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Level Mathematical Studies 2 year Route Map GCSE3 Mathematics Linear Route Map – Foundation Tier Common content: Common content: analysis of data Critical analysis Number Topic Algebra Topic Common content: maths for personal finance Geometry & Measures Topic Statistics Topic OR Optional content: Statistical Techniques ICT skills Common content: Estimation OR Optional content: Critical Path and Risk Analysis GCSE F Tier revision Optional content: Graphical Techniques GCSE H Tier revision Level 3 Mathematical Studies 2 year Route Map Year 12 OCTOBER SEPTEMBER Wk1 Introduction to spreadsheets Wk2 Wk3 Types of Data Collecting Data Wk4 Numerical Calculations NOVEMBER Wk11 Representing data numerically 1 Wk5 Wk6 Percentages Wk12 Wk13 Wk14 Holiday Wk15 Interest Rates Representing data diagrammatically 1 Wk22 Wk23 Optional content Topic 1 – (select one from the right) Wk24 Holiday Wk16 Wk32 Holiday REVISION AND END OF YEAR EXAMS Fermi Estimation Holiday Wk18 Wk33 Wk34 Similarity and Pythagoras Theorem Equation of a straight line Surface area and similarity Wk43 Wk44 Representing data numerically 1 Wk20 Collecting and Sampling Data MARCH Wk25 Wk26 Wk27 Wk28 Wk29 Solution to financial problems Review and recap 1 Wk35 Analyse Critically 1 Wk36 Wk30 Perimeter, Circumference and Area JUNE Wk37 REVISION AND END OF YEAR EXAMS Wk38 Holiday Wk39 Wk40 REVISION AND END OF YEAR EXAMIANTIONS JULY Wk42 Wk10 Wk19 MAY JUNE Wk41 Wk17 Holiday APRIL Wk31 Wk9 JANUARY FEBRUARY Wk21 Wk8 DECEMBER JANUARY Holiday Wk7 NOVEMBER Wk45 Project work: Analysis of Data or Personal Finance Year 13 Level 3 Mathematical Studies 2 year Route Map Year 13 OCTOBER SEPTEMBER Wk1 Wk2 Wk3 Review and recap 2 Wk4 Representing data diagrammatically 2 Wk12 Wk13 Wk14 Optional content Topic 2 – (select one from the right) JANUARY Graphical representation Wk22 Review and recap 4 Wk15 Review and recap 3 Wk16 Wk23 Holiday Wk32 Wk33 Wk24 Wk25 Holiday Wk26 Wk27 Optional content Topic 3 – (select one from the right) Wk34 Wk35 Graphical representation Option Topic 2 Wk18 Wk19 Repayments and credit Wk28 Wk43 Wk44 Wk20 Taxation: Value added tax (VAT) Wk29 Taxation: Income tax and National Insurance Wk36 Wk45 Wk30 Holiday JUNE Wk37 Wk38 Holiday JULY Wk42 Wk10 MARCH REVISION Analyse Critically 3 Year 12 Holiday Wk9 MAY JUNE Wk41 Wk17 Holiday APRIL Wk31 Wk8 JANUARY FEBRUARY Wk21 Holiday Wk7 DECEMBER Analyse Critically 2 Limits of accuracy Wk6 Representing data numerically 1 NOVEMBER Wk11 Wk5 NOVEMBER Wk39 REVISION Wk40 Introduction to Spreadsheets (Slide 1 of 2) Continued on next page Subject content: Online resources: It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification. Anthropometric Data - Nuffield Foundation Spreadsheet formulae will include: “=A1+A2+A3” to sum values in cells “=2*B3” to multiply a value in a given cell “=SUM(A1:A10)” DISCUSS Regression and Correlation - Nuffield Foundation Pay rates for men and women - Nuffield Foundation Stature - Nuffield Foundation Climate Prediction - Nuffield Foundation Cup of Coffee - Nuffield Foundation Test Run - Nuffield Foundation Ozone Holes - Nuffield Foundation Savings Growth - Nuffield Foundation Election Results 2005 and 2010 Health Data - Nuffield Foundation substituting numerical values into F1.1 spreadsheets Mammals - Nuffield Foundation Module Results - Nuffield Foundation Pulse Rates - Nuffield Foundation Exponential growth – MEI (Username: mei-imps Password: imps) Compound Interest – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI (Username: mei-imps Username: imps) Return to Routemap View next page Introduction to Spreadsheets (Slide 2 of 2) Subject content: Online resources: It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification. Student Loans 2 – MEI Spreadsheet formulae will include: “=A1+A2+A3” to sum values in cells “=2*B3” to multiply a value in a given cell “=SUM(A1:A10)” (Username: mei-imps Username: imps) Sport at School - TES Guide to creating comparison charts in Excel – TES Investigating y=mx+c spreadsheet - TES Intro to spreadsheets – TES Modelling with spreadheets - substituting numerical values into spreadsheets planning a festival - TES An introduction to spreadsheets F1.1 2 - TES Return to Routemap Return to previous page Types of Data Subject content: Online resources: appreciating the difference between qualitative and quantitative Parking Permits - Nuffield D1.1 data; Foundation What Is Data? - Maths Is Fun Types of data - discrete vs continuous – TES appreciating the difference between primary and secondary D1.2 data (including the use of secondary data that has been processed e.g. grouped) Return to Routemap Collecting Data Subject content: D1.3 collecting quantitative and qualitative primary and secondary data Online resources: Pulse Rates - Nuffield Foundation Reaction Times - Nuffield Foundation What Is Data? - Maths Is Fun E1.1 The modelling cycle: Parking Permits - Nuffield - representing a situation mathematically, making assumptions Runaway Train - Nuffield and simplifications Foundation Foundation Pulse Rates - Nuffield Foundation Modelling with spreadheets - E1.2 - selecting and using appropriate mathematical techniques for problems and situations E1.3 - interpreting results in the context of the given problem E1.4 - evaluating methods and situations including how they may have been affected by assumptions made Return to Routemap planning a festival - TES Numerical calculations Subject content: using conventional notation for priority of operations, including F1.2 brackets, powers, roots and reciprocals Online resources: BODMAS – MathsIsFun BIDMAS – Transum Order of Operation – CIMT BODMAS Notes PPT - Mr Barton Maths Order of Operation Jigsaw Maths With Graham substituting numerical values into formulae Climate Prediction - Nuffield Foundation F1.1 Financial Calculations - Nuffield Foundation Tarsia Substitution - TES Return to Routemap Continued on next page Percentages (Slide 1 of 2) Subject content: Online resources: interpreting percentages and percentage Percentages - Nuffield Foundation changes as a fraction or a decimal and Water Flow - Nuffield Foundation F2.1 interpreting these multiplicatively Gas Guzzlers - Nuffield Foundation Financial Calculations - Nuffield Foundation Income Tax - Nuffield Foundation expressing one quantity as a percentage Growth and Decay - Nuffield Foundations of another Guest1QM) Percentages - MEI Integral (Username: mei-iqm Password: Student Loans 1 – MEI (Username: mei-imps Username: imps) F2.3 comparing two quantities using percentages F2.4 working with percentages over 100% Return to Routemap Student Loans 2 – MEI (Username: mei-imps Username: imps) My Money Week 2014 - Inflation - Pfeg My Money Week 2014 - Inflation - Pfeg Percentages - Mathscentre View next page Percentages (Slide 2 of 2) F2.5 Subject content: Online resources: solving problems involving Percentages - Nuffield Foundation percentage change - including percentage increase/decrease and original value problems National Insurance - Nuffield Foundation (rules may need updating) - including simple and compound interest E1.2 selecting and using appropriate mathematical techniques for problems and situations Return to Routemap Income Tax - Nuffield Foundation (rules may need updating) Savings Growth - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation Growth and Decay - Nuffield Foundations Percentages - MEI Integral (Username: mei-iqm Password: Guest1QM) Compound Interest – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI (Username: mei-imps Username: imps) Percentages - Mathscentre Return to previous page Fermi Estimation E2.1 Subject content: Online resources: Fermi estimation - making fast, How should mathematics be taught to non-mathematicians? - Tim Gower's Blog rough estimates using quantities Fermi Maths Problems – Kidsjig which are either difficult or Classic Fermi Questions – Mathsforum Estimation - MathsIsFun How many piano tuners are there in Chicago? – TES F1.1 impossible to measure directly Fermi Problems - TES substituting numerical values Income Tax - Nuffield Foundation (rules may need updating) into financial expressions Savings Facts and Formulae - Nuffield Foundation (including bank accounts) F1.4 finding approximate solutions to problems in financial contexts Return to Routemap Savings Growth - Nuffield Foundation Growth and Decay - Nuffield Foundations Representing Data Numerically 1 D3.1 Subject content: Online resources: calculating/identifying mean, median, mode from raw data HE Applications - Nuffield Foundation Stature - Nuffield Foundation Mammals - Nuffield Foundation D3.1 calculating/identifying quartiles, percentiles, range, interquartile Module Results - Nuffield Foundation range, standard deviation from raw data Pulse Rates - Nuffield Foundation interpreting these numerical measures and reaching D3.2 conclusions based on these measures Return to Routemap Averages and Spread Standard Deviation - TeachIt Maths (PDF File is free access) Data Summaries - Statstutor Representing Data Diagrammatically 1 Subject content: Online resources: constructing and interpreting diagrams for grouped discrete HE Applications - Nuffield Foundation data and continuous data and know their appropriate use Module Results - Nuffield Foundation D4.1 - box and whisker plots - stem-and-leaf diagrams (including back-to-back) Return to Routemap Mammals - Nuffield Foundation Pulse Rates - Nuffield Foundation Box and Whisker Plots - Statstutor Stem and Leaf Diagrams - Maths is Fun Interest Rates F3.1 Subject content: Online resources: simple and compound interest Financial Calculations - Nuffield Foundation Annual Equivalent Rate (AER) National Insurance - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation (rules may need updating) Savings Growth - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation F3.2 savings and investments Growth and Decay - Nuffield Foundations Compound Interest – MEI (Username: mei-imps Username: imps) My Money Week 2014 - Inflation - Pfeg selecting and using appropriate E1.2 mathematical techniques for problems and situations Return to Routemap Equation of a straight line Subject content: Online resources: find the gradient of a line connecting Gas Guzzlers - Nuffield Foundation two different points. Smoke Strata - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation Water Flow - Nuffield Foundation Test Run - Nuffield Foundation Match Linear Functions and Graphs - Nuffield Foundation Exponential growth – MEI (Username: mei-imps Password: imps) knowledge and use of the formula = Equation of a Straight Line - Mathscentre + . Investigating y=mx+c spreadsheet - TES Return to Routemap The Gradient of a Straight Line Segment - Mathscentre Collecting and Sampling Data D2.2 Subject content: Online resources: appreciating the strengths and limitations of random, Parking Permits - Nuffield cluster, stratified and quota sampling methods and applying Reaction Times - Nuffield this understanding when designing sampling strategies appreciating that improving accuracy by removing bias and Foundation Foundation Parking Permits - Nuffield D2.2 Foundation increasing sample size may cost/save both time and money D2.1 inferring properties of populations or distributions from a HE Applications - Nuffield sample, whilst knowing the limitations of sampling Pulse Rates - Nuffield Foundation Return to Routemap Foundation Reaction Times - Nuffield Foundation The Normal Distribution (Slide 1 of 2) Continued on next page S1.1 Subject content: Online resources: knowledge that this is a symmetrical distribution and that the Normal Distribution - Maths Is area underneath the normal ‘bell’ shaped curve represents The Normal Distribution - SCool probability knowledge that approximately Fun The Normal Distribution - CIMT S1.1 2 3 The Normal Distribution - rds of observations lie within 1 standard deviation of the mean and that approximately 95% of observations lie within 2 standard deviations of the mean S2.1 use of the notation N(0, 1) for the standardised normal University of Oxford Stature - Nuffield Foundation Normal Distribution Tarsia – TES Autograph Activity - Normal Distribution Calculator - TES distribution with mean = 0 and standard deviation = 1 Return to Routemap View next page The Normal Distribution (Slide 2 of 2) S3.1 Subject content: Online resources: using a calculator or tables to find probabilities for normally Normal Distribution - Maths Is distributed data with mean = 0 and standard deviation = 1 The Normal Distribution - S- Fun Cool The Normal Distribution - CIMT using a calculator or tables to find probabilities for normally S3.1 distributed data with known mean and standard deviation The Normal Distribution University of Oxford Stature - Nuffield Foundation (the finding of an unknown mean or standard deviation by making use of percentage points will not be required) C1.1 presenting logical and reasoned arguments in context criticising the arguments of others C2.1 communicating mathematical approaches and solutions Return to Routemap Return to previous page Critical Path Analysis R1.1 R1.2 Subject content: Online resources: representing compound projects by activity networks Refurbishing a Room - Nuffield Foundation Critical Path Analysis – CIMT activity-on-node representation will be used Critical Path Analysis - Learn About OR Critical path analysis – TES R2.1 using early time and late time algorithms to identify critical activities and find the critical path(s) R3.1 using Gantt charts (cascade diagrams) to present project C1.1 presenting logical and reasoned arguments in context C2 communicating mathematical approaches and solutions activities criticising the arguments of others Return to Routemap Earliest and Latest Event Times – TES Gantt charts and resource histrograms – TES Thinking Skills Activities Lesson Decision Maths - TES Graphical Methods (Slide 1 of 2) Continued on next page G1.1 Subject content: Online resources: sketching and plotting curves defined by Minimum and Maximum Problems - Nuffield Foundation simple equations (a knowledge of the shapes of Coughs and Sneezes - Nuffield Foundation the graphs of linear, quadratic, cubic and Gas Guzzlers - Nuffield Foundation Cup of Coffee - Nuffield Foundation Climate Prediction - Nuffield Foundation G2.1 exponential functions will be expected) How Frequent are Earthquakes? - Nuffield Foundation plotting and interpreting graphs in real Smoke Strata - Nuffield Foundation contexts, to find approximate solutions to Test Run - Nuffield Foundation problems Return to Routemap How Frequent are Earthquakes? - Nuffield Foundation Water Flow - Nuffield Foundation Ozone Holes - Nuffield Foundation Runaway Train - Nuffield Foundation View next page Graphical Methods (Slide 2 of 2) Subject content: Online resources: interpreting the solutions of equations as the Liner quadratic cubic graph match – TES G2.2 intersection points of graphs and vice versa Solving linear equations graphically – TES Quadratic sketch treasure hunt – TES Solving equations graphically lesson – TES (ignore first three slides of the powerpoint) presenting logical and reasoned arguments in C1 context Minimum and Maximum Problems - Nuffield Foundation Gas Guzzlers - Nuffield Foundation Coughs and Sneezes - Nuffield Foundation C1.1 criticising the arguments of others Climate Prediction - Nuffield Foundation Smoke Strata - Nuffield Foundation Test Run - Nuffield Foundation Ozone Holes - Nuffield Foundation communicating mathematical approaches and Runaway Train - Nuffield Foundation C2 solutions Return to Routemap Return to previous page Review and recap 1 Subject content: Return to Routemap Online resources: Solution to financial problems (Slide 1 of 2) Continued on next page F7.1 Subject content: Online resources: the effect of inflation Financial Graphs and Charts - Nuffield Foundation Retail Price Index (RPI), Consumer Price My Money Week 2014 - Inflation - Pfeg Inflation Indices - Nuffield Foundation Index (CPI) setting up, solving and interpreting the F7.2 solutions to financial problems, including Financial Calculations - Nuffield Foundation Savings Growth - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation those that involve compound interest using iterative methods F7.3 currency exchange rates including commission Changing to a Foreign Currency - BBC Bitesize Currency Conversion - Maths is Fun Currency exchange Mathsopoly – TES Currency Conversion Exchange - World Travelling - TES Return to Routemap View next page Solution to financial problems (Slide 2 of 2) Subject content: Online resources: budgeting Income Tax - Nuffield Foundation (rules may need updating) F7.4 National Insurance - Nuffield Foundation (rules may need updating) Savings Growth - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation E1.2 selecting and using appropriate mathematical techniques for problems and situations Return to Routemap Student Loans 1 – MEI (Username: mei-imps Username: imps) Return to previous page Perimeter, Circumference and Area Subject content: Online resources: Knowledge and use of the perimeter of 2D shapes and their Area and Perimeter match up - areas TES Compound Rectangles - TES Maths Functional Skills: A New Floor - TES knowledge and use of the formulae for the circumference and the area of circle Circumference of a circle worksheet - TES Area and Perimeter of sectors worksheet - TES Arcs and sectors worksheet - Knowledge and use of the formulae for calculating fractional areas of circles and composite shapes TES Maths Valentines Card - Area and Perimeter – TES Perimeter of circles and semicircles - TES Return to Routemap Similarity and Pythagoras’ Theorem Subject content: Online resources: the application of the concepts of similarity Similar Shapes Worksheet – TES GCSE Similar Triangles Geometry Activity - TES including lengths in similar figures Pythagoras’ theorem applied to 2-D and 3-D figures. GCSE Introducing Pythagoras Theorem lesson – TES Pythagoras Theorem in 3D – TES Pythagoras Theorem Lesson – TES – incudes an algebraic proof of the theorem Pythagoras Theorem and coordinates – TES Pythagoras’ theorem applied to 3-D figures. Return to Routemap KS4 worksheet - using Pythagoras in 3D - TES Pythagoras worded question worksheet - TES Analyse Critically 1 Subject content: Online resources: C3.2 critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form The modelling cycle: Parking Permits - E1.1 Nuffield Foundation - representing a situation mathematically, making assumptions and simplifications Runaway Train Nuffield Foundation Pulse Rates - Nuffield E1.2 - E1.3 - interpreting results in the context of the given problem E1.4 selecting and using appropriate mathematical techniques for problems and - evaluating methods and situations including how they may have been affected Foundation Sport at School - TES situations by assumptions made Return to Routemap Surface area and similarity Subject content: Online resources: calculate surface areas of spheres, cones, pyramids and composite Area and Volume of similar solids, including the application of the concepts of similarity including lengths in similar figures shapes / solids – TES Ratio of lengths, areas, volumes of similar shpes – TES Activity for 3D shapes - TES Surface area and volume of prisms – TES Surface area and volume of buildings - TES Volume and surface area of a sphere Surface Area Worksheets TES Return to Routemap Project work: Analysis of data or Personal Finance Subject content: Online resources: Analysis of Data Mammals - Nuffield Foundation Reaction Times - Nuffield Foundation Sport at School - TES C1.1 Personal Finance Mathematical Applications of presenting logical and reasoned arguments in context Mathematical Applications of criticising the arguments of others Mammals - Nuffield Foundation C2.1 communicating mathematical approaches and solutions Summarising and report writing Return to Routemap Finance - Nuffield Foundation Finance - Nuffield Foundation Review and recap 2 Subject content: Return to Routemap Online resources: Representing Data Diagrammatically 2 Subject content: Online resources: constructing and interpreting diagrams for grouped Pay rates for men and women - Nuffield Foundation discrete data and continuous data and know their Mammals - Nuffield Foundation appropriate use Stature - Nuffield Foundation Module Results - Nuffield Foundation Pareto Charts - Nuffield Foundation D4.1 - histograms with equal and unequal class intervals Pulse Rates - Nuffield Foundation - cumulative frequency graphs Drawing Histograms - TES Cumulative Tables and Graphs - Maths is Fun GCSE Histograms Worksheet – TES Cumulative frequency Collective Memory – TES Plotting cumulative frequency curves video tutorial – TES Elephants Cumulative frequency - TES Return to Routemap Representing Data Numerically 2 Subject content: Online resources: calculating/identifying mean, median, mode from cumulative Stature - Nuffield Foundation D3.1 frequency diagrams, stem and leaf diagrams or boxplots Mammals - Nuffield Foundation Module Results - Nuffield Foundation Pareto Charts - Nuffield Foundation calculating/identifying quartiles, percentiles, range, interquartile Cumulative Tables and Graphs D3.1 - Maths is Fun range, standard deviation from cumulative frequency diagrams, stem and leaf diagrams or boxplots D3.2 interpreting these numerical measures and reaching conclusions based on these measures Standard Deviation Worksheet – TES Cumulative frequency and boxplots lessons – TES Median, quartiles and boxplots worksheet - TES Find ht quartiles and selecting and using appropriate mathematical techniques for E1.2 problems and situations Return to Routemap interquartile range - TES Graphical representation Subject content: Online resources: plotting points to create graphs and interpreting results from Financial Graphs and Charts - F5.1 graphs in financial contexts Nuffield Foundation Pareto Charts - Nuffield Foundation Match Linear Functions and Graphs - Nuffield Foundation representing a situation mathematically, making assumptions E1.1 and simplifications (students will engage in the tackling of 'open' mathematical problem-solving where there may not be a clear single approach or 'correct' answer) Return to Routemap Correlation and regression (Slide 1 of 3) Continued on next page S7.1 Subject content: Online resources: recognising when pairs of data are uncorrelated, correlated, strongly DISCUSS Regression and correlated, positively correlated and negatively correlated Anthropometric Data - Nuffield Correlation - Nuffield Foundation Foundation S7.2 appreciating that correlation does not necessarily imply causation Mammals - Nuffield Foundation understanding the idea of an outlier Coefficient - Statstutor Pearson’s Correlation Scatter Diagrams - Maths Is Fun S8.1 understanding that the strength of correlation is given by the pmcc Interactive correlation activity TES Statistics 1 Correlation – TES Ten point PMCC - TES S8.2 understanding that pmcc always has a value in the range from – 1 to S8.3 appreciating the significance of a positive, zero or negative value of +1 pmcc in terms of correlation of data Return to Routemap View next page Correlation and regression (Slide 2 of 3) Continued on next page Subject content: Online resources: the plotting of data pairs on scatter diagrams and the drawing, by eye, DISCUSS Regression and S9.1 Correlation - Nuffield Foundation of a line of best fit through the mean point (the idea of residuals will not be required) S9.2 S9.3 S9.4 S9.5 understanding the concept of a regression line Anthropometric Data - Nuffield Foundation Mammals - Nuffield Foundation Correlation and Regression TES plotting a regression line from its equation using interpolation with regression lines to make predictions understanding that there are problems concerning extrapolation where raw data is given, candidates will be expected to use a calculator DISCUSS Regression and S10.1 Correlation - Nuffield Foundation to calculate the pmcc and the equation of the regression line (calculations from grouped data will not be required) Anthropometric Data - Nuffield Foundation Pearson’s Correlation Coefficient - Statstutor Return to Routemap Return to previous page Correlation and regression (Slide 3 of 3) C1.1 Subject content: Online resources: presenting logical and reasoned arguments in context DISCUSS Regression and criticising the arguments of others Anthropometric Data - Nuffield communicating mathematical approaches and solutions Return to Routemap Correlation - Nuffield Foundation Foundation Mammals - Nuffield Foundation Return to previous page Expectation (Slide 1 of 2) Continued on next page Subject content: Online resources: understanding that uncertain outcomes can be modelled as random Probability - Nuffield R4.1 events with estimated probabilities knowing that the probabilities of an exhaustive set of outcomes sum to one R4.2 applying ideas of randomness, fairness and equally likely events to R5.1 understanding and applying Venn diagrams and simple tree diagrams Foundation Laws of Probability - Nuffield Foundation Crack the code - 5 lock problems - TES calculate expected outcomes Probability - Nuffield Foundation Laws of Probability - Nuffield R6.1 calculating the probability of combined events: both A and B; neither A nor B; either A or B (or both) to include independent and dependent events Foundation Three Dice - Nuffield Foundation Basic introduction to probability tree diagrams – TES Venn diagram lesson - TES Return to Routemap View next page Expectation (Slide 2 of 2) Subject content: Online resources: calculating the expected value of quantities such as financial R7.1 loss or gain presenting logical and reasoned arguments in context C1 criticising the arguments of others communicating mathematical approaches and solutions Return to Routemap Return to previous page Rates of change (slide 1 of 2) Continued on next page G3.1 Subject content: Online resources: interpreting the gradient of a straight line graph as a rate of Test Run - Nuffield Foundation change Gradients - Nuffield Foundation (rules for differentiation could be used as an extension activity) Model the Motion - Nuffield G3.2 interpreting the gradient at a point on a curve as an G3.3 estimating rates of change for functions from their graphs Foundation instantaneous rate of change knowing that the average speed of an object during a G4.1 distance travelled particular period of time is given by time taken Return to Routemap Model the Motion - Nuffield Foundation Tour de France problem solving – TES Speed time graphs - TES View next page Rates of change (slide 2 of 2) Subject content: Online resources: knowing that the gradient of a distance–time graph represents Test Run - Nuffield Foundation G5.1 speed and that the gradient of a velocity–time graph represents Model the Motion - Nuffield Foundation acceleration presenting logical and reasoned arguments in context Test Run - Nuffield Foundation C1 criticising the arguments of others communicating mathematical approaches and solutions Return to Routemap Return to previous page Analyse Critically 2 Subject content: Online resources: C3.2 critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form The modelling cycle: Parking Permits - Nuffield E1.1 Foundation - representing a situation mathematically, making assumptions and simplifications E1.2 - selecting and using appropriate mathematical techniques for problems and E1.3 - interpreting results in the context of the given problem E1.4 - evaluating methods and situations including how they may have been situations affected by assumptions made Return to Routemap Runaway Train - Nuffield Foundation Pulse Rates - Nuffield Foundation Sport at School - TES Review and recap 3 Subject content: Return to Routemap Online resources: Repayments and credit Subject content: Online resources: student loans and mortgages Credit Cards - Nuffield Foundation Annual Percentage Rate (APR) Financial Calculations - Nuffield Foundation APR - Nuffield Foundation Inflation Indices - Nuffield Foundation Compound Interest – MEI (Username: mei-imps F4.1 Username: imps) Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI (Username: mei-imps Username: imps) selecting and using appropriate mathematical techniques E1.2 for problems and situations Return to Routemap Taxation: Value Added Tax (VAT) Subject content: Online resources: Taxation: Value Added Tax (VAT) Government Spending and F6.1 selecting and using appropriate mathematical techniques for E1.2 problems and situations Return to Routemap VAT - TES Limits of accuracy Subject content: Online resources: applying and interpreting limits of accuracy, specifying simple Error Bounds, Limits of F1.3 error intervals due to truncation or rounding Accuracy in Measurement – TES Limits of Accuracy homework – TES Limits of accuracy powerpoint and worksheet - TES Return to Routemap Review and recap 4 Subject content: Return to Routemap Online resources: Probabilities and estimation (Slide 1 of 2) Continued on next page Subject content: Online resources: understand what is meant by the term ‘population’ in statistical S4.1 terms developing ideas of sampling to include the concept of a simple S4.2 random sample from a population knowing that the mean of a sample is called a ‘point estimate’ for S5.1 the mean of the population appreciating that accuracy is likely to be improved by increasing the sample size Return to Routemap View next page Probabilities and estimation (Slide 2 of 2) Subject content: Online resources: confidence intervals for the mean of a normally distributed S6.1 population of known variance using σ2 n confidence intervals will always be symmetrical; the confidence level required and the sample size will always be stated) ( presenting logical and reasoned arguments in context C1 criticising the arguments of others communicating mathematical approaches and solutions Return to Routemap Return to previous page Cost benefit analysis (Slide 1 of 2) Continued on next page Subject content: Online resources: R8.1 understanding that many decisions have to be made when outcomes cannot be predicted with certainty Control measures: understanding that the actions that can be taken R9.1 to reduce or prevent specific risks may have their own costs (to include the costs and benefits of insurance) using probabilities to calculate expected values of costs and benefits R10.1 of decisions other factors must be considered, for example - the regulatory framework (eg compulsory insurance) - minimising the maximum possible loss Return to Routemap View next page Cost benefit analysis (Slide 2 of 2) Subject content: Online resources: understanding that calculating an expected value is an important R10.2 part of such decision making presenting logical and reasoned arguments in context C1 criticising the arguments of others communicating mathematical approaches and solutions Return to Routemap Return to previous page Exponential Functions (Slide 1 of 2) Continued on next page G6.1 Subject content: Online resources: using a calculator to find values of the function (the Climate Prediction - Nuffield Foundation laws of logarithms will not be required) Gas Guzzlers - Nuffield Foundation Cup of Coffee - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation using a calculator log function to solve equations of the G6.2 form = and = Smoke Strata - Nuffield Foundation Growth and Decay - Nuffield Foundations Matching Graph Sketches - TeachIt Maths (Includes some extension graphs beyond the specification: PDF File has free access) understanding that e has been chosen as the standard Exponential growth – MEI (Username: meiimps Password: imps) base for exponential functions G7.1 knowing that the gradient at any point on the graph of = e is equal to the value of that point Return to Routemap View next page Exponential Functions (Slide 2 of 2) Subject content: Online resources: using exponential functions to model growth and decay in Climate Prediction - Nuffield Foundation G8.2 various contexts Gas Guzzlers - Nuffield Foundation Cup of Coffee - Nuffield Foundation How Frequent are Earthquakes? Nuffield Foundation Smoke Strata - Nuffield Foundation formulating and using equations of the form = and G8.1 = e Growth and Decay - Nuffield Foundations Exponential growth – MEI (Username: mei-imps Password: imps) presenting logical and reasoned arguments in context C1 criticising the arguments of others communicating mathematical approaches and solutions Return to Routemap Return to previous page Taxation: Income Tax and National Insurance Subject content: Online resources: Taxation: income tax, National Insurance, Income Tax - Nuffield Foundation (rules may need F6.1 updating) National Insurance - Nuffield Foundation (rules may need updating) selecting and using appropriate mathematical techniques for E1.2 problems and situations Return to Routemap Analyse Critically 3 Subject content: Online resources: C3.2 critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form E1.1 The modelling cycle: Parking Permits - Nuffield Foundation - representing a situation mathematically, making assumptions and simplifications Runaway Train - Nuffield Foundation E1.2 E1.3 - selecting and using appropriate mathematical techniques for problems and situations E1.4 - evaluating methods and situations including how they may have been affected - interpreting results in the context of the given problem by assumptions made Return to Routemap Pulse Rates - Nuffield Foundation Sport at School - TES