathematics beyond school, and with the belief that they can succeed by establishing secure foundations for lifelong learning.

The Mathematics Curriculum is a 5-year journey in which students develop their mathematical fundamentals, they then build upon these, extend their understanding, uncover where their knowledge can take them and how all of their knowledge is encompassed and interleaved into different topics.

What does progress through Key Stage 3 look like for a student in Maths?

Our curriculum is carefully designed and sequenced to ensure that all students, regardless of their prior attainment, can succeed in mathematics.  

We aim to provide an ambitious curriculum for all learners and with the development of Mastery remove barriers to learning for all learners and narrow the gaps for disadvantaged children. The KS3 curriculum builds on KS2 foundations and core number work is threaded throughout our Year 7 scheme of learning. We have shone a spotlight on the areas of our curriculum which could be impacted on by a student’s gap in social and cultural capital. Teachers can then take opportunities to bridge these gaps.

A strict scheme of learning (although flexible with time allocation) with central resources and assessment ensures consistency of experience for all students regardless of their individual teachers. Where opportunities allow, learning outside of the curriculum extends students’ experience beyond the National Curriculum.

What do students learn in Year 7?

In Year 7 students further develop their skills from Key Stage 2.  In addition students will study new areas of mathematics, including an introduction to Probability.

Students begin Year 7 by exploring in more depth Directed Numbers and their applications.  Students regularly use manipulatives in order to improve their level of understanding with negative numbers.  The use of manipulatives is extended when students move onto Algebraic Expressions, through the use of Algebra Tiles.  Students then continue to develop their KS2 skills of fractions to using mixed numbers and proper fractions with all four operations; students will also apply these skills to worded style problems.

Students then begin their first Geometry topic looking at an introduction to Angles as well as developing their understanding of the areas of more complex polygons (including compound shapes).  Having studied fractions, students will become more confident with percentages, particularly in context.  Students will end the year by studying Probability for the first time as well as new areas of Statistics.

What do students learn in Year 8?

In Year 8 students will build upon their knowledge from Year 7 by applying skills to new and more complex areas of mathematics.

At the start of Year 8 students will begin their year by building upon their shape knowledge by extending this to circles (and parts of circles).  Students then build upon this to understand their impact in 3D shapes in terms of both Surface Area and Volume.

Students then advance their understanding of Ratio and Proportion, including that of Compound Measures (including Kinematics).

Students then build significantly on their understanding of algebra of both linear and non-linear expressions.  Students begin to learn the difference between equalities and inequalities and how they, and their solutions, are represented graphically.

Finally students explore the ideas of transformations, including introducing the idea of similarity and congruence in an informal way.

What do students learn in Year 9?

In Year 9 students will extend their existing mathematical knowledge.  Students will begin to form links between areas of the curriculum and understand how to apply their knowledge to unfamiliar contexts.

At the beginning of Year 9 students revisit some previously taught content but extend these significantly, through introducing the ideas of Whole Numbers, Decimals and Surds, Standard Form and Bounds.  Students then begin to work with more complex Algebraic Expressions, including binomials (expanding and factorising) and trinomials.  Fraction knowledge is extended to include Algebraic Fractions, and students begin to understand the relationships between the sides and angles in right-angled triangles by studying Pythagoras’ Theorem and Trigonometry, both in 2D and 3D.  The idea of a Function is more formally defined and the idea of a sequence is extended to quadratic and geometric sequences.

Finally, students extend their knowledge of bar charts, and others, to understanding the difference between the statistical representations of Bar Charts, Frequency Polygons and Histograms.

What do students learn in Year 10?

In Year 10 students uncover how their previous knowledge can be applied and how to further understand how different areas of mathematics are linked.

Students uncover more complex angle problems, including Circle Theorems and understand more rigorously how area and volume are linked to Compound Measures.

Students uncover the links between parallel and perpendicular lines, the understand how graphs can transform and how this affects their equations.  Students discover how non-linear graphs, including circles, are graphed and how to solve problems with non-linear graphs.

More complex shapes are uncovered, including non-right-angled triangles in addition to a number of 3D shapes.  Students will understand how Bearings work in real-life contexts and how trigonometry can be used.

Finally, students uncover how linear and non-linear simultaneous equations are solved as well as quadratic equations.  Students understand where their existing knowledge isn’t sufficient to solve higher-order equations and how to overcome this through sophisticated iterative processes.

What do students learn in Year 11?

In Year 11 students encompass all of their existing knowledge and begin to understand the idea of a mathematical proof.

Students first encompass their knowledge of transformations, angles and properties of shapes to be able to prove shapes are mathematically similar and congruent.  Students then solve very sophisticated sets of both linear and non-linear equations and understand how their solutions are represented graphically.

Students finally intertwine their understanding of different representations of data and use and apply these to be able to calculate the probability of different real-life and abstract situations.

Finally, students have their first experience of mathematical proof, encompassing all existing algebraic knowledge and understanding, and preparing students for the mathematical concepts ahead of them in higher education.

Knowledge Organisers

Knowledge organisers for students in Key Stage 4 at Millthorpe School can be found here. All the key facts and essential knowledge you’ll need, right at your fingertips!