ࡱ>  acXYZ[\]^_`b X&jbjb 7mm>((((xxxvvv8:W2v"LF(,Rm^$xn"nn$((nB(8xd((((n`x& Wv2'0WxrDrNRICH  HYPERLINK "http://www.nrich.maths.org" www.nrich.maths.org problems linked to the Framework for Secondary Mathematics N.B. This is work in progress - last updated 20-08-2012. Please email any comments to HYPERLINK "mailto:enquiries.nrich@maths.org"enquiries.nrich@maths.org Ticked items (() identify problems that have detailed Teachers Notes suggesting how they can be integrated into lessons. Highlighted problems are ideal for using at the start of a topic. Asterisked problems (*) appear in two places. Year 7& !!!& Year 11ExtensionNumbers and the number systemPlace value, ordering and roundingunderstand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100, 1000, and explain the effect  HYPERLINK "http://nrich.maths.org/6606" Dicey Operations* (  HYPERLINK "http://nrich.maths.org/7208" Always a Multiple?* (read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01extend 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 10express numbers in standard index form, both in conventional notation and on a calculator display HYPERLINK "http://nrich.maths.org/6349" A Question of Scale (compare and order decimals in different contexts; know that when comparing measurements the units must be the same  HYPERLINK "http://nrich.maths.org/6605" Nice and Nasty (order decimals convert between ordinary and standard index form representationsuse standard index form to make sensible estimates for calculations involving multiplication and/or divisionround positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal placesuse rounding to make estimates and to give solutions to problems to an appropriate degree of accuracyround to a given number of significant figures; use significant figures to approximate answers when multiplying or dividing large numbersunderstand how errors can be compounded in calculations understand upper and lower boundsIntegers powers and rootsunderstand negative numbers as positions on a number line; order, add and subtract integers in context  HYPERLINK "http://nrich.maths.org/7821" Magic Letters (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5865" First Connect Three (add, subtract, multiply and divide integers  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5864" Playing Connect Three (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5958" Weights (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5868" Consecutive Negative Numbers( Article:  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5947" Adding & Subtracting Negative Numbers  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5798" Difference Sudokurecognise 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  HYPERLINK "http://nrich.maths.org/7520" Sieve of Eratosthenes (  HYPERLINK "http://nrich.maths.org/6650" How much can we spend? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=559&part=index&refpage=monthindex.php" Dozens (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5468&part=index&refpage=monthindex.php" Factors and Multiples Game (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5448" Factors and Multiples Puzzle( Article:  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1308" Divisibility Testsuse multiples, factors, common factors, highest common factors, lowest common multiples and primes; find the prime factor decomposition of a number, e.g. 8000 = 26 53  HYPERLINK "http://nrich.maths.org/6966" Counting Cogs (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2669&refpage=titlesearch.php" Stars (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6401" Power Mad! (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=480" 14 Divisors (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1866&part=index&refpage=monthindex.php" Take Three from Five (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=602" Differences (use the prime factor decomposition of a number  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4903&part=index&refpage=monthindex.php" Product Sudoku (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=740&part=index&refpage=monthindex.php" Funny Factorisation HYPERLINK "http://nrich.maths.org/7547" Filling the Gaps (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=796&part=index&refpage=monthindex.php" American Billions ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=582" Expensesrecognise the first few triangular numbers; recognise the squares of numbers to at least 12 12 and the corresponding rootsuse squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1163" Sissa's Rewarduse ICT to estimate square roots and cube roots HYPERLINK "http://nrich.maths.org/7282" Generating Triples (use index notation for integer powers; know and use the index laws for multiplication and division of positive integer powersuse index notation with negative and fractional powers, recognising that the index laws can be applied to these as well 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  HYPERLINK "http://nrich.maths.org/6448" Power Countdown (understand and use rational and irrational numbers know that n = "n and nS!= 3"n for any positive number n  Fractions, decimals, percentages, ratio and proportionexpress 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 recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals  HYPERLINK "http://nrich.maths.org/2086" Farey Sequences (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5617" Round and Round and Round understand the equivalence of simple algebraic fractions; know that a recurring decimal is an exact fractiondistinguish between fractions with denominators that have only prime factors 2 or 5 (terminating decimals), and other fractions (recurring decimals)  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1832" Tiny nines ( use an algebraic method to convert a recurring decimal to a fraction  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1853&part=index&refpage=monthindex.php" Repetitiously (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5467&part=index&refpage=monthindex.php" Fractions Jigsaw (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2312&part=index&refpage=monthindex.php" Peaches Today, Peaches Tomorrow... (add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction  HYPERLINK "http://nrich.maths.org/6700" Diminishing Returns ( use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2382&part=index&refpage=monthindex.php" Ben's Game (  HYPERLINK "http://nrich.maths.org/708" Fair Shares? (understand and apply efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5776" Twisting and Turning  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5777" More Twisting and Turningunderstand percentage as the number of parts per 100; calculate simple percentages and use percentages to compare simple proportions  HYPERLINK "http://nrich.maths.org/public/viewer.php?time=1202216842&obj_id=1249&part=index" Matching Fractions Decimals Percentages (interpret percentage as the operator so many hundredths of and express one given number as a percentage of another; calculate percentages and find the outcome of a given percentage increase or decreaserecognise when fractions or percentages are needed to compare proportions; solve problems involving percentage changescalculate an original amount when given the transformed amount after a percentage change; use calculators for reverse percentage calculations by doing an appropriate divisionrecognise the equivalence of percentages, fractions and decimalsuse the equivalence of fractions, decimals and percentages to compare proportionsunderstand 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  HYPERLINK "http://nrich.maths.org/6870" Mixing Lemonade (apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple problems involving ratio and direct proportionuse 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4793&part=index&refpage=monthindex.php" Mixing Paints  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4794&part=index&refpage=viewer.php" Mixing More Paintsunderstand and use proportionality and calculate the result of any proportional change using multiplicative methods  HYPERLINK "http://nrich.maths.org/6882" Ratios and Dilutions (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5611&refpage=titlesearch.php" A Chance to Win? calculate an unknown quantity from quantities that vary in direct proportion using algebraic methods where appropriate  HYPERLINK "http://nrich.maths.org/309" Areas and Ratios (understand and use direct and inverse proportion; solve problems involving inverse proportion (including inverse squares) using algebraic methods  HYPERLINK "http://nrich.maths.org/7586" Triathlon and Fitness (Number operationsunderstand and use the rules of arithmetic and inverse operations in the context of positive integers and decimals  HYPERLINK "http://nrich.maths.org/7405" What Numbers Can We Make?* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=31" Consecutive Numbers (  HYPERLINK "http://nrich.maths.org/746" Where Can We Visit? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2661&refpage=titlesearch.php" Consecutive Seven (understand and use the rules of arithmetic and inverse operations in the context of integers and fractions  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6540" Keep it Simple (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1173" Egyptian Fractions (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6541" The Greedy Algorithm (understand the effects of multiplying and dividing by numbers between 0 and 1; consolidate use of the rules of arithmetic and inverse operationsrecognise 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 defineduse a multiplier raised to a power to represent and solve problems involving repeated proportional change, e.g. compound interest  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5893" The Legacy  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5636" Dating Made Easieruse the order of operations, including brackets  HYPERLINK "http://nrich.maths.org/1013" Make 100 (use the order of operations, including brackets, with more complex calculationsunderstand the order of precedence of operations, including powers Mental calculation methodsrecall number facts, including positive integer complements to 100 and multiplication facts to 10 10, and quickly derive associated division facts  HYPERLINK "http://nrich.maths.org/7382" Missing Multipliers (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6499" Countdown  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1783" Remainders (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6402&part=" The Remainders Gamerecall 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 8strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple problems mentally  HYPERLINK "http://nrich.maths.org/786" Number Daisy  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1272" Got It (strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, cubes and cube roots; solve problems mentallyuse known facts to derive unknown facts; extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots; solve problems mentally  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1864" Cinema Problem (use surds and  in exact calculations, without a calculator; rationalise a denominator such as 1/"3 = "3/3  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=901" The Root of the Problem make and justify estimates and approximations of calculationsmake and justify estimates and approximations of calculations  HYPERLINK "http://nrich.maths.org/7500" Place Your Orders* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6046" Thousands and Millions* ( make and justify estimates and approximations of calculationsmake and justify estimates and approximations of calculations by rounding numbers to one significant figure and multiplying or dividing mentallyWritten Calculation Methodsuse efficient written methods to add and subtract whole numbers and decimals with up to two places  HYPERLINK "http://nrich.maths.org/6606" Dicey Operations* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=781&refpage=titlesearch.php" Two and Two ( use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal placesmultiply 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  HYPERLINK "http://nrich.maths.org/5612" Method in Multiplying Madness? (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=564" Legs Eleven (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1785" Largest Product ( 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2032&refpage=titlesearch.php" How Many Miles to Go? (Calculator methodscarry out calculations with more than one step using brackets and the memory; use the square root and sign change keyscarry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memoryuse 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,  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 functionsuse calculators to explore exponential growth and decay, using a multiplier and the power keyuse calculators, or written methods, to calculate the upper and lower bounds of calculations in a range of contexts, particularly when working with measurementsenter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures)  HYPERLINK "http://nrich.maths.org/6651" Going Round in Circles (enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time)use standard index form, expressed in conventional notation and on a calculator display; know how to enter numbers in standard formcalculate with standard index form, using a calculator as appropriate Checking resultscheck results by considering whether they are of the right order of magnitude and by working problems backwards  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=530" Rule of Threeselect from a range of checking methods, including estimating in context and using inverse operationscheck results using appropriate methodscheck results using appropriate methodscheck results using appropriate methodscheck results using appropriate methodsAlgebraEquations, formulae, expressions and identitiesuse letter symbols to represent unknown numbers or variables; know the meanings of the words term, expression and equation  HYPERLINK "http://nrich.maths.org/2289" Your Number Is ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2281"Number Pyramids (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6261" Crossed Ends ( recognise that letter symbols play different roles in equations, formulae and functions; know the meanings of the words formula and functiondistinguish the different roles played by letter symbols in equations, identities, formulae and functionsunderstand that algebraic operations follow the rules of arithmetic understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers use index notation for integer powers and simple instances of the index lawsknow and use the index laws in generalised form for multiplication and division of integer powerssimplify linear algebraic expressions by collecting like terms; multiply a single term over a bracket (integer coefficients)  HYPERLINK "http://nrich.maths.org/7208" Always a Multiple?* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2282&refpage=titlesearch.php" More Number Pyramids (simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket  HYPERLINK "http://nrich.maths.org/7283" Perimeter Expressions (  HYPERLINK "http://nrich.maths.org/2129" Special Numbers (simplify or transform algebraic expressions by taking out single-term common factors; add simple algebraic fractions  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4716&refpage=titlesearch.php" Harmonic Triangle (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 a2"b2=(a+b)(a"b)  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2278&refpage=titlesearch.php" Pair Products (  HYPERLINK "http://nrich.maths.org/742" What's Possible? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=658" Plus Minus (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2821&refpage=titlesearch.php" Multiplication Square factorise quadratic expressions, including the difference of two squares, e.g. x2"9=(x+3)(x"3) and cancel common factors in rational expressions, e.g. 2(x+1)2/(x+1)  HYPERLINK "http://nrich.maths.org/7490" Factorising with Multilink (  HYPERLINK "http://nrich.maths.org/7452" Finding Factors (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=541" Odd Squares (  HYPERLINK "http://nrich.maths.org/745" Why 24? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=517" 2-digit square (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2034" Always Perfect  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2286" Perfectly Square simplify simple algebraic fractions to produce linear expressions; use factorisation to simplify compound algebraic fractionsconstruct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations)  HYPERLINK "http://nrich.maths.org/7216" Your Number Was (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)  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1170" Think of Two Numbers construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution)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  HYPERLINK "http://nrich.maths.org/708" Fair Shares* (solve equations involving algebraic fractions with compound expressions as the numerators and/or denominatorsuse graphs and set up equations to solve simple problems involving direct proportionuse algebraic methods to solve problems involving direct proportion; relate algebraic solutions to graphs of the equations; use ICT as appropriateIntroductory work on simultaneous equations  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1053&refpage=titlesearch.php" What's it Worth? ( 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 no solution or an infinite number of solutions  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2670&part=index&refpage=monthindex.php" Arithmagons ( explore 'optimum' methods of solving simultaneous equations in different forms  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=849" CD Heaven (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5674" Matchless  HYPERLINK "http://nrich.maths.org/7447" Multiplication Arithmagons (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 quadratic in the other or of the form x2+y2=r2solve linear inequalities in one variable; represent the solution set on a number line  HYPERLINK "http://nrich.maths.org/7342" Which Is Cheaper? (solve linear inequalities in one and two variables; find and represent the solution set  HYPERLINK "http://nrich.maths.org/7344" Which Is Bigger? (use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x2 + x = 20solve quadratic equations by factorisation  HYPERLINK "http://nrich.maths.org/631" How Old Am I? (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=271" Golden Thoughts (explore ways of constructing models of real-life situations by drawing graphs and constructing algebraic equations and inequalities use simple formulae from mathematics and other subjects; substitute positive integers into linear expressions and formulae and, in simple cases, derive a formulause 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. 3x2 + 4 or 2x3; derive simple formulae use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5608" Temperature (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 r given that A=r2  HYPERLINK "http://nrich.maths.org/7366" Training Schedule (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1860&part=index&refpage=monthindex.php" Terminologyderive and use more complex formulae; change the subject of a formula, including cases where the subject occurs twicederive relationships between different formulae that produce equal or related resultsSequences, functions and graphsdescribe 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)  HYPERLINK "http://nrich.maths.org/7529" Odds, Evens and More Evens(  HYPERLINK "http://nrich.maths.org/6713" Shifting Times Tables (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5525&refpage=titlesearch.php" Triangle Numbers (generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculator  HYPERLINK "http://nrich.maths.org/7024" Charlies Delightful Machine (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2292&refpage=titlesearch.php" Coordinate Patterns* ( generate terms of a sequence using term-to-term and position-to-term rules, on paper and using ICT  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1019&part=index&refpage=monthindex.php" 1 Step 2 Step (  HYPERLINK "http://nrich.maths.org/6690" Tower of Hanoi ( HYPERLINK "http://nrich.maths.org/7016" A Little Light Thinking (generate sequences from patterns or practical contexts and describe the general term in simple cases HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=507&refpage=titlesearch.php"Summing Consecutive Numbers (  HYPERLINK "http://nrich.maths.org/7405" What Numbers Can We Make?* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2275&refpage=titlesearch.php" Picturing Square Numbers (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4835&refpage=titlesearch.php" Squares in Rectangles (use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=8111"Seven Squares ( NRICH Article:  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5531" Spaces for Explorationgenerate sequences from practical contexts and write and justify an expression to describe the nth term of an arithmetic sequence  HYPERLINK "http://nrich.maths.org/8280" What Numbers Can We Make Now? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2274&refpage=titlesearch.php" Picturing Triangle Numbers (  HYPERLINK "http://nrich.maths.org/6710" Slick Summing (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6390" Elevenses (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=308" Days and Dates (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  HYPERLINK "http://nrich.maths.org/900" Attractive Tablecloths (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2322&refpage=titlesearch.php" Painted Cube* (  HYPERLINK "http://nrich.maths.org/6703" Mystic Rose (  HYPERLINK "http://nrich.maths.org/7760" Steel Cables ( HYPERLINK "http://nrich.maths.org/6903" Partially Painted Cube (  HYPERLINK "http://nrich.maths.org/8096" Double Trouble (  HYPERLINK "http://nrich.maths.org/325" Picture Story ( express simple functions in words, then using symbols; represent them in mappings express simple functions algebraically and represent them in mappings or on a spreadsheet  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1867&refpage=titlesearch.php" Pick's Theorem* (find the inverse of a linear functionplot the graph of the inverse of a linear functiongenerate 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  HYPERLINK "http://nrich.maths.org/6951" Exploring Simple Mappings (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6603" How Steep Is the Slope? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5609" Parallel Lines ( 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 y = mx + c, given values for m and c  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5725" Diamond Collector (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6539" Translating Lines (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6471&part=" Reflecting Lines (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6461" At Right Angles (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5610" Perpendicular Lines (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6544&part=" Surprising Transformations  ( 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=494" Doesnt Add Up (plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphsconstruct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distancetime graphs  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=985&submit=submit" Walk and Ride (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2305&refpage=titlesearch.php" Buses (construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, e.g. time series graphs  HYPERLINK "http://nrich.maths.org/7419" Fill Me Up (  HYPERLINK "http://nrich.maths.org/6424" Maths Filler (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4808&refpage=titlesearch.php" How Far Does it Move? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4809&part=index&refpage=viewer.php" Speeding Up, Slowing Down (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4810&part=index&refpage=viewer.php" Up and Across  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4851" Steady Free Fall 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5871" Negatively Triangular find approximate solutions of a quadratic equation from the graph of the corresponding quadratic functionknow and understand that the intersection points of the graphs of a linear and quadratic function are the approximate solutions to the corresponding simultaneous equationsconstruct the graphs of simple loci, including the circle x2+y2=r2; find graphically the intersection points of a given straight line with this circle and know this represents the solution to the corresponding two simultaneous equationsexplore simple properties of quadratic functions; plot graphs of simple quadratic and cubic functions, e.g. y=x2, y=3x2+4, y=x3  HYPERLINK "http://nrich.maths.org/6952" Exploring Quadratic Mappings (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5872" Minus One Two Three plot graphs of more complex quadratic and cubic functions; estimate values at specific points, including maxima and minimaplot and recognise the characteristic shapes of graphs of simple cubic functions (e.g. y = x3), 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  HYPERLINK "http://nrich.maths.org/7502" What s That Graph? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6506" Back Fitter (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 constantapply 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  HYPERLINK "http://nrich.maths.org/773" Parabolic Patterns  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=802" Cubics  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6481" Tangled Trig 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 equationsGeometry and MeasuresGeometrical reasoninguse correctly the vocabulary, notation and labelling conventions for lines, angles and shapes distinguish between conventions, definitions and derived propertiesdistinguish between practical demonstration and proof in a geometrical context  HYPERLINK "http://nrich.maths.org/6536" Circles in Quadrilaterals (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4890&refpage=titlesearch.php" Areas of Parallelograms ( show step-by-step deduction in solving more complex geometrical problems HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2287"Squirty (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6323" Partly Circles ( understand the necessary and sufficient conditions under which generalisations, inferences and solutions to geometrical problems remain valid identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite anglesidentify alternate angles and corresponding angles; understand a proof that: the angle sum of a triangle is 180and of a quadrilateral is 360 the exterior angle of a triangle is equal to the sum of the two interior opposite anglesexplain how to find, calculate and use: the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons the interior and exterior angles of regular polygons  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4832&part=index&refpage=monthindex.php" Semi-regular Tessellations (  HYPERLINK "http://nrich.maths.org/7306" Which Solids Can We Make? (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 circleknow 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=548" Compare Areas (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2163" Circle-inprove and use the facts that: the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference the angle subtended at the circumference by a semicircle is a right angle angles in the same segment are equal opposite angles in a cyclic quadrilateral sum to 180  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2844&refpage=titlesearch.php" Triangles in Circles (  HYPERLINK "http://nrich.maths.org/6624" Cyclic Quadrilaterals (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2845" Subtended Angles* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2847" Right Angles* ( prove and use the alternate segment theoremidentify 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2927&refpage=titlesearch.php" Property Chart (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2925&part=index&refpage=monthindex.php" Shapely Pairs (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2924&refpage=titlesearch.php" Quadrilaterals Game (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2526&refpage=titlesearch.php" Square It (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6280" Eight Hidden Squares (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2667&refpage=titlesearch.php" Square Coordinates (  HYPERLINK "http://nrich.maths.org/7381" Opposite Vertices (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2844&refpage=titlesearch.php" Triangles in Circles (  HYPERLINK "http://nrich.maths.org/6624" Cyclic Quadrilaterals (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2845&part=index&refpage=monthindex.php" Subtended Angles* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2847&part=index&refpage=monthindex.php" Right Angles* (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  HYPERLINK "http://nrich.maths.org/8301" Kite in a Square ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6355"Making Sixty (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=665" Sitting Pretty (know that if two 2-D shapes are congruent, corresponding sides and angles are equalunderstand congruence and explore similarityknow 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4960" Trapezium Four (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5635" Nicely similar  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=510" Two ladders  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=700" Napkin (prove the congruence of triangles and verify standard ruler and compass constructions using formal arguments  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=483" Triangle Mid Points (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=726" Angle trisection( investigate Pythagoras theorem, using a variety of media, through its historical and cultural roots, including picture proofs  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2293" Tilted Squares ( HYPERLINK "http://nrich.maths.org/6553" Pythagoras Proofs (use 2-D representations to visualise 3-D shapes and deduce some of their properties visualise 3-D shapes from their nets; use geometric properties of cuboids and shapes made from cuboids; use simple plans and elevationsvisualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elevations  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=768&part=index&refpage=monthindex.php" Nine Colours (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=895" Marbles in a Box (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=573" Tet-trouble (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1157&refpage=titlesearch.php" Triangles to Tetrahedra (understand and apply Pythagoras' theorem when solving problems in 2-D and simple problems in 3-D  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2160&part=index&refpage=monthindex.php" Inscribed in a Circle  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1863&part=index&refpage=monthindex.php" Semi-detached  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=289" Ladder and Cube  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2658" Where to Land  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5689" Walking around a cube understand and use Pythagoras' theorem to solve 3-D problems  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2365" The Spider and the Fly  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=360" Qqq..cubedunderstand and use trigonometric relationships in right-angled triangles, and use these to solve problems, including those involving bearings  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5615" Where is the dot?  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5601" Trigonometric Protractor (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4798" Orbiting billiard balls use trigonometric relationships in right-angled triangles to solve 3-D problems, including finding the angles between a line and a plane  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2357" Far horizon draw, sketch and describe the graphs of trigonometric functions for angles of any size, including transformations involving scalings in either or both of the x and y directionsuse the sine and cosine rules to solve 2-D and 3-D problems HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1954"Hexy-metry ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1955"Three by One (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2690" Cubestick  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=312" Bendy Quad( calculate the area of a triangle using the formula absinCTransformations and co-ordinatesunderstand and use the language and notation associated with reflections, translations and rotationsrecognise and visualise the symmetries of a 2-D shape  HYPERLINK "http://nrich.maths.org/1868" Shady Symmetry (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1840" Reflecting Squarely ( identify all the symmetries of 2-D shapesidentify reflection symmetry in 3-D shapestransform 2-D shapes by: reflecting in given mirror lines rotating about a given point translating  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5458&refpage=titlesearch.php" Mirror, Mirror (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5459&part=index&refpage=viewer.php" ...on the Wall (  HYPERLINK "http://nrich.maths.org/6987" Attractive Rotations ( transform 2-D shapes by rotation, reflection and translation, on paper and using ICT  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5457&part=index&refpage=monthindex.php" Transformation Game (recognise that translations, rotations and reflections preserve length and angle, and map objects on to congruent imagestransform 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 angleexplore these transformations and symmetries using ICTtry out mathematical representations of simple combinations of these transformations explore and compare mathematical representations of combinations of translations, rotations and reflections of 2-D shapes, on paper and using ICTuse 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 vectorunderstand and use vector notation to describe transformation of 2-D shapes by combinations of translations; calculate and represent graphically the sum of two vectors  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5812" Spotting the Loophole  HYPERLINK "http://nrich.maths.org/7453" Vector Journeys (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 vectorsdevise instructions for a computer to generate and transform shapes understand and use the commutative and associative properties of vector additionsolve simple geometrical problems in 2-D using vectorsunderstand 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 ICTenlarge 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 perimeterenlarge 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 enlargement on perimeter  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5461&part=index&refpage=viewer.php" Who Is the Fairest of Them All? (understand and use the effects of enlargement on areas and volumes of shapes and solids  HYPERLINK "http://nrich.maths.org/6923" Growing Rectangles (  HYPERLINK "http://nrich.maths.org/7385" Fit for Photocopying (make scale drawings use and interpret maps and scale drawings in the context of mathematics and other subjectsuse conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometric information  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6288" Cops and Robbers (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2292&refpage=titlesearch.php" Coordinate Patterns* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5469&part=index&refpage=monthindex.php" Route to Infinity (find the midpoint of the line segment AB, given the coordinates of points A and Buse the coordinate grid to solve problems involving translations, rotations, reflections and enlargementsfind 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=737" Beelines (Construction and lociuse a ruler and protractor to: measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA)use straight edge and compasses to construct: the midpoint and perpendicular bisector of a line segment the bisector of an angle the perpendicular from a point to a line the perpendicular from a point on a line a triangle, given three sides (SSS)  HYPERLINK "http://nrich.maths.org/8098" Constructing Triangles (use straight edge and compasses to construct triangles, given right angle, hypotenuse and side (RHS) understand from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are notuse ICT to explore constructions use ICT to explore these constructionsuse ICT to explore constructions of triangles and other 2-D shapes use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prismfind simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2159&refpage=titlesearch.php" Roundabout find the locus of a point that moves according to a more complex rule, both by reasoning and by using ICT  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2162" Rollin Rollin Rollin ( Measures and Mensurationchoose 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  HYPERLINK "http://nrich.maths.org/7500" Place Your Orders* (  HYPERLINK "http://nrich.maths.org/6046" Thousands and Millions* (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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5994" All in a Jumble (  HYPERLINK "http://nrich.maths.org/8318" Olympic Measures (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)  HYPERLINK "http://nrich.maths.org/7571" Nutrition and Cycling (understand and use measures of speed (and other compound measures such as density or pressure); solve problems involving constant or average rates of change  HYPERLINK "http://nrich.maths.org/7322" Speed-time Problems at the Olympics (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2384&part=index&refpage=monthindex.php" An Unhappy End (  HYPERLINK "http://nrich.maths.org/6494" Speeding Boats (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 calculationsrecognise limitations in the accuracy of measurements and judge the proportional effect on solutionsdistinguish between and estimate the size of acute, obtuse and reflex angles  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1235" Estimating Angles (use bearings to specify directioninterpret 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 formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles  HYPERLINK "http://nrich.maths.org/7534" Changing Areas, Changing Perimeters (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6398" Can They Be Equal? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2663&refpage=titlesearch.php" Fence It (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4889&part=index&refpage=monthindex.php" Warmsnug Double Glazing (derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2666&refpage=titlesearch.php" Isosceles Triangles (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=1867&refpage=titlesearch.php" Pick's Theorem* ( know and use the formulae for the circumference and area of a circle  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2161&refpage=titlesearch.php" An Unusual Shape (solve problems involving lengths of circular arcs and areas of sectors  HYPERLINK "http://nrich.maths.org/6468" Curvy Areas (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2425" Salinon (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=866" Arclets understand and use the formulae for the length of a circular arc and area and perimeter of a sector  HYPERLINK "http://nrich.maths.org/7359" Track Design (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2095" Triangles and Petals ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=693" Of All the Areas (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2401&part=index&refpage=monthindex.php" On the Edge ( calculate the surface area of cubes and cuboids  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2383&refpage=titlesearch.php" Cuboids (know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6399" Cuboid Challenge (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2322&refpage=titlesearch.php" Painted Cube* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2650&part=index&refpage=monthindex.php" Sending a Parcelcalculate the surface area and volume of right prisms  HYPERLINK "http://nrich.maths.org/7535" Changing Areas, Changing Volumes ( solve problems involving surface areas and volumes of cylinders  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=2664&refpage=titlesearch.php" Efficient Cutting (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5888" Cola Can solve problems involving surface areas and volumes of cylinders, pyramids, cones and spheres  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5890" Funnelsolve problems involving more complex shapes and solids, including segments of circles and frustums of cones  HYPERLINK "http://nrich.maths.org/7499" Fill Me up Too (  HYPERLINK "http://nrich.maths.org/6439" Immersion (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=5673" Gutter consider the dimensions of a formula and begin to recognise the difference between formulae for perimeter, area and volume in simple contextsunderstand the difference between formulae for perimeter, area and volume by considering dimensions StatisticsSpecifying a problem, planning and collecting datasuggest possible answers, given a question that can be addressed by statistical methods  HYPERLINK "http://nrich.maths.org/7721" Statistical Shorts (discuss a problem that can be addressed by statistical methods and identify related questions to explore  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6044" Reaction Timer (suggest a problem to explore using statistical methods, frame questions and raise conjecturesindependently devise a suitable plan for a substantial statistical project and justify the decisions madeconsider possible difficulties with planned approaches, including practical problems; adjust the project plan accordinglyselect and justify a sampling scheme and a method to investigate a population, including random and stratified samplingdecide which data would be relevant to an enquiry and possible sources decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources; consider appropriate sample size  HYPERLINK "http://nrich.maths.org/7367" Whos the Best? (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  HYPERLINK "http://nrich.maths.org/7722" Retiring to Paradise (identify possible sources of bias and plan how to minimise itdeal with practical problems such as non-response or missing dataunderstand how different methods of sampling and different sample sizes may affect the reliability of conclusions drawnplan how to collect and organise small sets of data from surveys and experiments: design data collection sheets or questionnaires to use in a simple survey construct frequency tables for gathering discrete data, grouped where appropriate in equal class intervalsplan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data and two-way tables for recording discrete datadesign 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 tablesbreak a task down into an appropriate series of key statements (hypotheses), and decide upon the best methods for testing theseidentify what extra information may be required to pursue a further line of enquirycollect small sets of data from surveys and experiments, as plannedcollect data using a suitable method (e.g. observation, controlled experiment, data logging using ICT)gather data from specified secondary sources, including printed tables and lists, and ICT-based sources, including the internetgather data from primary and secondary sources, using ICT and other methods, including data from observation, controlled experiment, data logging, printed tables and lists Processing and representing datacalculate statistics for small sets of discrete data: find the mode, median and range, and the modal class for grouped data calculate the mean, including from a simple frequency table, using a calculator for a larger number of items  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6267" M, M and M (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6345" Searching for Mean(ing) (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4838&part=index&refpage=monthindex.php" Litov's Mean Value Theorem (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  HYPERLINK "http://nrich.maths.org/6957" How Would You Score It? (calculate statistics and select those most appropriate to the problem or which address the questions posed  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4834&refpage=titlesearch.php" Top Coach (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)  HYPERLINK "http://nrich.maths.org/8061" Olympic Triathlon (use an appropriate range of statistical methods to explore and summarise data; including calculating an appropriate moving average for a time seriesuse a moving average to identify seasonality and trends in time series data, using them to make predictionsconstruct, on paper and using ICT, graphs and diagrams to represent data, including: bar-line graphs frequency diagrams for grouped discrete data simple pie charts construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: pie charts for categorical data bar charts and frequency diagrams for discrete and continuous data simple line graphs for time series simple scatter graphs stem-and-leaf diagramsselect, construct and modify, on paper and using ICT, suitable graphical representations to progress an enquiry and identify key features present in the data. Include: line graphs for time series scatter graphs to develop further understanding of correlation 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: cumulative frequency tables and diagrams box plots scatter graphs and lines of best fit (by eye)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 intervalsconstruct histograms, including those with unequal class intervalswork through the entire handling data cycle to explore relationships within bi-variate data, including applications to global citizenship, e.g. how fair is our society?Interpreting and discussing resultsinterpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and simple statistics for a single distributioninterpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored  HYPERLINK "http://nrich.maths.org/7735" Charting Success (interpret graphs and diagrams and make inferences to support or cast doubt on initial conjectures; have a basic understanding of correlation analyse data to find patterns and exceptions, and try to explain anomalies; include social statistics such as index numbers, time series and survey data  HYPERLINK "http://nrich.maths.org/7489" Olympic Records ( HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4957"Substitution Cipher ( interpret and use cumulative frequency diagrams to solve problemsuse, interpret and compare histograms, including those with unequal class intervalsappreciate 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'compare two simple distributions using the range and one of the mode, median or meancompare two distributions using the range and one or more of the mode, median and meancompare two or more distributions and make inferences, using the shape of the distributions and appropriate statistics  HYPERLINK "http://nrich.maths.org/7731" Which List Is Which? (compare two or more distributions and make inferences, using the shape of the distributions and measures of average and spread, including median and quartileswrite a short report of a statistical enquiry, including appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of presentationwrite about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used review interpretations and results of a statistical enquiry on the basis of discussions; communicate these interpretations and results using selected tables, graphs and diagramsexamine critically the results of a statistical enquiry; justify choice of statistical representations and relate summarised data to the questions being exploredrecognise the limitations of any assumptions and the effects that varying the assumptions could have on the conclusions drawn from data analysis Probabilityuse vocabulary and ideas of probability, drawing on experience interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable  HYPERLINK "http://nrich.maths.org/7219" Sociable Cards (interpret results involving uncertainty and prediction  HYPERLINK "http://nrich.maths.org/7250" What Does Random Look Like? (use tree diagrams to represent outcomes of two or more events and to calculate probabilities of combinations of independent events  HYPERLINK "http://nrich.maths.org/7220" Last One Standing ( 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  HYPERLINK "http://nrich.maths.org/7478" Whos the Winner? (  HYPERLINK "http://nrich.maths.org/920" Chances Are (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 eventknow 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  HYPERLINK "http://nrich.maths.org/7541" Non-transitive Dice (  HYPERLINK "http://nrich.maths.org/7286" At Least One (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6033" Interactive Spinners ( 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  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4308&part=index&refpage=monthindex.php" Odds and Evens* (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=919" In a Box (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)נP(B)  HYPERLINK "http://nrich.maths.org/7238" Mathsland National Lottery (  HYPERLINK "http://nrich.maths.org/7221" Same Number! (recognise when and how to work with probabilities associated with independent and mutually exclusive events when interpreting dataestimate probabilities by collecting data from a simple experiment and recording it in a frequency table; compare experimental and theoretical probabilities in simple contexts  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4308&part=index&refpage=monthindex.php" Odds and Evens* (compare estimated experimental probabilities with theoretical probabilities, recognising that: if an experiment is repeated the outcome may, and usually will, be different increasing the number of times an experiment is repeated generally leads to better estimates of probability  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4304&part=index&refpage=monthindex.php" Flippin' Discs (compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence  HYPERLINK "http://nrich.maths.org/7222" Do You Feel Lucky? (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4311&part=index&refpage=monthindex.php" Two's Company (  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4313&part=index&refpage=monthindex.php" Cosy Corner ( understand relative frequency as an estimate of probability and use this to compare outcomes of experiments  HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=6123" Which Spinners? ( 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 HYPERLINK "http://nrich.maths.org/public/viewer.php?obj_id=4334"The Better Bet  Latest Additions January 2012 Triathlon and Fitness Speed-time Problems at the Olympics February 2012 Substitution Cipher March 2012: Magic Letters Double Trouble Slick Summing May 2012: Always a Multiple? What Numbers Can We Make Now? Factorising with Multilink? 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