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The Interactive Scheme of Work Creator Strand Topic Band Order YoT Module MPA REPR 1 1 7 MPA REPR 1 2 8 MPA REPR 1 3 9 MPA REPR 1 4 10 MPA REPR 1 5 11 MPA REPR 1 6 11 MPA ANAR 1 1 7 MPA ANAR 1 2 8 MPA ANAR 1 3 9 MPA ANAR 1 4 10 MPA ANAR 1 5 11 MPA ANAR 1 6 11 MPA ANAP 1 1 7 MPA ANAP 1 2 7 MPA ANAP 1 3 7 MPA ANAP 1 4 7 MPA ANAP 1 5 7 MPA ANAP 1 6 8 MPA ANAP 1 7 8 MPA ANAP 1 8 8 MPA ANAP 1 9 8 MPA ANAP 1 10 8 MPA ANAP 1 11 9 MPA ANAP 1 12 9 MPA ANAP 1 13 9 MPA ANAP 1 14 9 MPA ANAP 1 15 9 MPA ANAP 1 16 10 MPA ANAP 1 17 10 MPA ANAP 1 18 10 MPA ANAP 1 19 10 MPA ANAP 1 20 10 MPA ANAP 1 21 11 MPA ANAP 1 22 11 MPA ANAP 1 23 11 MPA ANAP 1 24 11 MPA ANAP 1 25 11 MPA IEVAL 1 1 7 MPA IEVAL 1 2 8 MPA IEVAL 1 3 9 MPA IEVAL 1 4 10 MPA IEVAL 1 5 11 MPA IEVAL 1 6 11 NUM PVOR 1 1 7 NUM PVOR 2 2 7 NUM PVOR 3 3 7 NUM PVOR 1 4 8 NUM PVOR 2 5 8 NUM PVOR 3 6 8 NUM PVOR 1 7 9 NUM PVOR 3 8 9 NUM PVOR 1 9 10 NUM PVOR 1 10 10 NUM PVOR 3 11 10 NUM PVOR 1 12 11 NUM PVOR 3 13 11 NUM PVOR 3 14 11 NUM PNIPR 1 1 7 NUM PNIPR 1 2 7 NUM PNIPR 1 3 7 NUM PNIPR 1 4 8 NUM PNIPR 1 5 8 NUM PNIPR 1 6 8 NUM PNIPR 1 7 9 NUM PNIPR 1 8 9 NUM PNIPR 1 9 9 NUM PNIPR 1 10 10 NUM PNIPR 1 11 10 NUM PNIPR 1 12 11 NUM PNIPR 1 13 11 NUM FDPRP 1 1 7 NUM FDPRP 2 2 7 NUM FDPRP 3 3 7 NUM FDPRP 3 4 7 NUM FDPRP 3 5 7 NUM FDPRP 1 6 8 NUM FDPRP 2 7 8 NUM FDPRP 3 8 8 NUM FDPRP 3 9 8 NUM FDPRP 3 10 8 NUM FDPRP 1 11 9 NUM FDPRP 2 12 9 NUM FDPRP 3 13 9 NUM FDPRP 3 14 9 NUM FDPRP 1 15 10 NUM FDPRP 2 16 10 NUM FDPRP 3 17 10 NUM FDPRP 3 18 10 NUM FDPRP 1 19 11 NUM FDPRP 3 20 11 NUM FDPRP 3 21 11 NUM NOPS 1 22 7 NUM NOPS 1 23 7 NUM NOPS 1 24 8 NUM NOPS 1 25 8 NUM NOPS 1 26 9 NUM NOPS 1 27 9 NUM NOPS 1 28 10 NUM NOPS 1 29 11 NUM MCM 1 1 7 NUM MCM 2 2 7 NUM MCM 3 3 7 NUM MCM 1 4 8 NUM MCM 2 5 8 NUM MCM 3 6 8 NUM MCM 1 7 9 NUM MCM 3 8 9 NUM MCM 3 9 10 NUM MCM 1 10 11 NUM WCM 1 1 7 NUM WCM 1 2 7 NUM WCM 1 3 8 NUM WCM 1 4 8 NUM WCM 1 5 9 NUM CALC 1 6 7 NUM CALC 1 7 7 NUM CALC 1 8 8 NUM CALC 1 9 8 NUM CALC 1 10 9 NUM CALC 1 11 10 NUM CALC 1 12 10 NUM CALC 1 13 11 NUM CALC 1 14 11 NUM CALC 1 15 11 NUM CHECK 1 1 7 NUM CHECK 1 2 8 NUM CHECK 1 3 9 NUM CHECK 1 4 10 NUM CHECK 1 5 11 ALG EFI 1 1 7 ALG EFI 2 2 7 ALG EFI 2 3 7 ALG EFI 2 4 7 ALG EFI 3 5 7 ALG EFI 1 6 8 ALG EFI 1 7 8 ALG EFI 2 8 8 ALG EFI 2 9 8 ALG EFI 2 10 8 ALG EFI 3 11 8 ALG EFI 1 12 9 ALG EFI 1 13 9 ALG EFI 2 14 9 ALG EFI 2 15 9 ALG EFI 2 16 9 ALG EFI 1 17 9 ALG EFI 1 18 9 ALG EFI 3 19 9 ALG EFI 1 20 10 ALG EFI 1 21 10 ALG EFI 2 22 10 ALG EFI 2 23 10 ALG EFI 2 24 10 ALG EFI 3 25 10 ALG EFI 1 26 11 ALG EFI 1 27 11 ALG EFI 2 28 11 ALG EFI 2 29 11 ALG EFI 2 30 11 ALG EFI 2 31 11 ALG EFI 2 32 11 ALG EFI 2 33 11 ALG EFI 3 34 11 ALG SFG 1 1 7 ALG SFG 1 2 7 ALG SFG 2 3 7 ALG SFG 3 4 7 ALG SFG 3 5 7 ALG SFG 1 6 8 ALG SFG 1 7 8 ALG SFG 2 8 8 ALG SFG 3 9 8 ALG SFG 3 10 8 ALG SFG 1 11 9 ALG SFG 1 12 9 ALG SFG 2 13 9 ALG SFG 2 14 9 ALG SFG 3 15 9 ALG SFG 4 16 9 ALG SFG 4 17 9 ALG SFG 1 18 10 ALG SFG 2 19 10 ALG SFG 2 20 10 ALG SFG 3 21 10 ALG SFG 3 22 10 ALG SFG 2 23 11 ALG SFG 2 24 11 ALG SFG 3 25 11 ALG SFG 3 26 11 ALG SFG 2 27 11 ALG SFG 2 28 11 ALG SFG 3 29 11 ALG SFG 3 30 11 GEOM GR 1 1 7 GEOM GR 1 2 7 GEOM GR 2 3 7 GR 4 4 7 GEOM GR 1 5 8 GEOM GR 2 6 8 GEOM GR 3 7 8 GEOM GR 4 8 8 GEOM GR 1 9 9 GEOM GR 1 10 9 GEOM GR 2 11 9 GEOM GR 2 12 9 GEOM GR 3 13 9 GEOM GR 4 14 9 GEOM GR 1 15 10 GEOM GR 1 16 10 GEOM GR 2 17 10 GEOM GR 3 18 10 GEOM GR 4 19 10 GEOM GR 4 20 10 GEOM GR 1 21 11 GEOM GR 2 22 11 GEOM GR 4 23 11 GEOM GR 4 24 11 GEOM GR 1 25 11 GEOM GR 2 26 11 GEOM GR 3 27 11 GEOM GR 4 28 11 GEOM GR 4 29 11 GEOM GR 4 30 11 GEOM TCOOR 1 1 7 GEOM TCOOR 2 2 7 GEOM TCOOR 2 3 7 GEOM TCOOR 2 4 7 GEOM TCOOR 6 5 7 GEOM TCOOR 2 6 7 GEOM TCOOR 2 7 8 GEOM TCOOR 2 8 8 GEOM TCOOR 4 9 8 GEOM TCOOR 5 10 8 GEOM TCOOR 6 11 8 GEOM TCOOR 2 12 9 GEOM TCOOR 2 13 9 GEOM TCOOR 2 14 9 GEOM TCOOR 3 15 9 GEOM TCOOR 4 16 9 GEOM TCOOR 5 17 9 GEOM TCOOR 6 18 9 GEOM TCOOR 2 19 10 GEOM TCOOR 2 20 10 GEOM TCOOR 4 21 10 GEOM TCOOR 6 22 10 GEOM TCOOR 4 23 11 GEOM TCOOR 6 24 11 GEOM TCOOR 6 25 11 GEOM TCOOR 6 26 11 GEOM TCOOR 6 27 11 GEOM CL 1 1 7 GEOM CL 1 2 7 GEOM CL 1 3 7 GEOM CL 1 4 8 GEOM CL 1 5 8 GEOM CL 1 6 8 GEOM CL 1 7 9 GEOM CL 1 8 9 GEOM CL 1 9 9 GEOM CL 1 10 10 GEOM CL 1 11 10 GEOM MMEN 1 1 7 GEOM MMEN 1 2 7 GEOM MMEN 3 3 7 GEOM MMEN 3 4 7 GEOM MMEN 1 5 8 GEOM MMEN 1 6 8 GEOM MMEN 3 7 8 GEOM MMEN 3 8 8 GEOM MMEN 1 9 9 GEOM MMEN 2 10 9 GEOM MMEN 3 11 9 GEOM MMEN 3 12 9 GEOM MMEN 1 13 10 GEOM MMEN 3 14 10 GEOM MMEN 3 15 10 GEOM MMEN 1 16 11 GEOM MMEN 3 17 11 GEOM MMEN 3 18 11 GEOM MMEN 3 19 11 GEOM MMEN 1 20 11 GEOM MMEN 3 21 11 GEOM MMEN 3 22 11 STATS SPEC 1 1 7 STATS SPEC 1 2 7 STATS SPEC 1 3 7 STATS SPEC 1 4 7 STATS SPEC 1 5 8 STATS SPEC 1 6 8 STATS SPEC 1 7 8 STATS SPEC 1 8 8 STATS SPEC 1 9 9 STATS SPEC 1 10 9 STATS SPEC 1 11 9 STATS SPEC 1 12 9 STATS SPEC 1 13 10 STATS SPEC 1 14 10 STATS SPEC 1 15 10 STATS SPEC 1 16 10 STATS SPEC 1 17 11 STATS SPEC 1 18 11 STATS SPEC 1 19 11 STATS SPEC 1 20 11 STATS SPEC 1 21 11 STATS PREP 1 1 7 STATS PREP 2 2 7 STATS PREP 1 3 8 STATS PREP 2 4 8 STATS PREP 1 5 9 STATS PREP 2 6 9 STATS PREP 3 7 9 STATS PREP 1 8 10 STATS PREP 2 9 10 STATS PREP 1 10 11 STATS PREP 1 11 11 STATS PREP 2 12 11 STATS PREP 2 13 11 STATS INTR 1 1 7 STATS INTR 1 2 7 STATS INTR 1 3 7 STATS INTR 1 4 8 STATS INTR 1 5 8 STATS INTR 1 6 8 STATS INTR 1 7 9 STATS INTR 1 8 9 STATS INTR 1 9 9 STATS INTR 1 10 10 STATS INTR 1 11 10 STATS INTR 1 12 10 STATS INTR 1 13 11 STATS INTR 1 14 11 STATS INTR 1 15 11 STATS INTR 1 16 11 STATS PROB 1 1 7 STATS PROB 1 2 7 STATS PROB 1 3 7 STATS PROB 1 4 8 STATS PROB 1 5 8 STATS PROB 1 6 8 STATS PROB 1 7 9 STATS PROB 1 8 9 STATS PROB 1 9 9 STATS PROB 1 10 10 STATS PROB 1 11 10 STATS PROB 1 12 10 STATS PROB 1 13 11 STATS PROB 1 14 11 STATS PROB 1 15 11 active Scheme of Work Creator Objective NC Level Identify the necessary information to understand or simplify a context or problem; represent problems, making correct use of symbols, words, diagrams, tables and graphs; use 5 appropriate procedures and tools, including ICT Identify the mathematical features of a context or problem; try out and compare mathematical representations; select 5 appropriate procedures and tools, including ICT Break down substantial tasks to make them more manageable; represent problems and synthesise information in algebraic, geometrical or graphical form; move from one 6 form to another to gain a different perspective on the problem Compare and evaluate representations; explain the features selected and justify the choice of representation in relation to 7 the context Choose and combine representations from a range of perspectives; introduce and use a range of mathematical 8 techniques, the most efficient for analysis and most effective for communication Systematically model contexts or problems through precise and consistent use of symbols and representations, and 8 sustain this throughout the work Classify and visualise properties and patterns; generalise in simple cases by working logically; draw simple conclusions and explain reasoning; understand the significance of a 4 counter-example; take account of feedback and learn from mistakes Visualise and manipulate dynamic images; conjecture and generalise; move between the general and the particular to test the logic of an argument; identify exceptional cases or counter-examples; make connections with related contexts Use connections with related contexts to improve the analysis of a situation or problem; pose questions and make convincing arguments to justify generalisations or solutions; recognise the impact of constraints or assumptions Identify a range of strategies and appreciate that more than one approach may be necessary; explore the effects of varying values and look for invariance and covariance in models and representations; examine and refine arguments, conclusions and generalisations; produce simple proofs Make progress by exploring mathematical tasks, developing and following alternative approaches; examine and extend generalisations; support assumptions by clear argument and follow through a sustained chain of reasoning, including proof Present rigorous and sustained arguments; reason inductively, deduce and prove; explain and justify assumptions and constraints Make accurate mathematical diagrams, graphs and constructions on paper and on screen Calculate accurately, selecting mental methods or calculating devices as appropriate Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Use accurate notation, including correct syntax when using ICT Record methods, solutions and conclusions; estimate, approximate and check working Make accurate mathematical diagrams, graphs and constructions on paper and on screen Calculate accurately, selecting mental methods or calculating devices as appropriate Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Use accurate notation, including correct syntax when using ICT Record methods, solutions and conclusions; estimate, approximate and check working Make accurate mathematical diagrams, graphs and constructions on paper and on screen Calculate accurately, selecting mental methods or calculating devices as appropriate Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Use accurate notation, including correct syntax when using ICT Record methods, solutions and conclusions; estimate, approximate and check working Make accurate mathematical diagrams, graphs and constructions on paper and on screen Calculate accurately, selecting mental methods or calculating devices as appropriate Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Use accurate notation, including correct syntax when using ICT Record methods, solutions and conclusions; estimate, approximate and check working Make accurate mathematical diagrams, graphs and constructions on paper and on screen Calculate accurately, selecting mental methods or calculating devices as appropriate Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Use accurate notation, including correct syntax when using ICT Record methods, solutions and conclusions; estimate, approximate and check working Interpret information from a mathematical representation or context; relate findings to the original context; check the accuracy of the solution; explain and justify methods and conclusions; compare and evaluate approaches Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches Justify the mathematical features drawn from a context and the choice of approach; generate fuller solutions by presenting a concise, reasoned argument using symbols, diagrams, graphs and related explanations Make sense of, and judge the value of, own findings and those presented by others; judge the strength of empirical evidence and distinguish between evidence and proof; justify generalisations, arguments or solutions Show insight into the mathematical connections in the context or problem; critically examine strategies adopted and arguments presented; consider the assumptions in the model and recognise limitations in the accuracy of results and conclusions Justify and explain solutions to problems involving an unfamiliar context or a number of features or variables; comment constructively on reasoning, logic, process, results and conclusions Understand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100, 1000, 4 and explain the effect Compare and order decimals in different contexts; know that when comparing measurements the units must be the same Round positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01 Order Decimals Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two 5 decimal places Extend knowledge of integer powers of 10; recognise the equivalence of 0.1, 1⁄10 and 10^(–1); multiply and divide by any integer power of 10 Use rounding to make estimates and to give solutions to problems to an appropriate degree of accuracy Express numbers in standard index form, both in conventional notation and on a calculator display Convert between ordinary and standard index form representations Round to a given number of significant figures; use significant figures to approximate answers when multiplying or dividing large numbers Use standard index form to make sensible estimates for 8 calculations involving multiplication and/or division Understand how errors can be compounded in calculations Understand upper and lower bounds EP Understand negative numbers as positions on a number line; order, add and subtract integers in context Recognise and use multiples, factors, primes (less than 100), common factors, highest common factors and lowest common multiples in simple cases; use simple tests of divisibility Recognise the first few triangular numbers; recognise the squares of numbers to at least 12 × 12 and the corresponding roots Add, subtract, multiply and divide integers 5 Use multiples, factors, common factors, highest common factors, lowest common multiples and primes; find the prime 6 factor decomposition of a number, e.g. 8000 = 2^6 × 5^3 Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer 6 powers Use the prime factor decomposition of a number Use ICT to estimate square roots and cube roots Use index notation for integer powers; know and use the index laws for multiplication and division of positive integer powers use index notation with negative and fractional powers, recognising that the index laws can be applied to these as well know that n^(1/2) = root(n) and n^(1/3) = CubeRoot(n) for any positive number n Use inverse operations, understanding that the inverse operation of raising a positive number to power n is raising the result of this operation to power 1/n Understand and use rational and irrational numbers EP Express a smaller whole number as a fraction of a larger one; simplify fractions by cancelling all common factors and identify equivalent fractions; convert terminating decimals to fractions, e.g. 0.23 = 23/100 ; use diagrams to compare two or more simple fractions Add and subtract simple fractions and those with common denominators; calculate simple fractions of quantities and measurements (whole-number answers); multiply a fraction by an integer Understand percentage as the ‘number of parts per 100’; calculate simple percentages and use percentages to compare simple proportions Recognise the equivalence of percentages, fractions and 6 decimals Understand the relationship between ratio and proportion; use direct proportion in simple contexts; use ratio notation, simplify ratios and divide a quantity into two parts in a given ratio; solve simple problems involving ratio and proportion using informal strategies Recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing 6 them with a common denominator or by converting them to decimals Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction 6 answers); multiply and divide an integer by a fraction Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; 6 calculate percentages and find the outcome of a given percentage increase or decrease Use the equivalence of fractions, decimals and percentages to 6 compare proportions Apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units, recognising links with fraction notation; divide 6 a quantity into two or more parts in a given ratio; use the unitary method to solve simple problems involving ratio and direct proportion Understand the equivalence of simple algebraic fractions; know that a recurring decimal is an exact fraction Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing Recognise when fractions or percentages are needed to compare proportions; solve problems involving percentage changes Use proportional reasoning to solve problems, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts Distinguish between fractions with denominators that have only prime factors 2 or 5 (terminating decimals), and other fractions (recurring decimals) Understand and apply efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse Understand and use proportionality and calculate the result of any proportional change using multiplicative methods Calculate an original amount when given the transformed amount after a percentage change; use calculators for reverse percentage calculations by doing an appropriate division Use an algebraic method to convert a recurring decimal to a fraction Calculate an unknown quantity from quantities that vary in direct proportion using algebraic methods where appropriate Understand and use direct and inverse proportion; solve problems involving inverse proportion (including inverse squares) using algebraic methods Understand and use the rules of arithmetic and inverse operations in the context of positive integers and decimals Use the order of operations, including brackets Understand and use the rules of arithmetic and inverse 6 operations in the context of integers and fractions Use the order of operations, including brackets, with more complex calculations Understand the effects of multiplying and dividing by numbers between 0 and 1; consolidate use of the rules of arithmetic and inverse operations Understand the order of precedence of operations, including powers Recognise and use reciprocals; understand ‘reciprocal’ as a multiplicative inverse; know that any number multiplied by its reciprocal is 1, and that zero has no reciprocal because division by zero is not defined Use a multiplier raised to a power to represent and solve problems involving repeated proportional change, e.g. compound interest Recall number facts, including positive integer complements to 100 and multiplication facts to 10 × 10, and quickly derive associated division facts Strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple problems mentally Make and justify estimates and approximations of calculations Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8 Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, and cubes and cube roots; solve problems mentally Make and justify estimates and approximations of calculations Use known facts to derive unknown facts; extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots; solve problems mentally Make and justify estimates and approximations of calculations Make and justify estimates and approximations of calculations by rounding numbers to one significant figure and multiplying or dividing mentally Use surds and pi in exact calculations, without a calculator; rationalise a denominator such as 1/root(3) = root(3)/3 Use efficient written methods to add and subtract whole numbers and decimals with up to two places Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers Use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal places Use efficient written methods for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations Use efficient written methods to add and subtract integers and decimals of any size; multiply by decimals; divide by decimals by transforming to division by an integer Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures) Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memory Enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time) Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, pi and sign change keys; use the function keys for powers, roots and fractions; use brackets and the memory Use an extended range of function keys, including the reciprocal and trigonometric functions Use standard index form, expressed in conventional notation and on a calculator display; know how to enter numbers in standard index form Use calculators to explore exponential growth and decay, using a multiplier and the power key Calculate with standard index form, using a calculator as appropriate Use calculators, or written methods, to calculate the upper and lower bounds of calculations in a range of contexts, particularly when working with measurements Check results by considering whether they are of the right order of magnitude and by working problems backwards 5 Select from a range of checking methods, including 6 estimating in context and using inverse operations Check results using appropriate methods 5 Check results using appropriate methods 5 Check results using appropriate methods 5 Use letter symbols to represent unknown numbers or variables; know the meanings of the words term, expression and equation Understand that algebraic operations follow the rules of arithmetic Simplify linear algebraic expressions by collecting like terms; multiply a single term over a bracket (integer coefficients) Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate 6 method (e.g. inverse operations) Use simple formulae from mathematics and other subjects; substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula Recognise that letter symbols play different roles in equations, formulae and functions; know the meanings of the words formula and function Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way) Use graphs and set up equations to solve simple problems involving direct proportion Use formulae from mathematics and other subjects; substitute integers into simple formulae, including examples that lead to an equation to solve; substitute positive integers into expressions involving small powers, e.g. 3x^2 + 4 or 2x^3 ; derive simple formulae Distinguish the different roles played by letter symbols in equations, identities, formulae and functions Use index notation for integer powers and simple instances of the index laws Simplify or transform algebraic expressions by taking out single-term common factors; add simple algebraic fractions Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution) Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such x^2 + x = 20 Use algebraic methods to solve problems involving direct proportion; relate algebraic solutions to graphs of the equations; use ICT as appropriate Explore ways of constructing models of real-life situations by drawing graphs and constructing algebraic equations and inequalities Use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject Know and use the index laws in generalised form for multiplication and division of integer powers Square a linear expression; expand the product of two linear expressions of the form xn± and simplify the corresponding quadratic expression; establish identities such as a^2 - b^2 = (a+b)(a-b) Solve linear equations in one unknown with integer and fractional coefficients; solve linear equations that require prior simplification of brackets, including those with negative signs anywhere in the equation Solve linear inequalities in one variable; represent the solution set on a number line Solve a pair of simultaneous linear equations by eliminating one variable; link a graph of an equation or a pair of equations to the algebraic solution; consider cases that have 7 no solution or an infinite number of solutions Derive and use more complex formulae; change the subject of a formula, including cases where a power of the subject appears in the question or solution, e.g. find given that A = (pi)r^2 Factorise quadratic expressions, including the difference of two squares, e.g. x^2 - 9 = (x+3)(x-3); cancel common factors in rational expressions eg, 2(x+1)^2 / (x+1) Simplify simple algebraic fractions to produce linear expressions; use factorisation to simplify compound algebraic fractions Solve equations involving algebraic fractions with compound expressions as the numerators and/or denominators Solve linear inequalities in one and two variables; find and represent the solution set Explore ‘optimum’ methods of solving simultaneous equations in different forms Solve quadratic equations by factorisation Solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, where one is linear in each unknown and the other is linear in one unknown and EP quadratic in the other or of the form x^2 + y^2 = r^2 Solve quadratic equations by factorisation, completing the square and using the quadratic formula, including those in which the coefficient of the quadratic term is greater than 1 Derive relationships between different formulae that produce equal or related results Describe integer sequences; generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence) Generate sequences from patterns or practical contexts and describe the general term in simple cases Express simple functions in words, then using symbols; represent them in mappings Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise straight-line graphs parallel to the x-axis or y-axis Plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphs Generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculator Use linear expressions to describe the term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated Express simple functions algebraically and represent them in mappings or on a spreadsheet Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y= mx + c correspond to straight-line graphs Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs Generate terms of a sequence using term-to-term and position-to-term rules, on paper and using ICT Generate sequences from practical contexts and write and justify an expression to describe the thn term of an arithmetic sequence Find the inverse of a linear function Generate points and plot graphs of linear functions, where y is given implicitly in terms of x (e.g. ay + bx = 0, y + bx + c = 0 ), on paper and using ICT; find the gradient of lines given by equations of the form , given values for m and c Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, e.g. time series graphs Use ICT to explore the graphical representation of algebraic equations and interpret how properties of the graph are related to features of the equation, e.g. parallel and perpendicular lines Interpret the meaning of various points and sections of straight-line graphs, including intercepts and intersection, e.g. solving simultaneous linear equations Find the next term and the nth term of quadratic sequences and explore their properties; deduce properties of the sequences of triangular and square numbers from spatial patterns Plot the graph of the inverse of a linear function Understand that equations in the form y=mx+c represent a straight line and that m is the gradient and c is the value of the y -intercept; investigate the gradients of parallel lines and lines perpendicular to these lines Explore simple properties of quadratic functions; plot graphs of simple quadratic and cubic functions, e.g. y=x^2, y=3x^2 + 4, y=x^3 Understand that the point of intersection of two different lines in the same two variables that simultaneously describe a real situation is the solution to the simultaneous equations represented by the lines Identify the equations of straight-line graphs that are parallel; find the gradient and equation of a straight-line graph that is perpendicular to a given line Plot graphs of more complex quadratic and cubic functions; estimate values at specific points, including maxima and minima Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function Identify and sketch graphs of linear and simple quadratic and cubic functions; understand the effect on the graph of addition of (or multiplication by) a constant Know and understand that the intersection points of the graphs of a linear and quadratic function are the approximate solutions to the corresponding simultaneous equations Construct the graphs of simple loci, including the circle x^2 + y^2 = r^2 ; find graphically the intersection points of a given straight line with this circle and know this represents the solution to the corresponding two simultaneous equations Plot and recognise the characteristic shapes of graphs of simple cubic functions (e.g. y = x^3 ), reciprocal functions (e.g. y= 1/x, x≠0 ), exponential functions ( y=kx= for integer values of x and simple positive values of k) and trigonometric functions, on paper and using ICT Apply to the graph y=f(x) the transformations y=f(x)+a, y=f(ax), y=f(x+a) and y=af(x) for linear, quadratic, sine and cosine functions Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles Identify and use angle, side and symmetry properties of triangles and quadrilaterals; explore geometrical problems involving these properties, explaining reasoning orally, using step-by-step deduction supported by diagrams Use 2-D representations to visualise 3-D shapes and deduce some of their properties Identify alternate angles and corresponding angles; understand a proof that: (i) the angle sum of a triangle is 180° and of a quadrilateral is 360°, (ii) the exterior angle of a triangle is equal to the sum of the two interior opposite angles Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties Know that if two 2-D shapes are congruent, corresponding sides and angles are equal Visualise 3-D shapes from their nets; use geometric properties of cuboids and shapes made from cuboids; use simple plans and elevations Distinguish between conventions, definitions and derived properties Explain how to find, calculate and use: (i) the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; (ii) the interior and exterior angles of regular polygons Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text Understand congruence and explore similarity Investigate Pythagoras’ theorem, using a variety of media, through its historical and cultural roots including ‘picture’ proofs Distinguish between practical demonstration and proof in a geometrical context Solve multi-step problems using properties of angles, of parallel lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text Know that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio; understand from this that any two circles and any two squares are mathematically similar while in general any two rectangles are not Understand and apply Pythagoras’ theorem when solving 7 problems in 2-D and simple problems in 3-D Understand and use trigonometric relationships in right- angled triangles, and use these to solve problems, including 8 those involving bearings Show step-by-step deduction in solving more complex geometrical problems Prove and use the facts that: (I) the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference; (ii) the angle subtended at the circumference by a semicircle is a right angle; (iii) angles in the same segment are equal; (iv) opposite angles on a cyclic quadrilateral sum to 180° Understand and use Pythagoras’ theorem to solve 3-D EP problems Use trigonometric relationships in right-angled triangles to solve 3-D problems, including finding the angles between a EP line and a plane Understand the necessary and sufficient conditions under which generalisations, inferences and solutions to geometrical problems remain valid Prove and use the alternate segment theorem Prove the congruence of triangles and verify standard ruler and compass constructions using formal arguments Calculate the area of a triangle using the formula 1/2absinC 8 Draw, sketch and describe the graphs of trigonometric functions for angles of any size, including transformations involving scalings in either or both of the xand y directions Use the sine and cosine rules to solve 2-D and 3-D problems Understand and use the language and notation associated with reflections, translations and rotations Recognise and visualise the symmetries of a 2-D shape Transform 2-D shapes by: (i) reflecting in given mirror lines; (ii) rotating about a given point; (iii) translating Explore these transformations and symmetries using ICT Use conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometric information Identify all the symmetries of 2-D shapes Transform 2-D shapes by rotation, reflection and translation, on paper and using ICT Try out mathematical representations of simple combinations of these transformations Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive integer scale factor; explore enlargement using ICT Make scale drawings Find the midpoint of the line segment AB, given the coordinates of points A and B Identify reflection symmetry in 3-D shapes Recognise that translations, rotations and reflections preserve length and angle, and map objects on to congruent images Devise instructions for a computer to generate and transform shapes Explore and compare mathematical representations of combinations of translations, rotations and reflections of 2-D shapes, on paper and using ICT Enlarge 2-D shapes, given a centre of enlargement and a positive integer scale factor, on paper and using ICT; identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments; recognise that enlargements preserve angle but not length, and understand the implications of enlargement for perimeter Use and interpret maps and scale drawings in the context of mathematics and other subjects Use the coordinate grid to solve problems involving translations, rotations, reflections and enlargements Transform 2-D shapes by combinations of translations, rotations and reflections, on paper and using ICT; use congruence to show that translations, rotations and reflections preserve length and angle Use any point as the centre of rotation; measure the angle of rotation, using fractions of a turn or degrees; understand that translations are specified by a vector Enlarge 2-D shapes using positive, fractional and negative scale factors, on paper and using ICT; recognise the similarity of the resulting shapes; understand and use the effects of 7 enlargement on perimeter Find the points that divide a line in a given ratio, using the properties of similar triangles; calculate the length of AB, given the coordinates of points A and B Understand and use the effects of enlargement on areas and volumes of shapes and solids Understand and use vector notation to describe transformation of 2-D shapes by combinations of translations; calculate and represent graphically the sum of two vectors Calculate and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector; calculate the resultant of two vectors Understand and use the commutative and associative properties of vector addition Solve simple geometrical problems in 2-D using vectors Use a ruler and protractor to: (i) measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree; (ii) construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA) Use ICT to explore constructions Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism Use straight edge and compasses to construct: (i) the midpoint and perpendicular bisector of a line segment; (ii) the bisector of an angle; (iii) the perpendicular from a point to a line; (iv) the perpendicular from a point on a line; (v) a triangle, given three sides (SSS) Use ICT to explore these constructions Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle Use straight edge and compasses to construct triangles, given right angle, hypotenuse and side (RHS) Use ICT to explore constructions of triangles and other 2-D shapes Find the locus of a point that moves according to a simple 7 rule, both by reasoning and by using ICT Understand from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not Find the locus of a point that moves according to a more complex rule, both by reasoning and by using ICT Choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts; convert one metric unit to another, e.g. grams to kilograms; read and interpret scales on a range of measuring instruments Distinguish between and estimate the size of acute, obtuse and reflex angles Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles Calculate the surface area of cubes and cuboids Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of imperial measures in common use, such as miles, pounds (lb) and pints Use bearings to specify direction Derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids Solve problems involving measurements in a variety of contexts; convert between area measures (e.g. mm2 to cm2, cm2 to m2, and vice versa) and between volume measures (e.g. mm3 to cm3, cm3 to m3, and vice versa) Interpret and explore combining measures into rates of change in everyday contexts (e.g. km per hour, pence per metre); use compound measures to compare in real-life contexts (e.g. travel graphs and value for money), using ICT as appropriate Know and use the formulae for the circumference and area of a circle Calculate the surface area and volume of right prisms Understand and use measures of speed (and other compound measures such as density or pressure); solve problems involving constant or average rates of change Solve problems involving lengths of circular arcs and areas of sectors Solve problems involving surface areas and volumes of cylinders Apply knowledge that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in either direction and use this to understand how errors can be compounded in calculations Solve problems involving surface areas and volumes of cylinders, pyramids, cones and spheres Understand and use the formulae for the length of a circular arc and area and perimeter of a sector Consider the dimensions of a formula and begin to recognise the difference between formulae for perimeter, area and volume in simple contexts Recognise limitations in the accuracy of measurements and judge the proportional effect on solutions Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones Understand the difference between formulae for perimeter, area and volume by considering dimensions Suggest possible answers, given a question that can be addressed by statistical methods Decide which data would be relevant to an enquiry and possible sources Plan how to collect and organise small sets of data from surveys and experiments: (i) design data collection sheets or questionnaires to use in a simple survey; (ii) construct 4 frequency tables for gathering discrete data, grouped where appropriate in equal class intervals Collect small sets of data from surveys and experiments, as planned 4 Discuss a problem that can be addressed by statistical methods and identify related questions to explore Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources; consider appropriate sample size Plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data and two- way tables for recording discrete data Collect data using a suitable method (e.g. observation, controlled experiment, data logging using ICT) suggest a problem to explore using statistical methods, frame questions and raise conjectures Discuss how different sets of data relate to the problem; identify possible primary or secondary sources; determine the sample size and most appropriate degree of accuracy Design a survey or experiment to capture the necessary data from one or more sources; design, trial and if necessary refine data collection sheets; construct tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals; design and use two-way tables Gather data from specified secondary sources, including printed tables and lists, and ICT-based sources, including the internet Independently devise a suitable plan for a substantial statistical project and justify the decisions made Identify possible sources of bias and plan how to minimise it Break a task down into an appropriate series of key statements (hypotheses), and decide upon the best methods for testing these gather data from primary and secondary sources, using ICT and other methods, including data from observation, controlled experiment, data logging, printed tables and lists Consider possible difficulties with planned approaches, including practical problems; adjust the project plan accordingly Deal with practical problems such as non-response or missing data Identify what extra information may be required to pursue a further line of enquiry Select and justify a sampling scheme and a method to investigate a population, including random and stratified sampling understand how different methods of sampling and different sample sizes may affect the reliability of conclusions drawn Calculate statistics for small sets of discrete data: (i) find the mode, median and range, and the modal class for grouped data; (ii) calculate the mean, including from a simple 5 frequency table, using a calculator for a larger number of items Construct, on paper and using ICT, graphs and diagrams to represent data, including: (i) bar-line graphs; (ii) frequency 5 diagrams for grouped discrete data; (iii) simple pie charts Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: (i) pie charts for categorical data; (ii) bar charts and frequency diagrams for discrete and continuous data; (iii) simple line graphs for time series; (iv) simple scatter graphs; (v) stem-and-leaf diagrams Calculate statistics and select those most appropriate to the problem or which address the questions posed Select, construct and modify, on paper and using ICT, suitable graphical representations to progress an enquiry and identify key features present in the data. Include: (i) line graphs for time series; (ii) scatter graphs to develop further understanding of correlation; Work through the entire handling data cycle to explore relationships within bivariate data, including applications to global citizenship, e.g. how fair is our society? Use an appropriate range of statistical methods to explore and summarise data; including estimating and finding the mean, median, quartiles and interquartile range for large data sets (by calculation or using a cumulative frequency diagram) Select, construct and modify, on paper and using ICT, suitable graphical representation to progress an enquiry and identify key features present in the data. Include: (i) cumulative frequency tables and diagrams; (ii) box plots; (iii) scatter graphs and lines of best fit (by eye) Use an appropriate range of statistical methods to explore and summarise data; including calculating an appropriate moving average for a time series Use a moving average to identify seasonality and trends in time series data, using them to make predictions Select, construct and modify, on paper and using ICT, suitable graphical representation to progress an enquiry, including histograms for grouped continuous data with equal class intervals Construct histograms, including those with unequal class EP intervals Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and 5 simple statistics for a single distribution Compare two simple distributions using the range and one of the mode, median or mean 5 Write a short report of a statistical enquiry, including appropriate diagrams, graphs and charts, using ICT as 5 appropriate; justify the choice of presentation Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored Compare two distributions using the range and one or more of the mode, median and mean Write about and discuss the results of a statistical enquiry using ICT as appropriate; justify Interpret graphs and diagrams and make inferences to support or cast doubt on initial conjectures; have a basic understanding of correlation Compare two or more distributions and make inferences, using the shape of the distributions and appropriate statistics Review interpretations and results of a statistical enquiry on the basis of discussions; communicate these interpretations and results using selected tables, graphs and diagrams Analyse data to find patterns and exceptions, and try to explain anomalies; include social statistics such as index numbers, time series and survey data Appreciate that correlation is a measure of the strength of association between two variables; distinguish between positive, negative and zero correlation, using lines of best fit; appreciate that zero correlation does not necessarily imply ‘no relationship’ but merely ‘no linear relationship’ Examine critically the results of a statistical enquiry; justify choice of statistical representations and relate summarised data to the questions being explored Interpret and use cumulative frequency diagrams to solve problems Recognise the limitations of any assumptions and the effects that varying the assumptions could have on the conclusions drawn from data analysis Compare two or more distributions and make inferences, using the shape of the distributions and measures of average and spread, including median and quartiles Use, interpret and compare histograms, including those with unequal class intervals Use vocabulary and ideas of probability, drawing on experience 4 Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts; identify all the possible mutually exclusive outcomes of a single event 5 Estimate probabilities by collecting data from a simple experiment and recording it in a frequency table; compare experimental and theoretical probabilities in simple contexts 5 Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable Know that if the probability of an event occurring is p, then the probability of it not occurring is 1-p ; use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events Compare estimated experimental probabilities with theoretical probabilities, recognising that: (i) if an experiment is repeated the outcome may, and usually will, be different; (ii) increasing the number of times an experiment is repeated generally leads to better estimates of probability; Interpret results involving uncertainty and prediction Identify all the mutually exclusive outcomes of an experiment; know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems Compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence Use tree diagrams to represent outcomes of two or more events and to calculate probabilities of combinations of independent events Know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A and B are independent events, the probability of A and B occurring is P(A) × P(B) Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments Use tree diagrams to represent outcomes of compound events, recognising when events are independent and distinguishing between contexts involving selection both with and without replacement Understand that if an experiment is repeated, the outcome may – and usually will – be different, and that increasing the sample size generally leads to better estimates of probability and population parameters Recognise when and how to work with probabilities associated with independent and mutually exclusive events when interpreting data Possible Possible Possible Teaching Hooks for Teaching Teaching Rich Tasks Resources Learning Resource Resource s s AAA Math AAA Math Decimal Places Rounding Decimal Places Powerpoint Powers of 10 Rounding Jigsaw Nearest Decimals 10th Powers of Ten Powers of 10 Website Video from IBM Universcale Additions Shortcuts Nrich Smallest AAA Math AAA Math Tutpup Powerpoint Number Challenge Add Subtract Factors and Prime Factors Powerpoint The Factor Game Multiples Minni Book Extracting Cube Finding Square Number Tables Powerpoint Roots Mentally Roots Manually Nrich Egyptian BBC Skillswise Introduction Fractions Clock Fractions Folding Fractions Cynthia Lanius How to Add Fractions Mini Book Fractions Nrich Sum of Nrich Fraction and QuickMath Nrich Percentages Powerpoint Percentages Percentage Percentag Mathland Problem Pelmanism es Election Nrich Percentages Pelmanism You Tube Golden AAA Math BBC Ratio Powerpoint Ratio Jigsaw Ratio Clip Ratio Skillswise Bodmas Podcast Nrich Reaching 50 Applications of Geometry Coordinat Properties of 2D shapes rotational Interactive free e Shape symmetry sample ATM challenge facts Triangle Constructions Explain why - Nrich Constructi ng triangles Cubic Conundrum Ominoes project Estimate angles game Census at school Crash Test - Bowland APP Year 7 Handling Questionnaire design ppt Census at school Data Pack Conduct a class survey on Using excel for IWB Teacher Led Resources data collection Mean, Crickweb' Nrich Litov's mean median Crickweb's Mean Machine Mr Reddy's poems s mean value theorem and mode runners song Mr Barton's http://www.subtangent.com Using Excel to Draw Statistical /maths/freqdiag1.php Charts Diagrams Census At School Missing label bar Kenny's Pouch Constructing charts - 3 starter Graphs activities Standards Unit Mr Using Kenny's Pouch Analysing CIMT Cricket Player Understanding Reddy's Excel to Statistics worksheet Ratings Mean, median, Cricket calculate mode and range problem averages GapMinder Beyond the Bar Chart Standards Unit S2 Probability vocabulary CIMT National Evaluating blockbusters Lottery Probability Statements Standards Standards Unit S3 Unit S1 Mr Barton's Nrich Experimenting Using Mr Barton's Coin races Ordering Probability Tools with probability Probability Probabiliti Computer es Games http://ww w.webmat Probability ESP Experiment Subtangent coins Nrich Experimenting hs.co.uk/ Teacher Led Resources and dice with probability worksheet bankindex .html Possible Possible Possible Hooks Hooks Teaching Teaching Teaching Rich Rich Rich for for Resource Resource Resource Tasks Tasks Tasks Learning Learning s s s AAA Math Rounding BBC YouTube Rounding Nearest Skillswise Clip Jigsaw 100th You Tube AAA Math AAA Math AAA Math Tom Multiply Divide Decimals Lehrer New Math Prime HCF LCM Number Podcast Factoriser Golden YouTube Ratio Ratio Ratio GCSE Words Jigsaw Investigati Question Jigsaw on Bodmas Year Podcast Game Rotation Symmetry symmetry game puzzles Tarsia jigsaw mymaths Play your cards right National Curriculum Attainment Targets Strand Level Mathematical Processes Level 4 and Applications Level 5 Level 6 Level 7 Level 8 Exceptional Performance Number and Algebra Level 4 Level 5 Level 6 Level 7 Level 8 Exceptional Performance Geometry and Measures Level 4 Level 5 Level 6 Level 7 Level 8 Exceptional Performance Handling Data Level 4 Level 5 Level 6 Level 7 Level 8 Exceptional Performance Attainment Targets Objectives Pupils develop their own strategies for solving problems and use these strategies both in working within mathematics and in applying mathematics to practical contexts. When solving problems, with or without a calculator, they check their results are reasonable by considering the context or the size of the numbers. They look for patterns and relationships, presenting information and results in a clear and organised way. They search for a solution by trying out ideas of their own. In order to explore mathematical situations, carry out tasks or tackle problems, pupils identify the mathematical aspects and obtain necessary information. They calculate accurately, using ICT where appropriate. They check their working and results, considering whether these are sensible. They show understanding of situations by describing them mathematically using symbols, words and diagrams. They draw simple conclusions of their own and explain their reasoning. Pupils carry out substantial tasks and solve quite complex problems by independently and systematically breaking them down into smaller, more manageable tasks. They interpret, discuss and synthesise information presented in a variety of mathematical forms, relating findings to the original context. Their written and spoken language explains and informs their use of diagrams. They begin to give mathematical justifications, making connections between the current situation and situations they have encountered before. Starting from problems or contexts that have been presented to them, pupils explore the effects of varying values and look for invariance in models and representations, working with and without ICT. They progressively refine or extend the mathematics used, giving reasons for their choice of mathematical presentation and explaining features they have selected. They justify their generalisations, arguments or solutions, looking for equivalence to different problems with similar structures. They appreciate the difference between mathematical explanation and experimental evidence. Pupils develop and follow alternative approaches. They compare and evaluate representations of a situation, introducing and using a range of mathematical techniques. They reflect on their own lines of enquiry when exploring mathematical tasks. They communicate mathematical or statistical meaning to different audiences through precise and consistent use of symbols that is sustained throughout the work. They examine generalisations or solutions reached in an activity and make further progress in the activity as a result. They comment constructively on the reasoning and logic, the process employed and the results obtained. Pupils critically examine the strategies adopted when investigating within mathematics itself or when using mathematics to analyse tasks. They explain why different strategies were used, considering the elegance and efficiency of alternative lines of enquiry or procedures. They apply the mathematics they know in a wide range of familiar and unfamiliar contexts. They use mathematical language and symbols effectively in presenting a convincing, reasoned argument. Their reports include mathematical justifications, distinguishing between evidence and proof and explaining their solutions to problems involving a number of features or variables. Pupils use their understanding of place value to multiply and divide whole numbers by 10 or 100. When solving number problems, they use a range of mental methods of computation with the four operations, including mental recall of multiplication facts up to 10 x 10 and quick derivation of corresponding division facts. They use efficient written methods of addition and subtraction and of short multiplication and division. They recognise approximate proportions of a whole and use simple fractions and percentages to describe these. They begin to use simple formulae expressed in words. Pupils use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers in context. They use all four operations with decimals to two places. They solve simple problems involving ratio and direct proportion. They calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. They construct, express in symbolic form and use simple formulae involving one or two operations. They use brackets appropriately. They use and interpret coordinates in all four quadrants. Pupils order and approximate decimals when solving numerical problems and equations, using trial and improvement methods. They evaluate one number as a fraction or percentage of another. They understand and use the equivalences between fractions, decimals and percentages, and calculate using ratios in appropriate situations. They add and subtract fractions by writing them with a common denominator. They find and describe in words the rule for the next term or nth term of a sequence where the rule is linear. They formulate and solve linear equations with whole-number coefficients. They represent mappings expressed algebraically, and use Cartesian coordinates for graphical representation interpreting general features. When making estimates, pupils round to one significant figure and multiply and divide mentally. They understand the effects of multiplying and dividing by numbers between 0 and 1. They solve numerical problems involving multiplication and division with numbers of any size, using a calculator efficiently and appropriately. They understand and use proportional changes, calculating the result of any proportional change using only multiplicative methods. They find and describe in symbols the next term or nth term of a sequence where the rule is quadratic. They use algebraic and graphical methods to solve simultaneous linear equations in two variables. Pupils solve problems that involve calculating with powers, roots and numbers expressed in standard form. They choose to use fractions or percentages to solve problems involving repeated proportional changes or the calculation of the original quantity given the result of a proportional change. They evaluate algebraic formulae or calculate one variable, given the others, substituting fractions, decimals and negative numbers. They manipulate algebraic formulae, equations and expressions, finding common factors and multiplying two linear expressions. They solve inequalities in two variables. They sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions, and graphs that model real situations. Pupils understand and use rational and irrational numbers. They determine the bounds of intervals. They understand and use direct and inverse proportion. In simplifying algebraic expressions, they use rules of indices for negative and fractional values. In finding formulae that approximately connect data, they express general laws in symbolic form. They solve simultaneous equations in two variables where one equation is linear and the other is quadratic. They solve problems using intersections and gradients of graphs. Pupils make 3D mathematical models by linking given faces or edges, and draw common 2D shapes in different orientations on grids. They reflect simple shapes in a mirror line. They choose and use appropriate units and tools, interpreting, with appropriate accuracy, numbers on a range of measuring instruments. They find perimeters of simple shapes and find areas by counting squares. When constructing models and drawing or using shapes, pupils measure and draw angles to the nearest degree and use language associated with angles. They know the angle sum of a triangle and that of angles at a point. They identify all the symmetries of 2D shapes. They convert one metric unit to another. They make sensible estimates of a range of measures in relation to everyday situations. They understand and use the formula for the area of a rectangle. Pupils recognise and use common 2D representations of 3D objects. They know and use the properties of quadrilaterals. They solve problems using angle and symmetry, properties of polygons and angle properties of intersecting and parallel lines, and explain these properties. They devise instructions for a computer to generate and transform shapes and paths. They understand and use appropriate formulae for finding circumferences and areas of circles, areas of plane rectilinear figures and volumes of cuboids when solving problems. Pupils understand and apply Pythagoras’ theorem when solving problems in two dimensions. They calculate lengths, areas and volumes in plane shapes and right prisms. They enlarge shapes by a fractional scale factor, and appreciate the similarity of the resulting shapes. They determine the locus of an object moving according to a rule. They appreciate the imprecision of measurement and recognise that a measurement given to the nearest whole number may be inaccurate by up to one half in either direction. They understand and use compound measures, such as speed. Pupils understand and use congruence and mathematical similarity. They use sine, cosine and tangent in right-angled triangles when solving problems in two dimensions. Pupils sketch the graphs of sine, cosine and tangent functions for any angle, and generate and interpret graphs based on these functions. They use sine, cosine and tangent of angles of any size, and Pythagoras’ theorem when solving problems in two and three dimensions. They construct formal geometric proofs. They calculate lengths of circular arcs and areas of sectors, and calculate the surface area of cylinders and volumes of cones and spheres. They appreciate the continuous nature of scales that are used to make measurements. Pupils collect discrete data and record them using a frequency table. They understand and use the mode and range to describe sets of data. They group data in equal class intervals where appropriate, represent collected data in frequency diagrams and interpret such diagrams. They construct and interpret simple line graphs. Pupils understand and use the mean of discrete data. They compare two simple distributions using the range and one of the mode, median or mean. They interpret graphs and diagrams, including pie charts, and draw conclusions. They understand and use the probability scale from 0 to 1. They find and justify probabilities and approximations to these by selecting and using methods based on equally likely outcomes and experimental evidence, as appropriate. They understand that different outcomes may result from repeating an experiment. Pupils collect and record continuous data, choosing appropriate equal class intervals over a sensible range to create frequency tables. They construct and interpret frequency diagrams. They construct pie charts. They draw conclusions from scatter diagrams, and have a basic understanding of correlation. When dealing with a combination of two experiments, they identify all the outcomes. When solving problems, they use their knowledge that the total probability of all the mutually exclusive outcomes of an experiment is 1. Pupils specify hypotheses and test them by designing and using appropriate methods that take account of variability or bias. They determine the modal class and estimate the mean, median and range of sets of grouped data, selecting the statistic most appropriate to their line of enquiry. They use measures of average and range, with associated frequency polygons, as appropriate, to compare distributions and make inferences. They understand relative frequency as an estimate of probability and use this to compare outcomes of experiments. Pupils interpret and construct cumulative frequency tables and diagrams. They estimate the median and interquartile range and use these to compare distributions and make inferences. They understand how to calculate the probability of a compound event and use this in solving problems. Pupils interpret and construct histograms. They understand how different methods of sampling and different sample sizes may affect the reliability of conclusions drawn. They select and justify a sample and method to investigate a population. They recognise when and how to work with probabilities associated with independent, mutually exclusive events.

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