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3 | Place Value • Understand place value for integers and decimals • Be able to exchange between place value columns • Experience different representations of place value Axioms and Arrays • Understand the commutative and associative properties of multiplication • Be able to represent multiplication through a variety of models • Experience manipulating models and calculations based on the associativity and commutativity 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 • Experience comparing and connecting calculations and representations of distributivity and associativity Factors and Multiples • Understand the factor properties of integers, prime numbers and square numbers • Be able list the factors of integers supported by appropriate representation • Experience decomposing and organising numbers based on their factors • Understand any set of integers as having a repeating pattern of common multiples • Be able list and organise common multiples for sets of integers • Experience representing and explaining patterns in common multiples | Order of Operations • Understand equal and unequal order of priority between addition, subtraction, multiplication and division • Be able interpret and write calculations involving the four operations and brackets • Experience connecting ordered calculations to a variety of contexts and representations Positive and Negative Numbers • Understand what a negative number is and how it is modelled on a number line • Understand that negative numbers have a value and an absolute value that are different • Be able to solve simple addition problems involving negative numbers • Understand how we can apply learning from addition to subtraction of negatives • Be able to subtract positive and negative numbers from positive and negative numbers • Be able to multiply with negative numbers, including with the negative as a multiplier and multiplicand • Be able to multiply and divide with negative numbers • Understand how multiplication and division models apply to negative numbers • Understand the connections between multiplication and division and deduce other known facts | Expressions, Equations and Inequalities • Understand that algebra is used to express mathematical structures, and that algebraic terms represent numbers that are unknown or variable • Be able to substitute (into), simplify, expand and factorise algebraic expressions • Understand what is meant by an equation and an inequality • Be able to manipulate equations and inequalities to form new equations and inequalities. • Be able to form expressions and inequalities in a new context • Be able to simplify and manipulate algebra in a new context • Experience generalising patterns and how algebra can be used to represent them. | Angles • Understand that one interpretation of angle is as a measure of turn • Experience generating equalities and inequalities using unknown angles • Be able to find missing angles around a point and in a straight line • Understand that two parallel straight lines will never meet • Understand that two lines that are not parallel will meet exactly once • Be able to identify angles that are equal and pairs of angles that sum to 180 degrees using angle rules in parallel lines Classifying 2D Shapes • Understand that symmetry, side length and angles can be used to compare and contrast triangles • Experience how different features of triangles follow from other features • Be able to find missing interior angles in a given triangle • Understand that a quadrilateral can be defined by side length and by how its diagonals intersect • Experience how to derive the interior angle sum for a quadrilateral from the interior angle sum of triangles • Be able to find missing interior angles in a given quadrilateral | Coordinates • Be able to use coordinates to identify a location on a 2-D plane • Understand that coordinates describe a ‘journey’ from the origin and that they describe a specific straight distance, either between the origin and a point, or between coordinates • Understand how to use the horizontal and vertical components of a line to identify the midpoint of a line and to identify lines that are equal in length • Be able to find the equation of a horizontal or vertical line • Understand how the equations of horizontal and vertical lines can form boundaries of shapes and lines of symmetry. Experience using quadrilaterals as a problem-solving context for coordinates. • Experience creating line segments of the same length through trying out coordinates and then examining their lengths through the use of right angled triangles Area of 2D Shapes • Understand that there are different units which can be used to describe perimeter or area • Be able to calculate the perimeter of a polygon • Be able to calculate the area of a different shapes by counting and a rectangle by multiplying the width and length • Experience the effect of combining shapes on the area and perimeter • Be able to identify a rectilinear shape and find its area and perimeter. • Be able to use the formulae for the area of a parallelogram and a triangle • Understand that in both formulae the height is the dimension which is perpendicular to the base • Experience finding areas of different types of triangles | |||||||||||||||||||||
4 | Assessment Map | |||||||||||||||||||||||||
5 | Year 8 | Constructing Triangles and Quadrilaterals • Understand how circle properties can be used to reason about the properties of other shapes • Be able to use a ruler and compasses to construct triangles • Understand which conditions lead to a non-unique triangle or a triangle that cannot be constructed • Understand how triangle constructions can be extended to constructing quadrilaterals •Be able to use ruler and compasses to construct quadrilaterals • Experience the properties of quadrilaterals in the context of constructions Conceptualising and Comparing Fractions • Understand that fractions describe equal parts of a whole •Understand that a fraction is also a division •Understand that a fraction can be a part of one whole or multiple wholes • Be able to describe the changing size of a fraction when the denominator or the numerator is changed • Be able to calculate equivalent fractions • Understand how the size of fractions can be compared by comparing the denominators or the numerators or their distance from key quantities • Be able to find equivalent fractions with a common denominator to compare fractions Experience using arrays to deepen understanding of decimal multiplication Manipulating and Calculating with Fractions • Be able to use different models including a ‘lots of’ model, a scaling model and an area model to represent multiplication of fractions • Be able to multiply fractions without a model • Be able to multiply decimal fractions • Understand that multiplying by a unit fraction is the same as dividing • Understand that when multiplying fractions the answer can be smaller than the original amounts • Understand that when dividing by a fraction, we multiply by the denominator and divide by the numerator • Be able to divide a fraction by an integer • Be able to divide a fraction by an fraction • Be able to add and subtract fractions with the same denominator • Be able to add and subtract fractions with a different denominator and find the lowest common denominator • Experience connecting fractions written using the lowest common denominator with the equivalent calculation written in its simplified form | Ratio • Be able to represent a multiplicative relationship between two or more numbers using ratio notation • Be able to scale a ratio and recognise equivalent ratios • Understand that the constant of proportionality is the multiplier within a ratio and will be the same between each pair of numbers in equivalent ratios • Understand that the scale factor is the multiplier used to create an equivalent ratio and can be any number • Understand the difference between the scale factor and the constant of proportionality in a geometrical context • Understand the difference between part part relationships and part whole relationships in geometrical contexts • Be able to represent ratio problems with bar models • Be able to share a quantity in a given ratio Percentages • To understand what percentage is and how it can be represented • To be able to convert between fractions, decimals and percentages • To be able to calculate percentage of amounts using a bar model • Understand bearing conventions and notation and relate it to prior knowledge of angles • Be able describe a position using a bearing and direction • Experience creating shapes and paths using bearings | Sequences • Understand linear sequences as patterns within number grid columns • Be able to use and form position-to-term rules for linear sequences • Experience generalising position-to-term rules using tracking calculations • Understand the features of linear and non-linear sequences • Be able to reason with a variety of sequences and representations • Experience representing sequences abstractly and pictorially Forming and Solving Equations • Understand equality in algebraic relationships • Be able to solve simple linear equations • Experience manipulating pictorial and abstract algebraic representations • Understand algebraic relationships embedded within various contexts • Be able to form and solve linear equations with unknowns on both sides • Experience representing and manipulating algebraic relationships | Forming and Solving Inequalities • Understand different representations of inequalities • Be able to test and solve linear inequalities • Experience manipulating and explaining different inequality representations • Understand inequalities as representations of numerical relationships from a range of contexts • Be able describe solve inequalities including with unknowns on both sides • Experience manipulating inequalities and exploring the conditions for preservation of the relationship Linear Graphs •Students start the unit on linear graphs by visiting and revisiting familiar contexts on the Cartesian plane, such as using coordinates, horizontal and vertical lines and inequalities •Understand a linear relationship can be recognised from a constant rate of change in the coordinates •Be able to identify the gradient of a line from its graph and from a set of coordinates Experience connecting a linear equation to its graphical representation •Understand a linear relationship can be described using algebra in the form 𝑦=𝑚𝑥+𝑐 •Be able to identify the equation of a line and draw a line from its equation •Experience moving between three representations of a linear relationship: coordinates, graphs and equations | Accuracy and Estimation • Understand rounding is a method of approximation • Be able round to decimal places and ‘to the nearest’ • Experience using rounded numbers to estimate • Understand how to identify significant figures • Be able round to a given number of significant figures • Experience using estimation to check calculations Ratio Review • Understand the relationship between ratio and other proportional descriptors • Be able to use models and equivalence to solve ratio problems • Experience models and contexts relating to ratio Real Life Graphs • Understand graphical representation of (changing) rate • Be able to interpret and express graphical linear and piecewise relationships • Experience describing, comparing and visualising changing rate • Understand rate as one measure per another • Be able to contextualise speed and compare it in different measures • Be able to read and draw displacement-time graphs | Direct and Inverse Proportion • Understand multiplicative relationships • Be able to use scale factor and constant of proportionality independently to find missing values in directly proportional relationships • Experience different representations of the constant of proportionality, including gradient • Be able to identify the scale factor and constant of proportionality for any two directly proportional measures (including non-integer values) • Understand key features of inversely proportional relationships • Be able to find missing values from directly and inversely proportional relationships, and state the constant of proportionality in each case • Be able to use algebraic notation to describe directly and inversely proportional relationships | |||||||||||||||||||
6 | Assessment Map | |||||||||||||||||||||||||
7 | Year 9 | Angles in a Polygon • Understand what is meant by a polygon, an interior angle, and develop a sense of an interior angle of a polygon. • Experience constructing and deconstructing polygons from triangles. • Understand how triangles can be used to find the sum of interior angles of polygons • Be able to find missing angles in polygons • Experience generalising methods using algebraic notation. • Understand what an ‘exterior angle’ is and key features of them. • Be able to find the sizes of missing angles in polygons, including interior and exterior angles of regular shapes. • Be able to use angle notation conventions to describe angles. Bearings • Understand bearing conventions and notation and relate it to prior knowledge of angles • Be able describe a position using a bearing and direction • Experience creating shapes and paths using bearings • Be able to find missing angle problems involving bearings • Experience generalising and pattern spotting with bearings A from B and B from A • Understand how bearings can form part of a position description | Circles • Understand Pi as the ratio between diameter and circumference • Be able to calculate circumference and arc lengths in perimeter problems • Experience reasoning geometrically using the features of circles • Understand Pi as the ratio between radius squared and circumference • Be able work out area of circles, sectors and compound shapes • Experience reasoning geometrically using circle properties Volume of Surface Area of Prisms • Understand solid shapes have three dimensions • Be able find the surface area of a cube and cuboid • Experience visualising 3-D shapes from 2-D representations and nets • Understand what a prism is • Be able to calculate the surface area of a prism • Experience visualising prisms from 2-D representations and nets • Understand the concept of volume • Be able to calculate the volume of prisms • Experience visualising constructing and deconstructing prisms | Probability • Understand probability is a numerical measure of chance from 0 to 1 inclusive • Be able to calculate the probability of single independent events • Experience comparing probabilities using a variety of representations • Understand a variety of representations of combined events • Be able to calculate the probability of a pair of combined events • Experience using a variety of techniques to solve problem • Understand the difference between theoretical and experimental probability • Be able to determine whether an experiment is fair or biased •Experience working with probabilities which are determined by two events Sets and Venns • Understand set notation for intersections, unions, complements and the universal set • Be able to identify and interpret sets described by notation and within Venn diagrams Experience interpreting a range of sets in qualitative and numerical contexts • Understand probability from set notation and Venn diagrams • Be able to form and interpret Venn diagrams in the context of probability • Experience representing probabilities and expected outcomes in different ways | GCSE Units begin Higher 1: Number: 1a. Calculations, checking and rounding 1b. Indices, roots, reciprocals and hierarchy of operations 1c. Factors, multiples, primes 1d. Standard form and surds 2: Algebra: 2a. Algebra: the basics 2b. Setting up, rearranging and solving equation 2c. Sequences Foundation 1: Number: 1a. Integers and place value 1b. Decimals 1c. Indices, powers and roots 1d. Factors, multiples and primes | Higher 3: Interpreting and representing data: 3a. Averages and range 3b. Representing and interpreting data 3c. Scatter graphs 4: Fractions, ratio and percentages: 4a. Fractions 4b. Percentages 4c. Ratio and proportion Foundation 2: Algebra: 2a. Algebra: the basics 2b. Expanding and factorising single brackets 2c. Expressions and substitution into formulae | 5: Angles and trigonometry: 5a. Polygons, angles and parallel lines 5b. Pythagoras’ Theorem and trigonometry Foundation 3: Graphs, tables and charts: 3a. Tables 3b. Charts and graphs 3c. Pie charts 3d. Scatter graphs | |||||||||||||||||||
8 | Assessment Map | |||||||||||||||||||||||||
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10 | Year 10 Higher Tier | 8: Transformations and constructions: 8a. Transformations 8b. Constructions, loci and bearings 9: Equations and inequalities: 9a. Solving quadratic and simultaneous equations 9b. Inequalities | 10: Probability: 10a. Combined events 10b. Mutually exclusive events 10c. Experimental probability 10d. Independent events and tree diagrams 10e. Conditional Probability 10f. Venn diagrams and set notation 11: Multiplicative reasoning: 11a. Growth and decay 11b. Compound Measures 11c. Ratio and proportion | 12: Similarity and congruence: 12a. in 2D 12b. in 3D 13: More trigonometry: 13a. Graphs of trigonometric functions 13b. Further trigonometry | 14: Further Statistics: 14a. Collecting data 14b. Cumulative frequency, box plots and histograms | 15: Equations and graphs: 15a. Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics | 16: Circle Theorems: 16a. Circle theorems 16b. Circle geometry | |||||||||||||||||||
11 | Year 10 Foundation Tier | 9: Graphs: 9a. Real-life graphs 9b. Straight-line graphs 10: Transformations: 10a. Transformations I: translations, rotations and reflections 10a. Transformations II: enlargements and combinations | 11: Ratio and proportion: 11a. Ratio 11b. Proportion | 12: Right-angled triangles: 12a. Right-angled triangles: Pythagoras and trigonometry 13: Probability: 13a. Probability I 13b. Probability II | 14: Multiplicative reasoning | 15: Constructions, loci and bearings: 15a. Plans and elevations 15b. Constructions, loci and bearings 16: Quadratic equations and graphs: 16a. Quadratic equations: expanding and factorising 16b. Quadratic equations: graphs | 17: Perimeter, area and volume 2: 17a. Circles, cylinders, cones and spheres | |||||||||||||||||||
12 | Assessment Map | |||||||||||||||||||||||||
13 | Year 11 Higher Tier | 17: More algebra: 17a. Changing the formulae subject (more complex), solving equations, algebraic fractions, rationalising surds, proof | 18: Vectors and geometric proof | 19: Proportion and graphs: 19a. Reciprocal and exponential graphs; Gradient and area under graphs 19b. Direct and inverse proportion | Exam Qs and Revision Focus: | Exam Qs and Revision Focus: | Exam Qs and Revision Focus: | |||||||||||||||||||
14 | Year 11 Foundation Tier | 18: Fractions, indices and standard form: 18a. Fractions and reciprocals 18b. Indices and standard form 19: Congruence, similarity and vectors: 19a. Similarity and congruence in 2D 19b. Vectors | 20: More algebra: 20a. Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations | Exam Qs and Revision Focus: | Exam Qs and Revision Focus: | Exam Qs and Revision Focus: | Exam Qs and Revision Focus: | |||||||||||||||||||
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17 | Year 12 | Algebra and functions Statistical sampling Data and interpretation Quantities and Units Kinematics | Coordinate geometry in the (x, y) plane Further algebra Data presentation and interpretation Kinematics 1 (constant acceleration) | Trigonometry Prereq: Pure (AS) Unit 1: Algebra and functions Vectors | Probability Statistical distributions Integration | Statistical hypothesis testing Forces & Newton’s laws Kinematics 2 (variable acceleration) | Algebraic and partial fractions Regression and correlation | |||||||||||||||||||
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19 | Year 13 | Functions and modelling Series and sequences Moments Statistical hypothesis testing Forces & Newton’s laws Kinematics 2 (variable acceleration) | The binomial theorem Trigonometry Parametric equations The Normal distribution Forces at any angle Applications of kinematics Proof Algebraic and partial fractions Regression and correlation | Differentiation Numerical methods - see Integration (part 2) for the trapezium rule Vectors (3D) Integration (part 1) | Integration (part 2) The Normal distribution Applications of forces The Normal distribution Further kinematics - Proof | Revision | Revision | |||||||||||||||||||
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