MATHEMATICS CONTINUUM ALGEBRA Year 7 Year 13 Begin using symbols and letters Manipulate algebraic expressions Expand a pair of brackets Factorise quadratic expressions Complete the square Use the binomial expansion Simplify algebraic expressions using partial fractions Solve simple linear equations Solve more complex linear equations Solve quadratic and cubic equations using trial and error Solve quadratic equations Solve simultaneous equations Solve cubic equations Solve equations with unknown powers using logs Solve polynomial equations with complex roots Continue a simple number sequence Identify the rule in a simple number sequence Find the nth term of a linear sequence Solve problems by identifying and analysing sequences Find the nth term of a quadratic sequence Solve problems involving geometric and arithmetic progressions Plot and read coordinates Draw graphs of simple linear functions such as x = 3 and y = -2 Draw graphs of more complex linear functions Draw and interpret real life graphs such as distance-time graphs Understand how gradient and y-intercept link to the equation of a linear graph Plot graphs of linear and quadratic functions Understand and draw transformations of graphs Substitute into expressions and formulae Use simple formulae Construct formulae Change the subject of a formulae Use the quadratic formula Differentiate and integrate polynomial functions Differentiate and integrate further functions including trigonometric functions
MATHEMATICS CONTINUUM NUMBER Year 7 Year 13 Know times tables to 12 × 12 Use simple mental methods for calculation Know the first ten squares, square roots and cubes Calculate mentally with more advanced strategies Use efficient and neat written methods for addition and subtraction Use efficient and neat written methods for simple multiplication and division Use efficient written methods accurately for calculations such as 264 × 36 and 630 ÷ 14 Work with simple fractions such as halves and quarters Add, subtract, multiply and divide simple fractions Calculate with more complicated fractions such as 1/5 + 2/3 Calculate with improper fractions and mixed numbers Round to the nearest 10, 100 or 1000 Round to the nearest decimal place Make sensible estimates to calculations and give justifications for these Round to the nearest 1st, 2nd or 3rd significant figure Work informally with numbers of any magnitude making accurate estimates and approximations Calculate upper and lower bounds for values and calculations Calculate simple percentages of quantities, e.g., 10% of 65 Calculate percentages of quantities such as 15% of 120 Efficiently calculate percentages of quantities using a calculator Calculate any percentage of any quantity including 16.5% of 82.3 Use percentages to solve problems involving interest rates and other real life contexts Use percentages to calculate percentage error Work with numbers in standard form Calculate with numbers in standard form Use a calculator efficiently with numbers in standard form Know and use simple index laws Know and use index laws involving fractional and negative powers Know what a logarithm is and what they are used for Use laws of logs and solve equations involving logs and exponentials Order decimals Order fractions Convert between fractions, decimals and percentages Order a mixture of fractions, decimals and percentages Understand simple ratio notation Simplify a ratio Divide a ratio in a quantity Solve problems where the quantities are in direct proportion Solve problems linked to exchange rates and other real life contexts Solve problems involving inverse or square proportion
MATHEMATICS CONTINUUM SHAPE, SPACE AND MEASURE Year 7 Year 13 Accurately measure and draw angles Use simple angles rules Use angle rules for polygons and shapes with parallel lines Know and use circle theorems Form geometric proofs using known angle rules Calculate area and perimeter of rectangles Calculate areas and perimeters of circles, triangles, trapezia and parallelograms Calculate volume and surface areas of cuboids and other prisms Understand the effects that enlargements will have on volume and area Calculate the area of a sector and the length of an arc Solve rates of change problems in volume contexts Use the trapezium rule to approximate definite integrals Use Pythagoras’ Theorem in right-angled triangles Use trigonometry in right-angled triangles Use trigonometry in non-right-angled triangles Solve trigonometric equations in degrees or radians Know different units of measurement for length, mass and capacity Convert between metric units of length, mass and capacity Convert between common metric and imperial units Identify lines of symmetry Rotate, reflect, enlarge and translate 2D shapes Identify similar and congruent shapes Calculate missing angles and sides in similar shapes by identifying the scale factor of enlargement Use a matrix to describe a translation Multiply 2 by 2 matrices and understand the link between matrices and transformations Find the inverse of a 2 by 2 matrix Understand vector notation and represent vectors with diagrams Construct vector proofs Work with vectors in 3D to find equations of lines Find the angle between two vectors, distance between two vectors and solve vector problems
MATHEMATICS CONTINUUM HANDLING DATA Year 7 Year 13 Collect data in a tally chart Construct a questionnaire and evaluate the questions asked Understand methods of sampling Conduct a stratified sample Draw pictograms and bar charts Construct and interpret graphs and charts such as pie charts and line graphs Construct and interpret scatter graphs Estimate and use line of best fit for linear correlation Give the equation of an estimated line of best fit Calculate product moment correlation coefficient Calculate equations of regression lines Calculate averages from simple sets of data Calculate averages from frequency tables Calculate averages from grouped frequency tables Construct cumulative frequency curves and use them to estimate median and quartiles Calculate the range of a set of data Calculate standard deviation and variance Use interpolation to estimate quartiles and percentiles Plan an investigation which involves collecting and representing data Interpret results and draw conclusions Identify possible sources of bias Identify limitations with methods of data collection and interpretation Choose appropriate representations given the data collected and the context of the investigation Used mathematical vocabulary to describe probability Find probabilities of simple events Efficiently list outcomes of more complex events and calculate probabilities Use tree diagrams to illustrate outcomes and calculate probabilities Calculate conditional probabilities Understand what a random variable is and construct and use a probability distribution table
MATHEMATICS CONTINUUM PROBLEM SOLVING Year 7 Year 13 Begin to solve problems making correct use of diagrams, symbols, tables and graphs Compare different mathematical representations when solving problems Break down tasks to make them more manageable and begin to use algebraic, graphical and geometric representations Justify the choice of representation in relation to the context of the problem Identify and use the most efficient representations for analysis and communication Model situations through precise and consistent use of symbols Classify objects and draw simple conclusions Make generalisations and give examples to support these Pose questions and provide convincing arguments Examine and refine arguments, conclusions and generalisations Support generalisations through chains of clear mathematical reasoning and begin constructing mathematical proofs Explore, explain and justify assumptions and constraints Check the accuracy of a solution and interpret information from a variety of mathematical representations Use logic to establish the truth of a statement Present a concise reasoned argument using symbols, diagrams, graphs and related explanatory text Distinguish between empirical evidence and proof Critically examine strategies and arguments adopted in problem solving Communicate own findings clearly, both orally and in writing Refine own findings on the basis of discussions with others Review and refine own findings and conclusions Communicate effectively to different audiences using a range of forms of communication Use mathematical symbols and language effectively to present convincing conclusions