Mathematics KS3 Curriculum

Curriculum Intent

Teaching and Learning in Mathematics

Teaching in the maths department first and foremost reflects the Catholic ethos of the school. We are constantly seeking to improve our practice so that we can make a difference for the young people who will shape the society of the future. We as a maths department have the highest expectations of attainment, progress and behaviour for all our classes.

Our Philosophy

When the new maths curriculum was introduced in 2015, with its triple emphasis on fluency, reasoning and problem solving, there was a need to revisit and introduce a curriculum aiming for ‘mastery’ and ‘depth’. Our curriculum and teaching approach places ‘problem solving’ at the heart of teaching Mathematics and is based on these principles:

Conceptual understanding is key. Our lessons focus on small step learning which also encourages deeper understanding. Concepts are not rushed but understood clearly and built upon.
Students must be able t use proper mathematical language and terminology as well as speak and write in full sentences.
Developing independent thinking skills. We aspire for all our students to be able to work on their concepts actively and independently and not just expect to follow step-by-step procedures and learn passively.
Retrieval practice is present in all lessons. As demonstrated in numerous studies, content needs to be continually revisited. Each lesson provides this opportunity and assessments always reflect this too.

Our lessons follow the principles of High-Performance Learning as well as Mastery through the NCETM. We aim to promote deep learning in the department through the use of these techniques. The schemes of work in all year groups are based around these principles. We break questions in lessons down into four areas that relate to the 3 'Assessment Objectives' (AOs) laid out by the department for education.

AO1 – Fluency AO1 – Application AO2 – Reasoning AO3 – Problem Solving

Regardless of the current level of performance of the student we believe they have the capability and are given the opportunity to access all levels and types of questions which is our philosophy on differentiation.

How do we set in Maths?

We have entirely non-prior attainment groupings in Maths and this follows the vision of the whole school. This promotes the principles of High-Performance Learning as all students move through the curriculum together and no matter what their prior attainment the students can see what high level learning looks like in the classroom. This also feeds into the Diversity and Inclusion work the school has prioritised where no students are denied from learning any concept in the courses based on their class.

How is the Maths department contributing to Extra-Curricular activities in the wider school?

We are active in the promotion of STEAM events and trips throughout the year. These encourage our students to look towards career paths in Science, Technology, Engineering, Art and Maths.
High attaining students in Years 7-11 sit the UK Maths Challenge every year and those who excel have the opportunity to progress to more complex and interesting challenges.
In Year 11 a weekly revision session is run for students by the teachers of their classes for one hour after school. Each teacher, each week does a different topic and the students select which one they attend based on their own needs.
In KS4 a Further Maths club aimed at high attaining students runs weekly where they learn content from the A-Level maths curriculum. This is to encourage a deeper understanding of the simpler topics from GCSE but also give a flavour of what the students are to expect post-16.
In KS3 a weekly homework club is run where any student can go along for help and support.

Themes (knowledge & understanding)

Skills

Provides a single curriculum map that all learners are expected to follow. This means that all learners have the same access to the curriculum content and there is no ceiling imposed on what learners can achieve.

While there is only one curriculum, we recognise that not all learners come to each lesson at the same starting point. For this reason, we provide additional resources designed to help learners access the main curriculum and teachers adapt lessons to provide scaffolding and depth according to the needs of their learners.

The curriculum is organised to be cumulative. This means that mathematical concepts that are taught earlier in the curriculum are revisited in the context of a new area of mathematics.

This helps learners to make connections between different mathematical concepts. Retrieving, using and applying concepts regularly, transferring to new contexts helps develop fluency as well as conceptual understanding.

Subject content is organised following a sequencing to allow a clear progression through the all maths strands:

Number
Algebra
Ratio, proportion and rates of change
Geometry and measures
Probability
Statistics

Our lessons follow the principles of Mastery as described by the NCETM. We aim to promote deep learning in the department through of the use of these techniques. The schemes of work in all year groups are based around these principles. We break questions in lessons down into four areas that relate to the 3 Assessment Objectives (AOs) laid out by the department for education.

AO1 – Fluency AO1 – Application

AO2 – Reasoning AO3 – Problem Solving

At the end of her mathematical education in Sacred Heart, each pupil will be able to:

Perform basic numeracy skills
Perform the basic mathematical skills needed in her chosen career or for entry to higher or further mathematical education
Understand the mathematics likely to be encountered in daily adult life
Reason clearly and logically, and to set out a rational argument
Identify patterns encountered in diverse situations and to extrapolate from these

to approach problems systematically, choosing appropriate techniques for their solution,

Follow logical instructions clearly expressed
Experience satisfaction in and enjoyment of her mathematical achievements

In addition, we aim for pupils to acquire the logical abilities characteristic of a mathematician.

Modules Taught

Year 7
Unit 1 - Number 1 Adding and Subtracting Negative Numbers Multiplying and Dividing Negative Numbers All four operations using Negative Numbers Cube and Cube Roots Powers >3 Prime Factors Converting between Standard Form and Ordinary Numbers Using a Calculator Using Standard Form with a Calculator Unit 2 - Algebra 1 Forming Expressions Substitution with Positive Integers Substitution with Integers Substitution of Positive Integers into Formulae Substitution of Integers into Formulae Collecting Like Terms Simplifying Terms using Multiplication and Division Multiplying and Dividing using Indices Power of Power and Zero Power Rules Expanding Single Brackets Expanding and Simplifying Brackets Factorising into Single Bracket Solving One Step Linear Equations with Negatives and Fractions Solving Two Step Linear Equations Solving Two Step Linear Equations with Negatives and Fractions	Unit 3 - Number 2 Converting Fractions to Decimals (all methods) Dividing Fractions Dividing Mixed Numbers Reciprocals Unit 4 - Geometry 1 Isosceles and Equilateral Triangles Angles in Parallel Lines Rotational Symmetry Interior Angles in Polygons Interior and Exterior Angles in Polygons Congruent Shapes Translations Reflections on Coordinate Grid Rotations Enlargements Unit 5a - Number 3 Multiplying Decimals Dividing Decimals by Whole Numbers Estimation Rounding to Significant Figures Checking Answers Converting between Percentages and Decimals	Unit 5b - Ratio and Proportion 1 Percentage Increase/Decrease Multipliers Reverse Percentages Simple Interest Simplifying More Complex Ratio Direct Proportion Sharing in a given Ratio Unit 7 - Algebra 2 Linear Sequence Rules (with terms arithmetic and linear) Nth term Nth term (Patterns) Rearranging Formulae Drawing Vertical and Horizontal Lines Drawing Straight Lines Gradient Drawing graphs using Gradient and y-intercept Identifying Gradient and y-intercept and Parallel Lines Drawing Quadratic Graphs Real Life Graphs Unit 8 - Probability 1 The Probability Scale Relative Frequency Single Event Probability Expectation Sample Space Diagrams Frequency Trees Mutually Exclusive Events Venn Diagrams
Year 8
Unit 9a - Ratio and Proportion 2 Speed/Distance/Time Scale Drawings Map Scales Unit 9b - Geometry 2 Area of Triangles Area of Parallelograms and Trapeziums Circumference of a Circle Perimeter of Semicircles and Quarter-circles Area of a Circle Area of Semicircles and Quarter-circles Surface Area and Volume of Cuboids Volume and Surface Area of Prisms Volume and Surface Area of Cylinders Identifying Similar Shapes Unit 10 – Statistics Mean Problem Solving and Choosing Best Average Stem and Leaf Diagrams Two-Way Tables Scatter Graphs (Use from Grade 4-5 Book M10.5 as well) Misleading Statistics Median and Mode from Frequency and Grouped Frequency Tables Mean from Frequency Tables Mean from Grouped Frequency Tables Comparing Sets of Listed Data Comparing Data from Graphs	Unit 11 - Geometry 3 Constructing Triangles using a Ruler and Protractor Constructing Triangles using a Ruler and Compass Construct a Net using Ruler and Compass Drawing 3D Shapes on Isometric Paper Plans and Elevations Understanding Bearings Measuring and Working out Bearings Problems involving Shapes on Coordinate Grids Unit 1 - Number 1 Negative Exponents Calculating with Roots HCF and LCM from Venn diagrams Calculating in Standard Form without a Calculator	Unit 2 - Algebra 1 Expanding and Simplifying Single Brackets Finding Simple Formulae Substituting Numbers into Formulae Expanding Double Brackets 1 Expanding Double Brackets 2 Expressions, Identities, Formulae, Inequalities and Terms Solving Equations with Brackets Solving Equations with Unknowns on Both Sides 1 Solving Equations with Unknowns on Both Sides 2 Forming and Solving Equations 1 Forming and Solving Equations 2 Solving Equations with Fractions Factorising Quadratics Difference of 2 Squares Unit 3 - Number 2 Using Short Division to put Fractions into Decimals Adding and Subtracting Fractions Review Multiplying and Dividing Fractions Review
Year 9
Unit 4 - Geometry 1 Angle Proof Angle Proof Advanced Congruent Triangles Describing Reflections Describing Rotations 1 Describing Rotations 2 Describing Enlargements Mixed Transformations Column Vectors Manipulating Vectors 1 Manipulating Vectors 2 Basic Vector Geometry Unit 5a - Number 3 Dividing by Decimals Unit 5b - Ratio and Proportion 1 Percentage Change 1 Percentage Change 2 Reverse Percentages 1 Reverse Percentages 2 Compound Interest and Depreciation 1 Compound Interest and Depreciation 2 Sharing in a Ratio Direct Proportion Inverse Proportion	Unit 7 - Algebra 2 Nth Term Types of Sequences Geometric Progressions Rearranging Basic Formulae Rearranging Formulae Powers and Roots Rearranging Formulae Subject Appears More than Once Writing Inequalities Solving Linear Inequalities Solving Quadratic Equations 1 Solving Quadratic Equations 2 Solving Quadratic Equations Graphically Turning Points and Intercepts Cover up Method for Drawing Straight Lines Simultaneous Equations Graphically Simultaneous Equations Algebraically 1 Simultaneous Equations Algebraically 2 Simultaneous Equations Worded Graphs of Cubics and Reciprocals Rates of Change Equations of Straight Lines 1 Equations of Straight Lines 2 Unit 8 - Probability 1 Venn Diagrams (Sets of Numbers) Venn Diagram (3 sets) Venn Diagrams (Frequencies) Independent Events Tree Diagrams (Independent) Tree Diagrams (Conditional)	Unit 9a - Number 4 Upper and Lower Bounds Truncation and Bounds Unit 9b - Geometry 2 Density/Mass/Volume and other compound measures 1 Density/Mass/Volume and other compound measures 2 Arcs of Circles Area of Sectors Converting between units of area and volume Volumes of Spheres, Pyramids and Cones Surface Area of Spheres, Pyramids and Cones Similar Shapes 1 Similar Shapes 2 Unit 10 - Statistics 1 Revision of previous Statistics topics Unit 11 - Geometry 3 Constructions 1 Constructions 2 Loci 1 Loci 2 Plans and Elevations Pythagoras’ Theorem Pythagoras’ Theorem Problem Solving Labelling Sides in Trigonometry Trigonometry – Finding Sides Trigonometry – Finding Angles Exact Values of Trigonometric Functions Mixed Trigonometry Problems 1 Mixed Trigonometry Problems 2

Assessment

As a department our marking is directly associated with our assessments. We assess once every 2-3 weeks. In Years 7-10, students are given the same assessments so we can compare progress across the year group. When an assessment is returned it is done so with a personalised learning checklist (PLC). This consists of:

An individual breakdown of marks by topic. This is linked to a relevant clip on the online learning platforms the students use for homework and revision.
Collective feedback. Having marked all the assessments the teacher creates comments that apply to a wide range of students on positives but also misconceptions they had from the assessment.
Individual comments are given by the teacher where appropriate and to serve a particular purpose.
EBI Questions. The teacher creates and selects for each student a series of questions based on the topics they need work on for that student to complete after having analysed the assessment itself.

Our marking policy also has at its core, staff wellbeing. We aim to produce the highest quality feedback but in an efficient and manageable amount of time.

Stretch & Challenge

High attaining students in Years 7-11 sit the UK Maths Challenge every year and those who excel have the opportunity to progress to more complex and interesting challenges. In addition, full participation is encouraged for local Masterclasses and other study days of interest. Schemes of work include investigational work and ICT tasks.

Enrichment Opportunities

We are active in the promotion of STEAM events and trips throughout the year. These encourage our students to look towards career paths in Science, Technology, Engineering, Art and Maths. In KS3 a weekly homework club is run where any student can go along for help and support.