Why do we learn maths?
Mathematics provides students with knowledge and skills to be effective problem solvers and logical thinkers. It is evident all around us, in the creation of the remarkable structures and buildings, that maths provides a foundation for understanding the world. Learning mathematics is key within everyday life, from making personal financial decisions, to making decisions within the world of business.
Secondary
In Key Stage 3, students continue to follow the Maths Mastery curriculum in mixed attainment classes, ensuring that all students continue to be exposed to the full higher tier curriculum until the end of Year 9. This gives every student, regardless of prior attainment, the opportunity to achieve grade 5+ at GCSE. Lead by the Key Stage 3 Lead, the team use a combination of the Maths Mastery resources and the Pilot ARK prototypes to tailor the learning for each class, providing scaffolding and depth according to the needs of their learners. The principles of Maths Mastery of conceptual understanding, language and communication and mathematical thinking can be seen in all Key Stage 3 Maths lessons.
In Key Stage 4, we are following a legacy curriculum that has been built over many years at KSA. This curriculum has since been adapted to support Year 10 and 11 prepare for the Edexcel GCSE exams following the disruption to education caused by the pandemic. Units are designed to build on content learnt in KS3, allowing students to apply their knowledge and skills to solve a range of new problems and increasingly complex and abstract topics, preparing them for A-Level study. Tiering decisions are made at the end of Year 9, meaning that students receive a tailored curriculum throughout Key Stage 4 best suited to help them prepare for their GCSE exams with confidence in either a higher or foundation group. We are looking forward to starting the Key Stage 4 Maths Mastery curriculum in September 2022.
Year 7
The first term of year 7 focusses on developing understanding of the axioms and structures of number that are fundamental to mathematics. This underpins understanding of the algebraic notation developed in this term and in subsequent years. The spring term of year 7 focusses on geometry, an important area of mathematics for students to engage with. The cumulative nature of the curriculum means that students apply algebraic reasoning in new contexts. Students’ understanding of fractions, decimals and percentages from KS2 is built upon throughout the year. This is developed more formally in the summer term where time is spent linking different interpretations of fractions and introducing ratio.
Autumn 1 | Autumn 2 |
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Making generalisations about the number system |
Making generalisations about the number system |
Knowledge Content: Number systems, axioms and properties Threshold Concepts: Humans have not always used base 10 and in specific situations other bases are preferential; a prime number has exactly two factors |
Knowledge Content: Positive and negative numbers; basic algebra Threshold Concepts: Negative values do exist in the real world in various contexts; it is convention to put the number ahead of the unknown e.g. 2y instead of y2 |
Spring 1 | Spring 2 |
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2-D geometry | The Cartesian plane |
Knowledge Content: Angles, classifying 2-D shapes and constructions Threshold Concepts: The rules for angles in parallel lines can be derived from the basic angle facts; Several shapes can share the same property e.g. having 4 right angles |
Knowledge Content: Coordinates, area of 2-D shapes and transformations Threshold Concepts: Co-ordinates require two pieces of information to fully map their location; The formula for the area of a triangle is directly linked to that of a rectangle; There can be several ways of describing a shape’s transformation. |
Summer 1 | Summer 2 |
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Fractions | Ratio and proportion |
Knowledge Content: Number properties and fractions Threshold Concepts: Every positive integer (greater than 1) has a unique prime factor decomposition; A fraction is a convenient way of representing one value being divided by another. |
Knowledge Content: Ratio and percentages Threshold Concepts; Ratios are inherently linked to fractions; A percentage can easily be converted to a fraction with a denominator of 100. |
Year 8
Autumn 1 | Autumn 2 |
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Equations and inequalities | Graphs |
Knowledge Content: Equations and inequalities Threshold Concepts: To solve an equation, the same operation must be done to both sides of the equation. |
Knowledge Content: Linear graphs, accuracy and estimation Threshold Concepts: A minimum of two points are required to draw a straight line; It is convention to round up with a ‘5’ as the decisive digit. There is no mathematically sound reason as to why – it is purely convention. |
Spring 1 | Spring 2 |
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Proportional reasoning | Representations and reasoning with data |
Knowledge Content: Real-life graphs and proportion Threshold Concepts: If two of speed, distance or time are known, the third can be found; Two values that are directly proportional have a fixed ratio. |
Knowledge Content: Univariate and bivariate data Threshold Concepts: The mean, mode and median are three different ways of finding and average. In real life, each has its own benefits depending on the situation; Using a line if best fit is a form of estimation. It is not exact but will give a fairly accurate answer. |
Summer 1 | Summer 2 |
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Angles | Area, volume and surface area |
Knowledge Content: Angles in parallel lines and in polygons; Bearings Threshold Concepts: The interior and exterior angle of a polygon will sum to 180; Bearings are always taken from North and in the clockwise direction. |
Knowledge Content: Circles, volume and surface area of prism Threshold Concepts: Pi (𝜋𝜋) is a fixed number that is the constant ratio between the circumference and diameter of any circle; The volume of a prism is the area of the cross section multiplied by the length. V = A x L; The surface area is the area of the net of the 3-D shape. |
Year 9
Autumn 1 | Autumn 2 |
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Probability | Quadratics |
Knowledge Content: Probability and sample spaces Threshold Concepts: Probably can be represented a fraction, decimal or percentage; Samples spaces represent different ways of interpreting probability problems. |
Knowledge Content: Quadratics Threshold Concepts: A quadratic expression is a polynomial of degree 2. |
Spring 1 | Spring 2 |
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Geometry of triangles | Ratio and proportion |
Knowledge Content: Constructions and Pythagoras’ theorem Threshold Concepts: The loci is the set of all points, whose location satisfies the given conditions; If two side lengths of a right-angled triangle are known, the third can always be found. |
Knowledge Content: Similar shapes, surds and trigonometry Threshold Concepts: When comparing 3-D objects there are three scale factors to consider: length; area; volume; A surd is a radical (square root) that cannot be reduced to an integer. |
Summer 1 | Summer 2 |
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Linear simultaneous equations | Reasoning with number |
Knowledge Content: Solving graphically and algebraically Threshold Concepts: The intersection point of two straight lines is the solution to the simultaneous equations; To solve algebraically, students can choose to use the elimination method or the substitution method. |
Knowledge Content: Indices, growth and decay Threshold Concepts: The laws of indices apply to numerical indices and also algebraic indices; A multiplier greater than 1 represents a percentage increase. A multiplier less than 1 represents a percentage decrease. |
Year 10
Foundation
The year 10 curriculum gives students the opportunity to revisit key topics allowing them to recap and extend their learning on these key topics. Each half-term has a key focus covering: number; algebra; probability; geometry; similarity and finally data handling. The focus will be on initially ensuring fluency on all topics. Students will then be able to attempt problemsolving questions which require knowledge from several domains.
Autumn 1 | Autumn 2 |
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Number | Applications of algebra |
Knowledge Content: Factors, multiples and primes; powers and roots; indices; standard form; sequences Threshold Concepts:
Link to Prior Learning: Builds on knowledge of prime factorisation and index laws |
Knowledge Content: Algebra KS3 review; quadratics; quadratic graphs; simultaneous equations Threshold Concepts:
Link to Prior Learning: Builds on knowledge of quadratics and equation solving |
Spring 1 | Spring 2 |
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Percentages and probability | Geometry |
Knowledge Content: FDP KS3 review; percentages; probability, sets, venn and sample space diagrams Threshold Concepts:
Link to Prior Learning: Builds on knowledge of FDP and probability |
Knowledge Content: Transformations; 2D shapes and circle geometry; 3D shapes; volume and surface area Threshold Concepts:
Link to Prior Learning: Builds on knowledge of 2D/3D shape properties (area, volume etc.) |
Summer 1 | Summer 2 |
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Similarity | Data Handling |
Knowledge Content: Ratio review; compound measures and direct and inverse proportion; Pythagoras’ theorem review; similarity and trigonometry Threshold Concepts:
Link to Prior Learning: Builds on knowledge of ratio and trigonometry |
Knowledge Content: Averages and range; data collection and sampling; presenting data including scatter diagrams Threshold Concepts:
Link to Prior Learning: Builds on knowledge of averages and data presentation |
Higher
The year 10 curriculum gives students the opportunity to revisit key topics allowing them to recap and extend their learning on these key topics. Each half-term has a key focus covering: number; algebra; probability; geometry; similarity and finally data handling. The focus will be on initially ensuring fluency on all topics. Students will then be able to attempt problemsolving questions which require knowledge from several domains.
Autumn 1 | Autumn 2 |
---|---|
Number | Applications of algebra |
Knowledge Content: Powers and roots; surds and irrational numbers; indices; standard form; sequences Threshold Concepts:
Link to Prior Learning: Builds on knowledge of prime factorisation and index laws |
Knowledge Content: Quadratics; quadratic graphs algebraic fractions; simultaneous equations Threshold Concepts:
Link to Prior Learning: Builds on knowledge of quadratics and equation solving |
Spring 1 | Spring 2 |
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Percentages and probability | Geometry |
Knowledge Content: KS3 FDP review; percentages; probability sets, venn and sample space diagrams (including conditional probability) Threshold Concepts:
Link to Prior Learning: Builds on knowledge of FDP and probability |
Knowledge Content: Transformations; upper and lower bounds; 2D shapes and circle geometry; 3D shapes; volume and surface area Threshold Concepts:
Link to Prior Learning: Builds on knowledge of 2D/3D shape properties (area, volume etc.) |
Summer 1 | Summer 2 |
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Similarity | Data Handling |
Knowledge Content: Ratio review; compound measures and proportion; Pythagoras review; similarity and trigonometry; 3D triangles Threshold Concepts:
Link to Prior Learning: Builds on knowledge of ratio and trigonometry |
Knowledge Content: Averages and range review; data collection and sampling; presenting data including scatter diagrams; further statistical diagrams Threshold Concepts:
Link to Prior Learning: Builds on knowledge of averages and data presentation |
Year 11
Foundation
After year 10, students will spend the Autumn term completing the curriculum covering proof and graph work. The remainder of the year will then be spent revisiting topics that students can improve on. Students will have time to get exam-practice and improve their confidence in preparation for their GCSE exams.
Autumn 1 | Autumn 2 |
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Reasoning and proof | Graphs |
Knowledge Content: Vectors; geometric reasoning; bearings; congruence; construction and loci Threshold Concepts:
Link to Prior Learning: Builds on knowledge of angles and constructions |
Knowledge Content: Linear inequalities; linear graphs, non-linear graphs Threshold Concepts:
Link to Prior Learning: Builds on knowledge of inequalities and graphs |
Spring 1 | Spring 2 |
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Revision | Revision |
Summer 1 | Summer 2 |
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Revision | Revision |
Higher
After year 10, students will spend the Autumn term completing the curriculum covering proof and graph work. The remainder of the year will then be spent revisiting topics that students can improve on. Students will have time to get exampractice and improve their confidence in preparation for their GCSE exams.
Autumn 1 | Autumn 2 |
---|---|
Reasoning and proof | Inequalities and graphs |
Knowledge Content: Vectors; geometric reasoning review; circle theorems; bearings; congruence; construction and loci Threshold Concepts:
Link to Prior Learning: Builds on knowledge of angles and constructions |
Knowledge Content: Inequalities; linear graphs, non-linear graphs; trig graphs Threshold Concepts:
Link to Prior Learning: Builds on knowledge of inequalities and graphs |
Spring 1 | Spring 2 |
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Algebra and graphs | Revision |
Knowledge Content: Algebraic proof and reasoning; recurrence relations; functions; transformation of graphs; further graphs Threshold Concepts:
Link to Prior Learning: Builds on knowledge of nonlinear graphs |
Summer 1 | Summer 2 |
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Revision | Revision |