We have designed our curriculum using the KS3 National Curriculum and it is delivered under the framework of the IB Middle Years programme. We have also referenced the KS2 Programmes of Study in our initial planning. We believe all students studying mathematics at Mascalls Academy should be successful, regardless of their background. Students will follow a five year curriculum that builds on mathematical concepts explored at Key stage two allowing student to develop a deep understanding of the subject. Conceptual understanding is a key principal to deepening student understanding. The curriculum encourages student to move between different representations of concepts using the concrete, pictorial and abstract, allowing student to develop a comprehensive conceptual understanding that can be used as a foundation for future learning.

Our curriculum has been designed using the content of the national curriculum as the starting point and is delivered under the framework of the IB Middle Years programme and Mathematics Mastery. Learning is sequenced to help learners build a narrative through different topics. These topics are then sequenced in a logical progression that allows learners to establish connections and draw comparisons. Multiple representations are carefully selected so that they are extendable within and between different areas of mathematics. Using these rich models encourages learners to develop different perspectives on a concept. The curriculum encourages the use of mathematical language to strengthen conceptual understanding by enabling our students to explain and reason using the correct language.

The creation of a conjecturing environment and considered use of questions and prompts are important elements of encouraging learners to think like mathematicians. Our curriculum is designed to give learners the opportunities to think mathematically, throughout the curriculum students are required to specialise and generalise, to work systematically, to generate their own examples, to classify and to make conjectures.

## KS3 Maths

Topic 1: Making Generalisations about Number System 1

Place valueUnderstand place value for integers and decimals. Exchange between place value columns. Experience different representations of place value.

Axioms and arrays – Understand the commutative and associative properties of multiplication. Understand the distributive property through a range of abstract and pictorial representations. Be able to represent and use the distributive property of multiplication over addition and subtraction.

Factors and multiples – Factors, primes and multiples. Square and cube numbers, roots. Representing the structure of number. Establishing the order of operations.

Order of operations – Establishing the order of operations.

Topic 2: Making Generalisations about Number System 2

Positive and negative numbers – Negative numbers in context, absolute value. Using negative numbers with all four operations, additive inverses.

Expressions, equations and inequalities – Writing and simplifying expressions. Recognising equivalent expressions. Forming equations. Forming inequalities.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: 2D Geometry

Angles – Measuring and drawing angles. Angles on a straight line and around a point. Angles in parallel lines. Creating equations from angle facts.

Classifying 2D Shapes – Classifying polygons according to their properties. Rotational and line symmetry. Internal angle sum of triangles and quadrilaterals.

Constructing triangles – Be able to use compasses to construct a triangle using SSS, SAS and ASA. Identify if a triangle can be construct or not.

Topic 2: Fractions

Primes, factors and multiples – Prime factor decomposition. LCM and HCF. Square roots and cube roots.

Fractions – Equivalent fractions. Converting between fractions and decimals. Recurring decimals. Multiply and divide fractions. Fractions of amounts. Mixed numbers and improper fractions. Addition and subtraction of fractions.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: Ratio and Proportion

Ratio – Ratio notation. Understand the relationship between ratio and fractions. Working with ratios and quantities.

Percentages – Equivalence to fractions and decimal fractions. Percentage of an amount. Percentage increase and decrease. Finding the original amount. Using percentages, fractions and decimals in different contexts including probability.

Topic 2: The Cartesian Plane

Coordinates – Plotting points in all four quadrants. Horizontal and vertical lines. Midpoints of line segments. Problem solving on a coordinate grid.

Area of 2D Shapes – Area of triangles and quadrilaterals. Formulae and solving equations.

Transforming 2-D figures – Translation, rotation and reflection of an object on a cartesian plane. Enlargement by a positive scale factor.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: Equations and Inequalities

Sequences – Use geometric patterns to derive sequences. Derive sequences from different contexts. Find the nth term of a linear sequences.

Forming and solving equations – Review year 7 algebra. Forming algebraic equations. Solving equations with unknown on both sides. Introduce solving equations involving algebraic fractions.

Forming and solving inequalities – Language and symbols. Using a number line. Forming algebraic inequalities. Solving algebraic inequalities (unknown on both sides). Using graphical representations.

Topic 2: Graphs

Linear graphs – Plot coordinates to generate straight lines. Identify key features of a linear graph. Make links between algebraic and linear representations. Identify parallel lines from algebraic equations.

Accuracy and estimation – Rounding to a given number of decimal places and significant figures. Upper and lower bounds. Estimations.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Percentages – Equivalence to fractions and decimal fractions. Percentage of an amount. Percentage increase and decrease. Finding the original amount. Using percentages, fractions and decimals in different contexts including probability.

Ratio, real life graphs and rate – Review year 7 ratio. Scales and reading maps. Read and interpret real life graphs. Rates of change including SDT.

Direct and inverse proportion – Similarity as an example of direct proportion. Represent proportional relationships algebraically in a table and on graphs.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: Representations and Reasoning with Data

Univariate data – Construct and interpret charts and graphs. Mean, mode, median and range. Examine outliers.

Bivariate data – Scatter graphs. Correlations. Constructing a line of best fit. Interpolation and extrapolation.

Topic 2: Angles

Parallel lines – Review year 7.

Angles in polygons – Review of year 7. Define the sum of interior and exterior angles of polygons. Problem solving involving angles and polygons.

Topic 3: Area, Volume and Surface Area

Circles and composite shapes- Explore the relationship between the circumference and diameter. Calculate the area and the circumference. Area and perimeter of composite shapes.

Volume of the prisms- Use the formulae to calculate the volume of cubes, prisms and composite solids. Changing between units of volume.

Surface area of prisms – Recognising and drawing nets of prisms. Use the formulae to calculate the surface area of cubes, prisms and composite solids.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: Probability

Probability – FDP review. Theoretical and experimental probability. Probability of single events. Probability of combined events.

Sample spaces – Venn diagrams. Sample spaces. Two way tables. Tree diagrams.

Topic 2: Simultaneous Equations

Review of linear equations

Solving simultaneous algebraically – Setting up simultaneous equations. Using algebraic methods to solve simultaneous equations.

Solving graphically – Setting up simultaneous equations. Finding the solutions graphically to a set of one or more simultaneous equations.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Topic 1: Geometry of Triangles

Constructions, congruence and loci – Ruler and compass and constructions. Congruence. Loci

Pythagoras’ Theorem – Using pythagoras to find missing sides in right angle triangles. Using pythagoras to solve problems with 3D objects.

Ratio Review – Review of year 7 and 8 ratio.

Topic 2: Ratio and Proportion

Enlargement and similarity – Similarity and enlargement. Area and volume of similar shapes.

Angle Recap – Naming Angles. Angles in parallel lines. Angles in triangles. Angles in polygons.

Trigonometry – Using trigonometric ratios to find unknown angles and sides. Solving problems using trigonometric ratios.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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Growth and decay – Compound percentage change. Reverse percentage change. Other growth and decay contexts.

Algebra review- Substitution. Simplifying expressions.

Quadratic expression and equations – Creating quadratics expressions. Expanding and factorising binomials. Plotting quadratic graphs. Solving quadratic graphs. Completing the square and turning points

Topic 2: Reasoning with Number

Indices and standard form – Index notations and rules. Fractional and negative indices. Comparing and ordering numbers in standard form. Calculating in standard form.

Statement of Inquiry

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Key Concept(s)

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Related Concept(s)

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## KS4 maths

Topic 1: Fractions, Decimals and Percentages

Angles and lines, triangles and quadrilaterals, congruence and similarity, angles in polygons.

Topic 2: Angles and Polygons

Fractions and percentages of a quantity, calculations with fractions, converting between fractions, decimals and percentages.

Topic 3: Formulae and Fractions

Formulae, functions, equivalences in algebra, expanding and factorising 2, substituting in formulae, using standard formulae, equations, identities and functions.

Topic 4: Working in 2D

Measuring lengths and angles, area of 2D shape, transformations.

Topic 5: Measures and Accuracy

Estimation and approximation, calculator methods, measures and accuracy.

Topic 6: Equations and Inequalities

Solving linear equations, quadratic equations, simultaneous equations, inequalities, approximate solutions.

Topic 1: Circles and Construction

Circles, constructions, loci, circle theorems.

Topic 2: Ratio and Proportion

Proportion. Ratio, percentage change.

Topic 1: Factors, Powers and Roots

Factors and multiples, prime factor decomposition, powers and roots, surds.

Topic 2: Graphs

Drawing straight line graphs, equation of a straight line, kinematic graph, linear and quadratic functions, properties of quadratic functions.

Topic 3: Working in 3D

3D shapes, volume of a prism, volume and surface area.

Topic 4: Calculations

Calculating with roots and indices, exact calculations, standard form.

Topic 1: Handling Data

Frequency diagrams, averages and speed 2, scatter graphs and correlation, time series, box plots and cumulative frequency graphs.

Topic 2: Graphs

Properties of quadratic functions, sketching functions, real-life graphs, cubic and reciprocal functions, exponential and trigonometric functions, gradients and area under graphs, equation of a circle.

Topic 3: Calculations

Calculating with roots and indices, exact calculations, standard form.

Topic 4: Pythagoras and Trigonometry

Pythagoras’ theorem, trigonometry 1 & 2, vectors, pythagoras and trigonometry problems.   NB Higher paper –  3 wks on this unit, Foundation paper a week on angle consolidation prior to beginning Unit 19.

Topic 1: Combined Events

Sets, possibility spaces, tree diagrams, conditional probability.

Topic 2: Sequences

Sequence rules, finding the nth term, special sequences, linear sequences, quadratic sequences.

Topic 3: Units and Proportionality

Compound units, direct proportion, inverse proportion, growth and decay, rates of change, converting between units.

Topic 4: Revision and Externally Set Exam

Revision and external exam

## KS5 maths

Topic 1: Algebra Skills

Laws of indices, Expanding Brackets, factorising, Surds, Rationalising the denominator, Solving quadratic equations, completing the square, Functions, Graphs of functions, the use of the discriminant, Modelling with quadratics, Linear and quadratic equations, Inequalities. Types of Graphs and transformations of graphs.

Topic 2: Co-ordinate Geometry and Algebraic Methods

y = mx + c, Understand the equation of a straight line graph, parallel and perpendicular equations, Modelling with straight line graphs. The equation of a circle and circle geometry. Use of Circle theorems to find equations of straight lines, tangents and chords.  Simplifying algebraic fractions and using polynomial long division. Use of the Factor theorem. Methods of Proof. Trigonometric graphs, the use of the sine rule and cosine rule in triangles. The area of a triangle and transforming trig graphs. Solving trigonometric equations including simple trig identities. Pascals Triangle and the Binomial expansion. Using the binomial expansion to make estimations and solve problems.

Topic 1: Statistics and Analysing Data

Population and Sampling, Random and non-random sampling,m types of data.  Range, interquartile range and percentiles. Median and mean. Standard deviation and  variance.  Coding. Representing data in Box Plots Cumulative Frequency diagrams and histograms, understanding Outliers and anomalies. Making comparisons between data sets.

Topic 2: Differentiation

Gradient of a curve from first principles, finding the derivative, differentiating polynomials, gradients of tangents and normals. Increasing and decreasing functions.

Topic 4: Differentiation and Integration

Second order derivatives, stationary points, sketching the gradient function, modelling with differentiation. Integrating polynomials, indefinite integrals and definite integrals.

Topic 2: Differentiation

Gradient of a curve from first principles, finding the derivative, differentiating polynomials, gradients of tangents and normals. Increasing and decreasing functions.

Topic 1: Mechanics

Modelling assumptions, quantities and units. Displacement time graphs, velocity time graphs. SUVAT constant acceleration formulae and vertical motion under gravity. Force diagrams, forces as a vector, forces with acceleration, motion in two directions, connected particles and pulleys.

Topic 2: Integration

Area under curves, between curves and straight lines and under the axis.

Topic 3: Mechanics

Functions of time, using differentiation, maxima / minima problems, using integration, constant acceleration formulae.

Topic 4: Exponentials and Vectors

Exponential functions and modelling, Logarithms and laws of logarithms. Solving equations using logarithms. Natural logarithms. Logarithms with non linear data. Representing vectors, magnitude and direction, position vector, solving geometric problems and modelling with vectors.

Topic 1: Algebra

Proof by contradiction, Algebraic fractions,Partial Fractions and Algebraic division. The modulus Function, mapping, composite functions, Inverse functions, transformations of functions, solving modulus problems. Arithmetic sequences and series, Geometric sequences and series, Sum to infinity, Sigma notation and recurrence relationships. Binomial expansion for negative and fractional indices.

Topic 2: Trigonometry

Radians, Arc length and area of a sector or segment. Solving trig equations, small angle approximations. Reciprocal Trig functions, Graphs of reciprocal trig functions. Using identities with reciprocal functions. Inverse trig functions and their graphs. The Addition Formulae, Double Angle Formulae, Solving equations using the Addition Formulae and double Angle formulae, Rsin(x + y), proving identities and Modelling with trig Functions.

Topic 3: Statistics

Exponential Models, Measuring correlation, Hypothesis testing for zero correlation, Set Notation, Conditional Probability and Venn diagrams, Probability Formulae, Tree diagrams, The Normal Distribution, finding probabilities from the Normal distribution, The inverse Normal distribution, the Standard Normal distribution, Finding Mean and Standard deviation, Approximating the Normal Distribution, Hypothesis Testing.

Topic 1: Parametrics

Parametric Equations and graphs, rewriting as a Cartesian equation, using trig identities, points of intersection, modelling with parametric equations.

Topic 2: Mechanics

Moments and Resultant Moments, Equilibrium, Centre of Mass, Tilting, Resolving Forces, Inclined Plane, Friction, Statics of a particle, Modelling with statics, Friction and Static particles, static rigid bodies, Dynamics and inclined planes, connected particles.

Topic 3: Mechanics

Horizontal projection, Horizontal and vertical projection, projection at any angle, projectile motion formulae, Vectors in Kinematics, vectors with projectiles, Variable acceleration in one dimension, differentiating vectors, Integrating vectors.

Topic 4: Differentiation and Iteration

Differentiation sinx and cosx, exponentials and logarithms, The Chain Rule, The Product Rule, the Quotient Rule, Differentiating trig functions, parametric differentiation, implicit differentiation, using second derivatives, rates of change. Numerical Methods – locating roots, iteration, Newton Raphson Method, application to modelling.

Topic 1: Integration and Vectors

Integrating standard functions, integrating f(ax +b), Using Trig identities, the Reverse Chain Rule, Integration by substitution, Integration by Parts, Partial fractions, finding area, the Trapezium rule, Solving differential equations and Modelling. Vectors in 3D , Solving Geometric Problems, Application to Mechanics.

Topic 2: Externally Set Exam

External exam