  # Mathematics

Key Stage 3

## Mathematics

### Why is the study of Mathematics important?

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. – William Paul Thurston

Mathematics is an essential discipline in today’s world, from the use of mathematical methods every day to the multitude of professions that use mathematics. Everyone needs some level of mathematical proficiency to understand how to understand data, or to be able to find the steps to solve a problem.

Studying the connections between topics allows students to realise that all Mathematical concepts are related- the connections are endless. This means that studying Mathematics allows students to notice connections, think critically about information and find a way to efficiently solve problems- a skill all universities and employers will find desirable.

Upon entry to Sirius Academy West, students will focus on mastering the key skills from Key Stage 2- building an understanding of the connections and ensuring the component skills are embedded. Too often, students feel Maths is memorising several methods so we show them why each method works and how this links to the fundamental properties of number. The discussions had can lead to a lifelong love of learning, and widen the ability to solve composite problems.

The aim for every Maths lesson taught is to be thought-provoking and full of questions. Physical resources and pictorial representations may be used to show students the nature of the problem, linking concepts to the abstract method traditionally taught. This will help develop the mathematicians of the future.

Mathematics Learning Journey – VIEW

• What will you learn?

Upon entering the academy in year 7, students start with a review of the fundamentals of mathematics. Using a variety of methods and representations, the structure of numbers and the four operations are investigated deeply before negative numbers are introduced.

The fundamentals of algebra are investigated, using the operations and number structures students are now confident with.

Geometry in Year 7 involves developing a large mathematical vocabulary, using newly discovered algebra skills to represent angle and area problems.

Finally, fractions are considered and deeply investigated. Working with fractions can show deep concepts of division and proportion and build confidence with the four operations of any number.

In Year 8, Fractions are extended to consider the links with percentages. Algebra skills are extended to include sequences, linear graphs and more complex equations and inequalities. Ratio and proportion problems follow on, requiring students to use the fractions and percentages concepts, but represent these using different notation and vocabulary- finding more efficient methods.

At this stage, data representations are considered and critically evaluated building the skills needed to evaluate data presented in the media or in various career fields.

Finally; perimeter, area and volume are investigated using the vocabulary built in Year 7 and expanded to 3-Dimensions.

In the final year of key stage 3, students begin by considering all the connections between fractions, decimals and percentages and how to calculate with these. Probabilities are then investigated and risk management is discussed. Algebra is considered as a tool of representation, with algebraic manipulation skills being developed and applied to geometrical problems.

In spring, angles in polygons are investigated and Pythagoras’ theorem is learnt- bringing a new dimension to Geometry. Ratio and proportion are returned to, with a focus on shapes and measure. This leads to accurate constructions of shapes and scale drawings.

Before the end of the key stage, algebra is revisited and extended further using the large foundation of skills students have developed. Finally, Trigonometry is introduced pulling a range of skills together.

Year 7:

• Numbers and numerals
• Axioms and arrays
• Factors and multiples
• Order of operations
• Positive and negative numbers
• Expressions, equations and sequences
• Angles
• Classifying 2-D Shapes
• Coordinates
• Area of 2D Shapes
• Transforming 2D Shapes
• Prime Factor Decomposition
• Equivalent Fractions
• All operations with fractions

Year 8:

• All Operations Acting on Fractions
• Percentages
• Sequences
• Forming and solving equations
• Forming & Solving Inequalities
• Linear Graphs
• Transforming 2D Shapes (One Year Only, then replaced with Angles in Polygons)
• Ratio
• Real life graphs and rates of change
• Direct and Inverse Proportion
• Positive & Negative Numbers Recap
• Univariate Data
• Bivariate Data
• Accuracy, Estimation
• Perimeter including Circles
• Area of 2D Shapes including Circles
• Volume & Surface Area of 3D Shapes

Year 9:

• FDP Review
• Probability
• Sets, Venn and sample space diagrams
• Volume and Surface Area of 3D Shapes
• Angles in Polygons (As Needed)
• Pythagoras’ Theorem
• Ratio review
• Similarity, enlargement & standard form
• Constructions, Congruence & Loci
• Representing and Solving Linear and Quadratic Equations
• Indices & Surd
• Trigonometry

• Mathematical Education

At Sirius Academy West, the Mathematics curriculum makes heavy use of the Mathematics Mastery and White Rose Maths schemes, both highly acclaimed. These schemes use a variety of concrete, pictorial and abstract representations to investigate mathematical concepts and give students questions with variation that allows them to notice patterns and identify procedures. Using the Mathematics Mastery scheme with elements of the White Rose Maths allows us to adapt the topics to be suitable for a wide range of learners that are at different stages in their mathematical journey.

In every lesson, whether students have the prior knowledge of required component skills will be checked and students who have gaps in their understanding will receive support whilst those who are ready will be challenged with composite questions.

Through the lesson, discussion will be used to allow for investigation and various representations will be used to allow students to make connections between topics. Questions with variation embedded will allow students to have intelligent practice with support offered where necessary.

At the end of the lesson, students will complete a short task allowing for identification of misconceptions and for these to be addressed the next lesson- reducing the accumulation of misconceptions that leads to poor understanding of a topic.

White Rose Maths: https://whiterosemaths.com/for-parents/

• Maths after Sirius Academy West

The skills learnt in Mathematics are needed every day. Whilst we may spend our lives carrying a smartphone calculator in our pockets, mathematical education is about problem solving, critical thinking and identifying connections far more than knowing how to calculate.

These skills will be used in every career, hobby or passion.

Students who become passionate about Maths may go on to enjoy careers in Engineering, Architecture, Mechanics, Research, Astrophysics,, Data Science or a range of other subjects. Mathematics is often required study for Medicine, Computing, Engineering and some Science programmes at University.

## Student Testimonial

I want to continue to study maths at A Level as I really enjoy the challenge of learning new things, especially algebra which I find really interesting. 