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 = 3andy = -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 inter-quartile 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