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GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content:

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Presentation on theme: "GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content:"— Presentation transcript:

1 GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content: Statistical Techniques Optional content: Graphical Techniques Optional content: Critical Path and Risk Analysis GCSE H Tier revision Common content: maths for personal finance GCSE F Tier revision ICT skills Common content: analysis of data Common content: Critical analysis Level 3 Mathematical Studies 2 year Route Map There are 3 optional topics You must chose one optional content topic to fully cover OR

2 Wk1Wk2Wk3Wk4Wk5Wk6Wk7Wk8Wk9Wk10 Wk11Wk12Wk13Wk14Wk15Wk16Wk17Wk18Wk19Wk20 Wk21Wk22Wk23Wk24Wk25Wk26Wk27Wk28Wk29Wk30 Wk31Wk32Wk33Wk34Wk35Wk36Wk37Wk38Wk39Wk40 Wk41Wk42Wk43Wk44Wk45 SEPTEMBER OCTOBERNOVEMBER DECEMBERJANUARY FEBRUARYMARCH APRILMAYJUNE JULY Holiday Fermi Estimation Fermi Estimation Introduction to spreadsheets Introduction to spreadsheets Collecting and Sampling Data Collecting and Sampling Data Types of Data Types of Data Year 12 Perimeter, Circumference and Area Perimeter, Circumference and Area Equation of a straight line Equation of a straight line Year 13 Analyse Critically 1 Analyse Critically 1 Interest Rates Interest Rates Collecting Data Collecting Data Numerical Calculations Numerical Calculations Representing data diagrammatically 1 Representing data diagrammatically 1 Optional content Topic 1 – (select one from the right) Optional content Topic 1 – (select one from the right) Project work: Analysis of Data or Personal Finance Project work: Analysis of Data or Personal Finance Review and recap 1 Review and recap 1 Level 3 Mathematical Studies 2 year Route Map STATISTICAL TECHNIQUES 1 STATISTICAL TECHNIQUES 1 The Normal Distribution The Normal Distribution CRITICAL PATH AND RISK ANALYSIS 1 CRITICAL PATH AND RISK ANALYSIS 1 Critical Path Analysis Critical Path Analysis GRAPHICAL TECHNIQUES 1 GRAPHICAL TECHNIQUES 1 Graphical Methods Graphical Methods Percentages Representing data numerically 1 Representing data numerically 1 Representing data numerically 1 Representing data numerically 1 REVISION AND END OF YEAR EXAMIANTIONS Solution to financial problems Solution to financial problems Similarity and Pythagoras Theorem Similarity and Pythagoras Theorem REVISION AND END OF YEAR EXAMS Surface area and similarity Surface area and similarity REVISION AND END OF YEAR EXAMS Drag your selected optional content topic 1 into the Route Map OR

3 Wk1Wk2Wk3Wk4Wk5Wk6Wk7Wk8Wk9Wk10 Wk11Wk12Wk13Wk14Wk15Wk16Wk17Wk18Wk19Wk20 Wk21Wk22Wk23Wk24Wk25Wk26Wk27Wk28Wk29Wk30 Wk31Wk32Wk33Wk34Wk35Wk36Wk37Wk38Wk39Wk40 Wk41Wk42Wk43Wk44Wk45 SEPTEMBER OCTOBERNOVEMBER DECEMBERJANUARY FEBRUARYMARCH APRILMAYJUNE JULY Holiday Year 13 REVISION Year 12 Taxation: Income tax and National Insurance Taxation: Income tax and National Insurance Graphical representation Graphical representation STATISTICAL TECHNIQUES 2 STATISTICAL TECHNIQUES 2 Correlation and regression Correlation and regression STATISTICAL TECHNIQUES 3 STATISTICAL TECHNIQUES 3 Probabilities and estimation Probabilities and estimation CRITICAL PATH AND RISK ANALYSIS 3 CRITICAL PATH AND RISK ANALYSIS 3 Cost benefit analysis Cost benefit analysis CRITICAL PATH AND RISK ANALYSIS 2 CRITICAL PATH AND RISK ANALYSIS 2 Expectation GRAPHICAL TECHNIQUES 2 GRAPHICAL TECHNIQUES 2 Rates of change Rates of change GRAPHICAL TECHNIQUES 3 GRAPHICAL TECHNIQUES 3 Exponential Functions Exponential Functions Review and recap 2 Review and recap 2 Representing data diagrammatically 2 Representing data diagrammatically 2 Representing data numerically 1 Representing data numerically 1 Optional content Topic 2 – (select one from the right) Optional content Topic 2 – (select one from the right) Optional content Topic 3 – (select one from the right) Optional content Topic 3 – (select one from the right) Option Topic 2 Option Topic 2 Analyse Critically 2 Analyse Critically 2 Graphical representation Graphical representation Review and recap 3 Review and recap 3 Repayments and credit Repayments and credit Analyse Critically 3 Analyse Critically 3 Taxation: Value added tax (VAT) Taxation: Value added tax (VAT) Limits of accuracy Limits of accuracy Review and recap 4 Review and recap 4 Level 3 Mathematical Studies 2 year Route Map Drag your selected optional content topics 2 and 3 into the Route Map OR AND OR AND

4 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification. 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)”  Anthropometric Data - Nuffield Foundation Anthropometric Data - Nuffield Foundation  DISCUSS Regression and Correlation - Nuffield Foundation DISCUSS Regression and Correlation - Nuffield Foundation  Pay rates for men and women - Nuffield Foundation Pay rates for men and women - Nuffield Foundation  Stature - Nuffield Foundation Stature - Nuffield Foundation  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  Cup of Coffee - Nuffield Foundation Cup of Coffee - Nuffield Foundation  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Ozone Holes - Nuffield Foundation Ozone Holes - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Election Results 2005 and 2010 Election Results 2005 and 2010  Health Data - Nuffield Foundation Health Data - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Module Results - Nuffield Foundation Module Results - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Exponential growth – MEI (Username: mei-imps Password: imps) Exponential growth – MEI  Compound Interest – MEI (Username: mei-imps Username: imps)Compound Interest – MEI  Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI F1.1  substituting numerical values into spreadsheets Introduction to Spreadsheets (Slide 1 of 2) Continued on next page View next page

5 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification. 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)”  Student Loans 2 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI  Sport at School - TESSport at School - TES  Guide to creating comparison charts in Excel – TES Guide to creating comparison charts in Excel – TES  Investigating y=mx+c spreadsheet - TES Investigating y=mx+c spreadsheet - TES  Intro to spreadsheets – TES Intro to spreadsheets – TES  Modelling with spreadheets - planning a festival - TES Modelling with spreadheets - planning a festival - TES  An introduction to spreadsheets 2 - TES An introduction to spreadsheets 2 - TES F1.1  substituting numerical values into spreadsheets Introduction to Spreadsheets (Slide 2 of 2) Return to previous page

6 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D1.1  appreciating the difference between qualitative and quantitative data;  Parking Permits - Nuffield Foundation Parking Permits - Nuffield Foundation  What Is Data? - Maths Is Fun What Is Data? - Maths Is Fun  Types of data - discrete vs continuous – TES Types of data - discrete vs continuous – TES D1.2  appreciating the difference between primary and secondary data (including the use of secondary data that has been processed e.g. grouped) Types of Data

7 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D1.3  collecting quantitative and qualitative primary and secondary data  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Reaction Times - Nuffield Foundation Reaction Times - Nuffield Foundation  What Is Data? - Maths Is Fun What Is Data? - Maths Is Fun E1.1  The modelling cycle: - representing a situation mathematically, making assumptions and simplifications  Parking Permits - Nuffield FoundationParking Permits - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Modelling with spreadheets - planning a festival - TES Modelling with spreadheets - planning a festival - TES 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 Collecting Data

8 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F1.2  using conventional notation for priority of operations, including brackets, powers, roots and reciprocals  BODMAS – MathsIsFun BODMAS – MathsIsFun  BIDMAS – Transum BIDMAS – Transum  Order of Operation – CIMT Order of Operation – CIMT  BODMAS Notes PPT - Mr Barton Maths BODMAS Notes PPT - Mr Barton Maths  Order of Operation Jigsaw - Maths With Graham Order of Operation Jigsaw - Maths With Graham F1.1  substituting numerical values into formulae  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  Financial Calculations - Nuffield Foundation Financial Calculations - Nuffield Foundation  Tarsia Substitution - TES Tarsia Substitution - TES Numerical calculations

9 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F2.1  interpreting percentages and percentage changes as a fraction or a decimal and interpreting these multiplicatively  expressing one quantity as a percentage of another  Percentages - Nuffield Foundation Percentages - Nuffield Foundation  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  Water Flow - Nuffield Foundation Water Flow - Nuffield Foundation  Financial Calculations - Nuffield Foundation Financial Calculations - Nuffield Foundation  Income Tax - Nuffield Foundation Income Tax - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations  Percentages - MEI Integral (Username: mei-iqm Password: Guest1QM) Percentages - MEI Integral  Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI  Student Loans 2 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI  My Money Week Inflation - Pfeg My Money Week Inflation - Pfeg  My Money Week Inflation - Pfeg My Money Week Inflation - Pfeg  Percentages - Mathscentre Percentages - Mathscentre F2.3  comparing two quantities using percentages F2.4  working with percentages over 100% Percentages (Slide 1 of 2) Continued on next page View next page

10 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F2.5  solving problems involving percentage change - including percentage increase/decrease and original value problems - including simple and compound interest  Percentages - Nuffield Foundation Percentages - Nuffield Foundation  Income Tax - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation  National Insurance - Nuffield Foundation (rules may need updating) National Insurance - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations  Percentages - MEI Integral (Username: mei-iqm Password: Guest1QM) Percentages - MEI Integral  Compound Interest – MEI (Username: mei-imps Username: imps)Compound Interest – MEI  Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI  Student Loans 2 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI  Percentages - Mathscentre Percentages - Mathscentre E1.2  selecting and using appropriate mathematical techniques for problems and situations Percentages (Slide 2 of 2) Return to previous page

11 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: E2.1  Fermi estimation - making fast, rough estimates using quantities which are either difficult or impossible to measure directly  How should mathematics be taught to non-mathematicians? - Tim Gower's Blog How should mathematics be taught to non-mathematicians? - Tim Gower's Blog  Classic Fermi Questions – Mathsforum Classic Fermi Questions – Mathsforum  Fermi Maths Problems – Kidsjig Fermi Maths Problems – Kidsjig  Estimation - MathsIsFun Estimation - MathsIsFun  How many piano tuners are there in Chicago? – TES How many piano tuners are there in Chicago? – TES  Fermi Problems - TES Fermi Problems - TES F1.1  substituting numerical values into financial expressions (including bank accounts)  Income Tax - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations F1.4  finding approximate solutions to problems in financial contexts Fermi Estimation

12 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D3.1  calculating/identifying mean, median, mode from raw data  HE Applications - Nuffield Foundation HE Applications - Nuffield Foundation  Stature - Nuffield Foundation Stature - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Module Results - Nuffield Foundation Module Results - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Averages and Spread - Standard Deviation - TeachIt Maths (PDF File is free access) Averages and Spread - Standard Deviation - TeachIt Maths  Data Summaries - Statstutor Data Summaries - Statstutor D3.1  calculating/identifying quartiles, percentiles, range, interquartile range, standard deviation from raw data D3.2  interpreting these numerical measures and reaching conclusions based on these measures Representing Data Numerically 1

13 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D4.1  constructing and interpreting diagrams for grouped discrete data and continuous data and know their appropriate use - box and whisker plots - stem-and-leaf diagrams (including back-to-back)  HE Applications - Nuffield Foundation HE Applications - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Module Results - Nuffield Foundation Module Results - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Box and Whisker Plots - Statstutor Box and Whisker Plots - Statstutor  Stem and Leaf Diagrams - Maths is Fun Stem and Leaf Diagrams - Maths is Fun Representing Data Diagrammatically 1

14 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F3.1  simple and compound interest  Annual Equivalent Rate (AER)  Financial Calculations - Nuffield Foundation Financial Calculations - Nuffield Foundation  Income Tax - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation  National Insurance - Nuffield Foundation (rules may need updating) National Insurance - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations  Compound Interest – MEI (Username: mei-imps Username: imps)Compound Interest – MEI  My Money Week Inflation - Pfeg My Money Week Inflation - Pfeg F3.2  savings and investments E1.2  selecting and using appropriate mathematical techniques for problems and situations Interest Rates

15 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources:  find the gradient of a line connecting two different points.  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  How Frequent are Earthquakes? - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation  Smoke Strata - Nuffield Foundation Smoke Strata - Nuffield Foundation  Water Flow - Nuffield Foundation Water Flow - Nuffield Foundation  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Match Linear Functions and Graphs - Nuffield Foundation Match Linear Functions and Graphs - Nuffield Foundation  Exponential growth – MEI (Username: mei-imps Password: imps) Exponential growth – MEI  Equation of a Straight Line - Mathscentre Equation of a Straight Line - Mathscentre  The Gradient of a Straight Line Segment - Mathscentre The Gradient of a Straight Line Segment - Mathscentre  Investigating y=mx+c spreadsheet - TES Investigating y=mx+c spreadsheet - TES Equation of a straight line

16 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D2.2  appreciating the strengths and limitations of random, cluster, stratified and quota sampling methods and applying this understanding when designing sampling strategies  Parking Permits - Nuffield Foundation Parking Permits - Nuffield Foundation  Reaction Times - Nuffield Foundation Reaction Times - Nuffield Foundation D2.2  appreciating that improving accuracy by removing bias and increasing sample size may cost/save both time and money  Parking Permits - Nuffield Foundation Parking Permits - Nuffield Foundation D2.1  inferring properties of populations or distributions from a sample, whilst knowing the limitations of sampling  HE Applications - Nuffield Foundation HE Applications - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Reaction Times - Nuffield Foundation Reaction Times - Nuffield Foundation Collecting and Sampling Data

17 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S1.1  knowledge that this is a symmetrical distribution and that the area underneath the normal ‘bell’ shaped curve represents probability  Normal Distribution - Maths Is Fun Normal Distribution - Maths Is Fun  The Normal Distribution - S- Cool The Normal Distribution - S- Cool  The Normal Distribution - CIMT The Normal Distribution - CIMT  The Normal Distribution - University of Oxford The Normal Distribution - University of Oxford  Stature - Nuffield Foundation Stature - Nuffield Foundation  Normal Distribution Tarsia – TES Normal Distribution Tarsia – TES  Autograph Activity - Normal Distribution Calculator - TES Autograph Activity - Normal Distribution Calculator - TES S1.1 S2.1 The Normal Distribution (Slide 1 of 2) Continued on next page View next page

18 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S3.1  using a calculator or tables to find probabilities for normally distributed data with mean = 0 and standard deviation = 1  Normal Distribution - Maths Is Fun Normal Distribution - Maths Is Fun  The Normal Distribution - S- Cool The Normal Distribution - S- Cool  The Normal Distribution - CIMT The Normal Distribution - CIMT  The Normal Distribution - University of Oxford The Normal Distribution - University of Oxford  Stature - Nuffield Foundation Stature - Nuffield Foundation S3.1  using a calculator or tables to find probabilities for normally distributed data with known mean and standard deviation (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 The Normal Distribution (Slide 2 of 2) Return to previous page

19 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: R1.1  representing compound projects by activity networks  Refurbishing a Room - Nuffield Foundation Refurbishing a Room - Nuffield Foundation  Critical Path Analysis – CIMT Critical Path Analysis – CIMT  Critical Path Analysis - Learn About OR Critical Path Analysis - Learn About OR  Critical path analysis – TES Critical path analysis – TES  Earliest and Latest Event Times – TES Earliest and Latest Event Times – TES  Gantt charts and resource histrograms – TES Gantt charts and resource histrograms – TES  Thinking Skills Activities Lesson Decision Maths - TES Thinking Skills Activities Lesson Decision Maths - TES R1.2  activity-on-node representation will be used 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 activities C1.1  presenting logical and reasoned arguments in context  criticising the arguments of others C2  communicating mathematical approaches and solutions Critical Path Analysis

20 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G1.1  sketching and plotting curves defined by simple equations (a knowledge of the shapes of the graphs of linear, quadratic, cubic and exponential functions will be expected)  Minimum and Maximum Problems - Nuffield Foundation Minimum and Maximum Problems - Nuffield Foundation  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  Coughs and Sneezes - Nuffield Foundation Coughs and Sneezes - Nuffield Foundation  Cup of Coffee - Nuffield Foundation Cup of Coffee - Nuffield Foundation  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  How Frequent are Earthquakes? - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation  How Frequent are Earthquakes? - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation  Smoke Strata - Nuffield Foundation Smoke Strata - Nuffield Foundation  Water Flow - Nuffield Foundation Water Flow - Nuffield Foundation  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Ozone Holes - Nuffield Foundation Ozone Holes - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation G2.1  plotting and interpreting graphs in real contexts, to find approximate solutions to problems Graphical Methods (Slide 1 of 2) Continued on next page View next page

21 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G2.2  interpreting the solutions of equations as the intersection points of graphs and vice versa  Liner quadratic cubic graph match – TES Liner quadratic cubic graph match – TES  Solving linear equations graphically – TES Solving linear equations graphically – TES  Quadratic sketch treasure hunt – TES Quadratic sketch treasure hunt – TES  Solving equations graphically lesson – TES (ignore first three slides of the powerpoint) Solving equations graphically lesson – TES C1  presenting logical and reasoned arguments in context  Minimum and Maximum Problems - Nuffield Foundation Minimum and Maximum Problems - Nuffield Foundation  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  Coughs and Sneezes - Nuffield Foundation Coughs and Sneezes - Nuffield Foundation  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  Smoke Strata - Nuffield Foundation Smoke Strata - Nuffield Foundation  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Ozone Holes - Nuffield Foundation Ozone Holes - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation C1.1  criticising the arguments of others C2  communicating mathematical approaches and solutions Graphical Methods (Slide 2 of 2) Return to previous page

22 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: Review and recap 1

23 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F7.1  the effect of inflation  Retail Price Index (RPI), Consumer Price Index (CPI)  Financial Graphs and Charts - Nuffield Foundation Financial Graphs and Charts - Nuffield Foundation  Inflation Indices - Nuffield Foundation Inflation Indices - Nuffield Foundation  My Money Week Inflation - Pfeg My Money Week Inflation - Pfeg F7.2  setting up, solving and interpreting the solutions to financial problems, including those that involve compound interest using iterative methods  Financial Calculations - Nuffield Foundation Financial Calculations - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation F7.3  currency exchange rates including commission  Changing to a Foreign Currency - BBC Bitesize Changing to a Foreign Currency - BBC Bitesize  Currency Conversion - Maths is Fun Currency Conversion - Maths is Fun  Currency exchange Mathsopoly – TES Currency exchange Mathsopoly – TES  Currency Conversion Exchange - World Travelling - TES Currency Conversion Exchange - World Travelling - TES Solution to financial problems (Slide 1 of 2) Continued on next page View next page

24 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F7.4  budgeting  Income Tax - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation  National Insurance - Nuffield Foundation (rules may need updating) National Insurance - Nuffield Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI E1.2  selecting and using appropriate mathematical techniques for problems and situations Solution to financial problems (Slide 2 of 2) Return to previous page

25 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources:  Knowledge and use of the perimeter of 2D shapes and their areas  Area and Perimeter match up - TES Area and Perimeter match up - TES  Compound Rectangles - TES Compound Rectangles - TES  Maths Functional Skills: A New Floor - 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 Circumference of a circle worksheet - TES  Area and Perimeter of sectors worksheet - TES Area and Perimeter of sectors worksheet - TES  Arcs and sectors worksheet - TES Arcs and sectors worksheet - TES  Maths Valentines Card - Area and Perimeter – TES Maths Valentines Card - Area and Perimeter – TES  Perimeter of circles and semicircles - TES Perimeter of circles and semicircles - TES  Knowledge and use of the formulae for calculating fractional areas of circles and composite shapes Perimeter, Circumference and Area

26 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources:  the application of the concepts of similarity including lengths in similar figures  Pythagoras’ theorem applied to 2-D and 3-D figures.  Similar Shapes Worksheet – TES Similar Shapes Worksheet – TES  GCSE Similar Triangles Geometry Activity - TES GCSE Similar Triangles Geometry Activity - TES  GCSE Introducing Pythagoras Theorem lesson – TES GCSE Introducing Pythagoras Theorem lesson – TES  Pythagoras Theorem in 3D – TES Pythagoras Theorem in 3D – TES  Pythagoras Theorem Lesson – TES – incudes an algebraic proof of the theorem Pythagoras Theorem Lesson – TES  Pythagoras Theorem and coordinates – TES Pythagoras Theorem and coordinates – TES  KS4 worksheet - using Pythagoras in 3D - TES KS4 worksheet - using Pythagoras in 3D - TES  Pythagoras worded question worksheet - TES Pythagoras worded question worksheet - TES  Pythagoras’ theorem applied to 3-D figures. Similarity and Pythagoras’ Theorem

27 Return to Routemap Return to Routemap Return to Routemap Return to Routemap 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: - representing a situation mathematically, making assumptions and simplifications  Parking Permits - Nuffield FoundationParking Permits - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Sport at School - TESSport at School - TES 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 Analyse Critically 1

28 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources:  calculate surface areas of spheres, cones, pyramids and composite solids, including the application of the concepts of similarity including lengths in similar figures  Area and Volume of similar shapes / solids – TES Area and Volume of similar shapes / solids – TES  Ratio of lengths, areas, volumes of similar shpes – TES Ratio of lengths, areas, volumes of similar shpes – TES  Activity for 3D shapes - TES Activity for 3D shapes - TES  Surface area and volume of prisms – TES Surface area and volume of prisms – TES  Surface area and volume of buildings - TES Surface area and volume of buildings - TES Volume and surface area of a sphereVolume and surface area of a sphere  Surface Area Worksheets - TES Surface Area Worksheets - TES Surface area and similarity

29 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources:  Analysis of Data  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Reaction Times - Nuffield Foundation Reaction Times - Nuffield Foundation  Sport at School - TESSport at School - TES  Personal Finance  Mathematical Applications of Finance - Nuffield Foundation Mathematical Applications of Finance - Nuffield Foundation C1.1  presenting logical and reasoned arguments in context  criticising the arguments of others  Mathematical Applications of Finance - Nuffield Foundation Mathematical Applications of Finance - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation C2.1  communicating mathematical approaches and solutions  Summarising and report writing Project work: Analysis of data or Personal Finance

30 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: Review and recap 2

31 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D4.1  constructing and interpreting diagrams for grouped discrete data and continuous data and know their appropriate use - histograms with equal and unequal class intervals - cumulative frequency graphs  Pay rates for men and women - Nuffield Foundation Pay rates for men and women - Nuffield Foundation  Stature - Nuffield Foundation Stature - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Module Results - Nuffield Foundation Module Results - Nuffield Foundation  Pareto Charts - Nuffield Foundation Pareto Charts - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Cumulative Tables and Graphs - Maths is Fun Cumulative Tables and Graphs - Maths is Fun  Drawing Histograms - TESDrawing Histograms - TES  GCSE Histograms Worksheet – TES GCSE Histograms Worksheet – TES  Cumulative frequency Collective Memory – TES Cumulative frequency Collective Memory – TES  Plotting cumulative frequency curves video tutorial – TES Plotting cumulative frequency curves video tutorial – TES  Elephants Cumulative frequency - TES Elephants Cumulative frequency - TES Representing Data Diagrammatically 2

32 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: D3.1  calculating/identifying mean, median, mode from cumulative frequency diagrams, stem and leaf diagrams or boxplots  Stature - Nuffield Foundation Stature - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Module Results - Nuffield Foundation Module Results - Nuffield Foundation  Pareto Charts - Nuffield Foundation Pareto Charts - Nuffield Foundation  Cumulative Tables and Graphs - Maths is Fun Cumulative Tables and Graphs - Maths is Fun  Standard Deviation Worksheet – TES Standard Deviation Worksheet – TES  Cumulative frequency and boxplots lessons – TES Cumulative frequency and boxplots lessons – TES  Median, quartiles and boxplots worksheet - TES Median, quartiles and boxplots worksheet - TES  Find ht quartiles and interquartile range - TES Find ht quartiles and interquartile range - TES D3.1  calculating/identifying quartiles, percentiles, range, interquartile 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 E1.2  selecting and using appropriate mathematical techniques for problems and situations Representing Data Numerically 2

33 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F5.1  plotting points to create graphs and interpreting results from graphs in financial contexts  Financial Graphs and Charts - Nuffield Foundation Financial Graphs and Charts - Nuffield Foundation  Pareto Charts - Nuffield Foundation Pareto Charts - Nuffield Foundation  Match Linear Functions and Graphs - Nuffield Foundation Match Linear Functions and Graphs - Nuffield Foundation E1.1  representing a situation mathematically, making assumptions 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) Graphical representation

34 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S7.1  recognising when pairs of data are uncorrelated, correlated, strongly correlated, positively correlated and negatively correlated  DISCUSS Regression and Correlation - Nuffield Foundation DISCUSS Regression and Correlation - Nuffield Foundation  Anthropometric Data - Nuffield Foundation Anthropometric Data - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Pearson’s Correlation Coefficient - Statstutor Pearson’s Correlation Coefficient - Statstutor  Scatter Diagrams - Maths Is Fun Scatter Diagrams - Maths Is Fun  Interactive correlation activity - TES Interactive correlation activity - TES  Statistics 1 Correlation – TES Statistics 1 Correlation – TES  Ten point PMCC - TES Ten point PMCC - TES S7.2  appreciating that correlation does not necessarily imply causation  understanding the idea of an outlier S8.1  understanding that the strength of correlation is given by the pmcc S8.2  understanding that pmcc always has a value in the range from – 1 to + 1 S8.3  appreciating the significance of a positive, zero or negative value of pmcc in terms of correlation of data Correlation and regression (Slide 1 of 3) Continued on next page View next page

35 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S9.1  the plotting of data pairs on scatter diagrams and the drawing, by eye, of a line of best fit through the mean point (the idea of residuals will not be required)  DISCUSS Regression and Correlation - Nuffield Foundation DISCUSS Regression and Correlation - Nuffield Foundation  Anthropometric Data - Nuffield Foundation Anthropometric Data - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation  Correlation and Regression - TES Correlation and Regression - TES S9.2  understanding the concept of a regression line S9.3  plotting a regression line from its equation S9.4  using interpolation with regression lines to make predictions S9.5  understanding that there are problems concerning extrapolation S10.1  where raw data is given, candidates will be expected to use a calculator to calculate the pmcc and the equation of the regression line (calculations from grouped data will not be required)  DISCUSS Regression and Correlation - Nuffield Foundation DISCUSS Regression and Correlation - Nuffield Foundation  Anthropometric Data - Nuffield Foundation Anthropometric Data - Nuffield Foundation  Pearson’s Correlation Coefficient - Statstutor Pearson’s Correlation Coefficient - Statstutor Correlation and regression (Slide 2 of 3) Return to previous page Continued on next page

36 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: C1.1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions  DISCUSS Regression and Correlation - Nuffield Foundation DISCUSS Regression and Correlation - Nuffield Foundation  Anthropometric Data - Nuffield Foundation Anthropometric Data - Nuffield Foundation  Mammals - Nuffield Foundation Mammals - Nuffield Foundation Correlation and regression (Slide 3 of 3) Return to previous page

37 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: R4.1  understanding that uncertain outcomes can be modelled as random events with estimated probabilities  knowing that the probabilities of an exhaustive set of outcomes sum to one  Probability - Nuffield Foundation Probability - Nuffield Foundation  Laws of Probability - Nuffield Foundation Laws of Probability - Nuffield Foundation  Crack the code - 5 lock problems - TES Crack the code - 5 lock problems - TES R4.2  applying ideas of randomness, fairness and equally likely events to calculate expected outcomes R5.1  understanding and applying Venn diagrams and simple tree diagrams  Probability - Nuffield Foundation Probability - Nuffield Foundation  Laws of Probability - Nuffield Foundation Laws of Probability - Nuffield Foundation  Three Dice - Nuffield Foundation Three Dice - Nuffield Foundation  Basic introduction to probability tree diagrams – TES Basic introduction to probability tree diagrams – TES  Venn diagram lesson - TES Venn diagram lesson - TES 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 Expectation (Slide 1 of 2) Continued on next page View next page

38 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: R7.1  calculating the expected value of quantities such as financial loss or gain C1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions Expectation (Slide 2 of 2) Return to previous page

39 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G3.1  interpreting the gradient of a straight line graph as a rate of change  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Gradients - Nuffield Foundation (rules for differentiation could be used as an extension activity) Gradients - Nuffield Foundation  Model the Motion - Nuffield Foundation Model the Motion - Nuffield Foundation G3.2  interpreting the gradient at a point on a curve as an instantaneous rate of change G3.3  estimating rates of change for functions from their graphs G4.1  Model the Motion - Nuffield Foundation Model the Motion - Nuffield Foundation  Tour de France problem solving – TES Tour de France problem solving – TES  Speed time graphs - TES Speed time graphs - TES Rates of change (slide 1 of 2) Continued on next page View next page

40 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G5.1  knowing that the gradient of a distance–time graph represents speed and that the gradient of a velocity–time graph represents acceleration  Test Run - Nuffield Foundation Test Run - Nuffield Foundation  Model the Motion - Nuffield Foundation Model the Motion - Nuffield Foundation C1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions  Test Run - Nuffield Foundation Test Run - Nuffield Foundation Rates of change (slide 2 of 2) Return to previous page

41 Return to Routemap Return to Routemap Return to Routemap Return to Routemap 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: - representing a situation mathematically, making assumptions and simplifications  Parking Permits - Nuffield FoundationParking Permits - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Sport at School - TESSport at School - TES 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 Analyse Critically 2

42 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: Review and recap 3

43 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F4.1  student loans and mortgages  Annual Percentage Rate (APR)  Credit Cards - Nuffield Foundation Credit Cards - Nuffield Foundation  APR - Nuffield Foundation APR - Nuffield Foundation  Financial Calculations - Nuffield Foundation Financial Calculations - Nuffield Foundation  Inflation Indices - Nuffield Foundation Inflation Indices - Nuffield Foundation  Compound Interest – MEI (Username: mei-imps Username: imps)Compound Interest – MEI  Student Loans 1 – MEI (Username: mei-imps Username: imps) Student Loans 1 – MEI  Student Loans 2 – MEI (Username: mei-imps Username: imps) Student Loans 2 – MEI E1.2  selecting and using appropriate mathematical techniques for problems and situations Repayments and credit

44 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F6.1  Taxation: Value Added Tax (VAT)  Government Spending and VAT - TES Government Spending and VAT - TES E1.2  selecting and using appropriate mathematical techniques for problems and situations Taxation: Value Added Tax (VAT)

45 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F1.3  applying and interpreting limits of accuracy, specifying simple error intervals due to truncation or rounding  Error Bounds, Limits of Accuracy in Measurement – TES Error Bounds, Limits of Accuracy in Measurement – TES  Limits of Accuracy homework – TES Limits of Accuracy homework – TES  Limits of accuracy powerpoint and worksheet - TES Limits of accuracy powerpoint and worksheet - TES Limits of accuracy

46 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: Review and recap 4

47 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S4.1  understand what is meant by the term ‘population’ in statistical terms S4.2  developing ideas of sampling to include the concept of a simple random sample from a population S5.1  knowing that the mean of a sample is called a ‘point estimate’ for the mean of the population appreciating that accuracy is likely to be improved by increasing the sample size Probabilities and estimation (Slide 1 of 2) Continued on next page View next page

48 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: S6.1 C1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions Probabilities and estimation (Slide 2 of 2) Return to previous page

49 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: R8.1  understanding that many decisions have to be made when outcomes cannot be predicted with certainty R9.1  Control measures: understanding that the actions that can be taken to reduce or prevent specific risks may have their own costs (to include the costs and benefits of insurance) R10.1  using probabilities to calculate expected values of costs and benefits of decisions  other factors must be considered, for example - the regulatory framework (eg compulsory insurance) - minimising the maximum possible loss Cost benefit analysis (Slide 1 of 2) Continued on next page View next page

50 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: R10.2  understanding that calculating an expected value is an important part of such decision making C1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions Cost benefit analysis (Slide 2 of 2) Return to previous page

51 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G6.1  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  Cup of Coffee - Nuffield Foundation Cup of Coffee - Nuffield Foundation  How Frequent are Earthquakes? - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation  Smoke Strata - Nuffield Foundation Smoke Strata - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations  Matching Graph Sketches - TeachIt Maths (Includes some extension graphs beyond the specification: PDF File has free access) Matching Graph Sketches - TeachIt Maths  Exponential growth – MEI (Username: mei- imps Password: imps) Exponential growth – MEI G6.2 G7.1 Exponential Functions (Slide 1 of 2) Continued on next page View next page

52 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: G8.2  using exponential functions to model growth and decay in various contexts  Climate Prediction - Nuffield Foundation Climate Prediction - Nuffield Foundation  Gas Guzzlers - Nuffield Foundation Gas Guzzlers - Nuffield Foundation  Cup of Coffee - Nuffield Foundation Cup of Coffee - Nuffield Foundation  How Frequent are Earthquakes? - Nuffield Foundation How Frequent are Earthquakes? - Nuffield Foundation  Smoke Strata - Nuffield Foundation Smoke Strata - Nuffield Foundation  Growth and Decay - Nuffield Foundations Growth and Decay - Nuffield Foundations  Exponential growth – MEI (Username: mei-imps Password: imps) Exponential growth – MEI G8.1 C1  presenting logical and reasoned arguments in context  criticising the arguments of others  communicating mathematical approaches and solutions Exponential Functions (Slide 2 of 2) Return to previous page

53 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Subject content: Online resources: F6.1  Taxation: income tax, National Insurance,  Income Tax - Nuffield Foundation (rules may need updating) Income Tax - Nuffield Foundation  National Insurance - Nuffield Foundation (rules may need updating) National Insurance - Nuffield Foundation E1.2  selecting and using appropriate mathematical techniques for problems and situations Taxation: Income Tax and National Insurance

54 Return to Routemap Return to Routemap Return to Routemap Return to Routemap 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: - representing a situation mathematically, making assumptions and simplifications  Parking Permits - Nuffield FoundationParking Permits - Nuffield Foundation  Runaway Train - Nuffield Foundation Runaway Train - Nuffield Foundation  Pulse Rates - Nuffield Foundation Pulse Rates - Nuffield Foundation  Sport at School - TESSport at School - TES 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 Analyse Critically 3


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