GCSE



Scheme of Work

Mathematics in Context

Pearson Edexcel Level 3 Certificate in Mathematics in Context (7MC0)

Issue 2

Contents

Introduction 4

Suggested course plan 5

Overview of content descriptors within the topics 6

The topics 10

Introduction

This scheme of work comprises a suggestion of twelve context-led topics which have been chosen to show the wide range of applications of mathematics. Through these topics the content within the Mathematics in Context specification can be brought out and elements of GCSE Mathematics revised and consolidated.

The total teaching time set out in this scheme of work is estimated at between 135 and 160 hours. The balance of the 180 guided learning hours can be used for revision and consolidation.

A suggested course plan is provided based on a five term model over two years. The scheme of work is however designed to be flexible and can be adapted to other models of delivery.

The following objectives apply to all the topics:

Students will:

• Use a range of mathematical methods and techniques, including using contemporary calculator technology and knowledge and use of a spreadsheet, to find solutions to problems.

• Use a variety of mathematical and statistical approaches to represent and analyse problems.

• Generate and apply mathematical solutions to non-routine questions and problems taking creative approaches where appropriate, and test and evaluate answers and conclusions.

The topics have been chosen on the basis of potential relevance and appeal to a range of 16–19 years old learners. Teachers and tutors may however wish to replace some of the suggested topics with others more suited to their particular learners and circumstances. For example, in classes where students are studying a common main programme, the inclusions of topics related to their other studies may be beneficial.

Each topic within the scheme of work contains the following elements:

• Teaching time – the teaching time is approximate and may be adapted according to individual teaching needs and student interest.

• Specification references.

• Overview – topic overview.

• Resources:

o Includes suggested sources of comprehension material as well as teaching and learning resources.

o For access to some of the third party resources it may be necessary to create a free user account.

o The vast majority of the resources cited have not been written specifically for the Mathematics in Context specification and therefore may include topics outside the specification.

Mastery of the content of the specification will be achieved by working through the twelve topics. The table on pages 6–9 indicates how the content descriptors from the specification can be exemplified within the topics. Most of the descriptors will be encountered more than once. This will enable students to reinforce their learning, and to appreciate how specific mathematical concepts can be applied across a range of settings.

Suggested course plan

There are a number of ways in which the topics can be ordered and the following is one suggestion. This suggestion ensures progression through associated content descriptors. Individual teachers may wish to establish their own order and adapt or develop their own topics and resources.

|Year/Term |Topic |Title |Estimated teaching time |

|Year 1 Term 1 |Topic 1 |Social media |4–6 hours |

| |Topic 2 |Society |20–22 hours |

| |Topic 3 |Sport |8–10 hours |

|Year 1 Term 2 |Topic 4 |Clothing industry |16–18 hours |

| |Topic 5 |Finance |13–15 hours |

|Year 1 Term 3 |Topic 6 |Creative arts |11–13 hours |

| |Topic 7 |Health |18–20 hours |

|Year 2 Term 1 |Topic 8 |Economy |15–18 hours |

| |Topic 9 |Travel |6–8 hours |

|Year 2 Term 2 |Topic 10 |Environment |10–12 hours |

| |Topic 11 |Disasters |4–6 hours |

| |Topic 12 |Engineering |10–12 hours |

| | | |Total: 135–160 hours |

Overview of content descriptors within the topics

A brown tick indicates the first occurrence of a content descriptor.

Ref |Content descriptor |Topic 1

Social media |Topic 2

Society |Topic 3

Sport |Topic 4

Clothing Industry |Topic 5

Finance |Topic 6

Creative arts |Topic 7

Health |Topic 8

Economy |Topic 9

Travel |Topic 10

Environ-ment |Topic 11

Disasters |Topic 12

Engineer-ing | |A1 |infer properties of populations or distributions from a sample, while knowing the limitations of sampling |( | |( | |( | |( | |( | |( |( | |A2 |interpret and construct tables and line graphs for time series data; calculate, interpret and use moving averages | |( | | | | | |( |( |( | | | |A3 |construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and use them appropriately |( |( |( | |( | |( |( |( | |( |( | |A4 |interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation, including box plots |( |( |( |( |( | |( | |( | |( |( | |A5 |interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency, including quartiles, inter-quartile range, calculate and use variance and standard deviation |( |( |( | |( | |( | |( |( |( |( | |A6 |recognise correlation and know that it does not indicate causation |( |( |( | | | |( | |( |( |( | | |A7 |apply and interpret explanatory (independent) and response (dependent) variables, interpolate and extrapolate apparent trends while knowing the dangers of doing so | |( |( | | | |( | |( |( |( | | |A8 |draw estimated lines of best fit and make predictions; use and interpret the product moment correlation coefficient, recognising its limitations |( |( |( | | | |( |( |( |( |( |( | |A9 |use, apply and interpret linear regression; calculate the equation of a linear regression line using the method of least squares (candidates may be asked to draw this regression line on a scatter diagram) | |( |( | | | | | |( |( |( | | |A10 |use, apply and interpret Spearman’s rank; calculate Spearman’s rank correlation coefficient and use it as a measure of agreement or for comparisons of the degree of correlation (tied ranks may be tested in the examination papers). | | |( | | |( | | | | | | | |P1 |understand and demonstrate that empirical unbiased samples tend towards theoretical probability distributions, as sample size increases | | | | | | |( | | | | | | |P2 |enumerate sets and combinations of sets systematically using tree diagrams | | |( |( | | | |( | | | | | |P3 |calculate the probability of independent and dependent combined events, including sampling with and without replacement, using tree diagrams and other representations, Venn diagrams, sum and product laws | | |( | | | |( |( | | | | | |P4 |calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams | | |( | | | |( |( | | | |( | |P5 |understand, use and interpret probability notation, its application to Venn diagrams, exclusive and complementary events, independence of two events and conditional probability | | |( | | | |( | | | | | | |P6 |understand, interpret and use appropriately the following formulae: P(A′) = 1− P(A) ; P ∪ B = P(A) + P(B) − P (A ∩ B);

P(A ∩ B) = P(A)P(B|A); P(B|A) = P(B) and P(A|B) = P(A);

P(A ∩ B) = P(A)P(B) | | | |( | | | | | | | |( | |P7 |understand and interpret risk; the probability of something happening multiplied by the resulting cost or benefit if it does; comparison of levels of risk; application of risk to real-life contexts such as finance, insurance and trading. | |( | |( |( | |( | | | | | | |LP1 |translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution | |( | |( |( |( | | |( | | |( | |LP2 |plot graphs of equations that correspond to straight line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient | |( |( |( | |( | |( |( |( | |( | |LP3 |recognise, sketch and interpret graphs of linear functions | | | |( | |( | |( |( |( | | | |LP4 |solve algebraically linear equations in one unknown with the unknown on both sides of the equation | | | |( | | | | | | | | | |LP5 |solve two simultaneous equations in two variables (linear/linear) algebraically; find approximate solutions using a graph | | | |( | | | | |( | | | | |LP6 |solve linear inequalities in one variable, representing the solution on a number line using set notation | |( | |( | | | | |( | | | | |LP7 |solve linear inequalities in two variables, representing the solution on a graph | |( | |( | | | | | | | |( | |LP8 |use algebra to support and construct arguments | |( | |( | | | | | | | |( | |LP9 |formulate problems as linear programs with up to three variables | |( | |( | | | | | | | |( | |LP10 |solve and interpret two-variable problems graphically, using ruler and vertex methods | |( | |( | | | | | | | |( | |LP11 |consider problems where solutions must have integer values. | | | |( | | | | | | | |( | |SG1 |set up, solve and interpret the answers to growth and decay problems, including compound interest | | | |( |( | |( |( | |( |( | | |SG2 |calculate simple interest and compound interest; use and interpret graphical representation of simple and compound interest | | | | |( | | |( | |( | | | |SG3 |recognise, sketch and interpret graphs of quadratic functions, reciprocal functions, polynomial functions of the form y = xn and exponential functions y = k x for positive values of k | | | | |( |( | |( |( |( |( |( | |SG4 |interpret the gradient at a point on a curve as the instantaneous rate of change and apply the concepts of average and instantaneous rates of change (gradients of chords and tangents) in numerical and graphical contexts | | | | | | | |( |( |( | |( | |SG5 |calculate with roots, and with integer and fractional indices | | | |( |( | | |( | |( |( | | |SG6 |recognise and interpret linear and quadratic sequences; deduce expressions to calculate the nth term of linear and quadratic sequences | | | | |( | | | | |( | | | |SG7 |recognise, use and interpret sequences, including those given by a formula for the nth term, those generated by a simple relation of the form xn + 1 = f(xn), Fibonacci sequences and the golden ratio | |( | | |( |( |( | | | |( | | |SG8 |understand and use sigma notation | | | | |( | | | |( | | | | |SG9 |recognise, use and interpret arithmetic series, including the general term of an arithmetic series and the sum to n terms of an arithmetic series | |( | | | |( | | | | | | | |SG10 |recognise, use and interpret geometric series, including the general term of a geometric series, the sum to n terms of a geometric series and the sum to infinity of a convergent geometric series including the use of |r| < 1. | |( | | |( |( | | | | | | | |

Topic 1: Social media

Teaching time

4–6 hours

Specification references

A1, A3, A4, A5, A6, A8

Overview

An increasing number of people access and use social media in some form. The number of adults accessing the Internet every day in Great Britain increased from 16 million to 33 million between 2006 and 2012. One of the most significant changes to the ways in which individuals communicate over the Internet has been the recent growth in social networking. Almost half of all adults in Great Britain, (48%) used social networking sites such as Facebook and Twitter in 2012. The websites identified below give access to a wealth of data which students can use to compare and analyse the use of social media by age group and gender. They can also use primary data to investigate the use of social media, for example amongst their peers. Students need to understand the limitations of sampling techniques and be able to perform statistical calculations on relevant grouped discrete and continuous data and interpret their results. They should also recognise correlation and know that it does not indicate causation.

Resources

MEI: Critical Maths: Guessing the answers (A1)

Nuffield Foundation: Parking permits (A1)

Nuffield Foundation: Pay rates for men and women (A3)

MEI: Critical Maths: Is this a valid argument? (A6)

CMSP: Averages and spread 2 (A3, A4, A5)

CMSP: Averages and spread 3 (A3, A4, A5)

Source material for comprehension

CMSP: Scams

PewResearchCenter

Ofcom

Office for National Statistics

Ericsson

Topic 2: Society

Teaching time

20–22 hours

Specification references

A2, A3, A4, A5, A6, A7, A8, A9, P7, LP2, LP6, LP7, LP8, LP9, LP10, SG7, SG9 SG10

Overview

This topic looks at society and social trends. Social trends explain the behaviour of people. They relate to social and cultural values and practices within a society and are relevant to all members of that society. Students need to be able to use and apply standard statistical techniques to compare and analyse data. They should be able to compare distributions through appropriate graphical representations as well as use, apply and interpret linear regression. Students should be able to understand and interpret risk. They should be able to translate simple situations or procedures into algebraic expressions and apply linear programming techniques to solve and interpret two-variable problems including problems where solutions must have integer values. Students also need to be able to recognise, use and interpret arithmetic series. They should be able to use calculators and spreadsheets effectively to support their calculations. Examples of trends which are impacting on society at present include: the distribution of entrants to HE by previous educational institution; changes in type of house ownership, various measures of inequality and how they correlate, Data based on the recent history of the proportional take up of consumer durables can form the basis of student investigations.

Resources

Nuffield Foundation: HE applications (A2, A3, A4, A5)

CMSP: Population data (A3, A4, A5, A6, A7, A8, A9)

University of Cambridge: Evaluating Risk (P7)

National Stem Centre: Linear programming (LP7, LP8, LP9, LP10)

Nuffield Foundation: Chaotic population (SG7)

Maths Tutoring: Modelling with sequences (SG7, SG10)

CMSP: Maximising profit (LP1, LP2, LP7, LP9, LP10)

CMSP: Assessment one: basic skills − rates of pay (A1, A3, A4, A5)

CMSP: Assessment two: basic skills − banks (A1, A3, A4, A5)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 12 Moving Averages (A2)

Chapter 13 Risk (P7)

Chapter 9 Linear Programming (LP9, LP10)

Link to zip file

Source material for comprehension

Office for National Statistics: Social Trends

.UK: Social trends

The Guardian: Social trends

Population Reference Bureau

Gap Minder

Maths Surrey.ac.uk

mathmaine.

Topic 3: Sport

Teaching time

8–10 hours

Specification references

A1, A3, A4, A5, A6, A7, A8, A9, A10, P2, P3, P4, P5, LP1, LP2

Overview

There is a wealth of data available for students to be able to investigate areas related to sport, including attendances at fixtures, revenue, comparison of scores and pay rates of players. The ranking systems used in sports such as tennis, football and golf give students opportunities to review the validity of measures, and the use of Time-based averages. Developing models of the improvements in athletics world records will give students insights into the limits of extrapolation. Students need to be able interpret and construct statistical diagrams, perform statistical calculations on relevant data and interpret their results. They need to use statistical diagrams to compare outcomes, for example on team performance, and work with probability to look at areas such as drug testing. There are opportunities for students to consider combinations of probabilities and how they are represented diagrammatically.

The Mascil Project has a number of projects which could be used as part of class discussion.

Sports physiology and statistics looks at the correlation between heart rate and physical fitness.

Resources

Pearson Mathematics in Context Winter Olympics (A1, A4, A5, A8, A10)

Nuffield Foundation: Sports injuries (A3)

Nuffield Foundation: Pay rates for men and women (A3, A4, A5)

Nuffield Foundation: Football figures (A3, A4, A5)

Nuffield Foundation: Sports injuries (A3, A4, A5)

University of Cambridge: Drug testing (P5)

CMSP: 100 m sprint (A6, A7, A8, A9)

CMSP: Experiments with marbles (P2, P3, P4)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 4 Probability and Venn Diagrams (P3, P5, P6)

Link to zip file

Source material for comprehension

University of Cambridge: Maths and Sport

Statistics in Sports

Sport and Recreation Alliance

+Plus Magazine

Topic 4: Clothing industry

Teaching time

16–18 hours

Specification references

A4, P2, P6, P7, LP1, LP2, LP3, LP4, LP5, LP6, LP7, LP8, LP9, LP10, LP11, SG1, SG5

Overview

There is a wealth of data associated with the clothing industry that lends itself to a variety of investigations and problem solving tasks. Applications include borrowing money, compound interest, maximising profit, assessing risk, comparing and analysing sales, assurance and budgeting. Students need to be able interpret statistical diagrams, perform statistical calculations on relevant data and interpret their results. They need to work with probability, percentages and formulae for compound interest. Students need to be familiar with graphical inequalities and linear programming techniques. Linear Programming is particularly useful in manufacturing industries to assist in decision making regarding the best product mix to meet objectives. They should also be able to use calculators and spreadsheets effectively to support their calculations.

Resources

Nuffield Foundation: Pareto charts (A4)

Standards unit: Interpreting Bar Charts, Pie Charts, Box and Whisker Plots (A4)

Nuffield Foundation: Laws of probability (P6)

MEI: Screening (P6)

Teachit maths: Conditional probability puzzler (P6)

NRICH: probability – conditional (P6)

EBP: Balancing risk and reward (P7)

MEI: Making decisions involving risk (P7)

MEI: Business and risk (P7)

Nuffield Foundation: Linear programming (LP1, LP2, LP5, LP7, LP9, LP10, LP11)

CMSP: Maximising profit (LP1, LP2, LP5, LP7, LP8, LP9, LP10, LP11)

Nuffield Foundation: Linear inequalities (LP2, LP7)

Khan Academy: Solve linear equations in one unknown (LP4)

CIMT: Linear Programming (LP1, LP2, LP3, LP5, LP9 LP10) (Not simplex method)

MEI: Product pricing (SG1)

MEI: Additional Resources for Twinned Pair Pilot: Finance (SG1)

CMSP: Borrowing Money (SG1)

MEI: The Mathematics of Business and Finance: Compound interest (SG1, SG5)

CMSP: Experiments with marbles (P2, P3, P4)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 6 Financial and Business Applications (SG1)

Chapter 9 Linear Programming (LP9, LP10, LP11)

Chapter 13 Risk (P7)

Link to zip file

Source material for comprehension

FashionUnited

Office for National Statistics

Topic 5: Finance

Teaching time

13–15 hours

Specification references

A1, A3, A4, A5, P7, LP1, SG1, SG2, SG3, SG5, SG6, SG7, SG8, SG10

Overview

The topic of finance includes aspects which are directly relevant to students of all ages. Applications include savings accounts, student finance, credit cards, tax, loans, mortgages, ISAs, pensions, insurance and budgeting. Students need to be able to use statistical diagrams like histograms and cumulative frequency charts to communicate financial information, and to perform statistical calculations on relevant data and interpret their results. They need to work with percentages and formulae for compound interest. Students also need to be able to compare financial terms, for example when considering loans and mortgages, to decide on the best deal.

They need to be able to work with data to assess risk, for example when considering investments and be able to work with exponential functions, for example in calculations involving depreciation. Students should be familiar with relevant vocabulary and acronyms such as AER and APR. Opportunities to practice and develop skills in financial maths can be found on the Core Maths Support Project website.

Some students’ courses of study will include subjects for which financial literacy is a key part. This topic offers opportunities for support and further development in those areas.

Resources

University of Cambridge: Evaluating Risk (P7)

Nuffield Foundation: Plumbers prices (LP1)

MEI: The Mathematics of Economics: Real Terms (SG1)

MEI: Additional Resources for Twinned Pair Pilot: Finance (SG1)

CMSP: Borrowing Money (SG1, SG2)

Nuffield Foundation: Working with percentages (SG1, SG2, SG5, SG10)

MEI: The Mathematics of Business and Finance: Student Loans (Part 1) (SG1, SG2)

MEI: The Mathematics of Business and Finance: Student Loans (Part 2) (SG1, SG2)

MEI: Working with Percentages: C Repeated Percentage Change (SG1, SG2)

Nuffield Foundation: Mathematical applications of finance (SG1, SG2, SG5)

Nuffield Foundation: Savings facts and formulae (SG1, SG2, SG5)

Nuffield Foundation: Savings growth (SG1, SG2, SG5, SG7)

Nuffield Foundation: Growth and decay (SG1, SG3, SG5)

Nuffield Foundation: Annual Percentage Rate (APR) (SG1, SG5)

Nuffield Foundation: APR with more than one instalment (SG1, SG5, SG8)

Nuffield Foundation: Credit Cards (SG1, SG7)

MEI: The Mathematics of Business and Finance: Compound Interest (SG2, SG3, SG5)

Nuffield Foundation: Financial calculations (SG5)

MEI: The Mathematics of Business and Finance: Multipliers (SG10)

CMSP: Assessment one: basic skills − rates of pay (A1, A3, A4, A5)

CMSP: Assessment two: basic skills − banks (A1, A3, A4, A5)

CMSP: Exponential growth and decay (SG2, SG3)

CMSP: Simple compound interest (SG1, SG2)

CMSP: Percentages in finance: assessment (SG1)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 6 Financial and Business Applications (SG1, SG2)

Chapter 5 Exponential Growth and Decay (SG1, SG3)

Chapter 13 Risk (P7)

Link to zip file

Source material for comprehension

Rates and Allowances: HM Revenue and Customs

Financial Times

The Economist

Exchange Rates

Topic 6: Creative arts

Teaching time

11–13 hours

Specification references

A10, LP1, LP2, LP3, SG3, SG7, SG9, SG10

Overview

The Creative Arts offer many examples of the application of mathematics. The functional relationships between the lengths of a taut string and the frequency of the note produced gives an example of inverse proportionality. Similarly the relation between aperture and f numbers in photography offers another functional relationship. A study of the Fibonacci sequence and how it leads to the ratio of the “golden section” provides a fundamental link between mathematics and aesthetics. Students need to be able to use, apply and interpret Spearman’s rank. They should be able to translate simple situations or procedures into algebraic expressions and apply linear programming techniques to solve and interpret two-variable problems including problems where solutions must have integer values. Students also need to be able to recognise, use and interpret arithmetic series. They should be able to use calculators and spreadsheets effectively to support their calculations.

The Mascil Project has a number of projects which could be used as part of class discussion. Circular paving stones looks at arranging paving leaving the minimum empty space. Design your own non standard bookshelf looks at using regular polygonal cells for storing books. Tesselations and the World of Work is a 7 minute video based on student experience of building a bookcase.

Resources

CMSP: Best Song Ever (A10)

Get the Math: Math in special effects (LP2, LP3)

Photography and Math (SG3)

The magical mathematics of music (SG3, SG7) 

Fibonacci numbers and the golden section in art, architecture and music (SG7)

Visual Thesaurus: Where math meets poetry (SG7)

Arts Edge: How the hidden life of numbers makes memorable music (SG7)

TES: Maths of the fretboard (SG7, SG10)

CMSP: Maximising profit (LP1, LP2, LP7, LP9, LP10)

Source material for comprehension

+plus Magazine: Art+Math=X

+plus Magazine: Maths and Art

Math for Grownups: The math of poetry

Filmmaker IQ: The history of aspect ratio

Digital video theory

Information is Beautiful by David McCandless, Collins ISBN 978-0-00-729466-4

The Visual Display of Quantitative Information by Edward R Tufte, Graphics Press Connecticut ISBN 978-0-9613921-4-7

Topic 7: Health

Teaching time

18–20 hours

Specification references

A1, A3, A4, A5, A6, A7, A8, P1, P3, P4, P5, P7, SG1, SG7

Overview

The topic of health covers a wide range of aspects from disease to diet and healthy eating. Students need to be able to use and apply standard statistical techniques to compare and analyse data. They should be able to compare distributions through appropriate graphical representations as well as use, apply and interpret the product moment correlation coefficient. Standard growth charts of young children provide opportunities for reinforcing concepts like the median and the various percentiles. There are also opportunities to explore functional relationships in areas like radiography and the administration of drugs. Students should be able to calculate the probability of independent and dependent combined events; calculate and interpret conditional probabilities as well as understand and interpret risk. They should be able to translate simple situations or procedures into algebraic expressions and apply linear programming techniques to solve and interpret two-variable problems including problems where solutions must have integer values. Students also need to be able to translate simple situations into algebraic expressions then derive an equation and solve it. The understanding of how epidemics occur, develop and can be controlled is a vital aspect of health and the application of mathematical sequences enables health professionals to manage epidemics.

The Mascil Project has a number of projects which could be used as part of class discussion.

Drug concentration looks at how the level of medication in the blood changes over time.

Resources

Pearson Mathematics in Context Ebola (A3, A4, A5, SG1, SG7)

Nuffield Foundation: Five a day (A1, A3, A5)

Nuffield Foundation: Heart rate (A3, A4, A5, A6, A7, A8)

CMSP: Well or unwell (A4)

CMSP: Baby boom (A5)

University of Cambridge: Disease Dynamics Schools Pack (P3)

University of Cambridge: The test is positive: But what are the odds it’s wrong? (P3, P4, P5)

MEI: Screening (P4)

University of Cambridge: Life-saving maths: How does vaccination work? (P7)

Bowland: How Risky is Life? (P7)

CMSP: Cormathzadrine (SG1)

CMSP: Averages and spread 2 (A3, A4, A5)

CMSP: Averages and spread 3 (A3, A4, A5)

CMSP: Anthropometric data (A1−A10)

CMSP: Bivariate data (A7)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 1 Venn Diagrams (Prior knowledge for P3, P4)

Chapter 4 Probability and Venn Diagrams (P3, P5)

Chapter 13 Risk (P7)

Chapter 5 Exponential Growth and Decay (SG1)

Link to zip file

Source material for comprehension

World Health Organization

Centers for Disease Control and Prevention

Health and Social Care Information Centre

OECD Health Statistics 2015

The World Bank: Health, nutrition and population statistics

Topic 8: Economy

Teaching time

15–18 hours

Specification references

A2, A3, A8, P2, P3, P4, LP2, LP3, SG1, SG2, SG3, SG4, SG5

Overview

This topic covers many aspects which lend themselves to relevant mathematical scenarios related to everyday life. These include inflation, retail price index, pay rates, housing prices, marketing and stocks and shares. Students need to be able to perform statistical calculations on relevant data and work with given formula and percentages, including the effective use of multipliers. They also need to be able to work out the equation of a straight line and interpret the meaning of the gradient and intercepts on the axes related to the given data, giving students the opportunity to model economic variables. Students should be familiar with relevant vocabulary such as inflation and retail price index. Opportunities to practice and develop skills in the Economy can be found on the

CMSP website.

Resources

Nuffield Foundation: House price moving averages (A2)

Nuffield Foundation: Pay rates for men and women (A3)

Khan Academy: Fitting a line to data (A8) (A8)

Nuffield Foundation: Correlation (A8)

University of Cambridge: The economics of health: How do we decide? (P2, P3, P4)

Nuffield Foundation: Probability (P3)

Nuffield Foundation: Laws of probability (P3)

Nuffield Foundation: Linear graphs (LP2, LP3)

Nuffield Foundation: Match linear functions and graphs (LP3)

MEI: The Mathematics of Economics: Real Terms (SG1)

MEI: The Mathematics of Business and Finance: Elasticity (SG3, SG4)

CMSP: Percentages in finance: assessment (SG1)

CMSP: Simple compound interest (SG1, SG2)

CMSP: Annual percentage rate (SG2, SG5)

CMSP: Borrowing money (SG1, SG2)

CMSP: Build or buy? (SG1, SG2, SG5)

CMSP: Stocks and Shares (SG1)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 1 Venn Diagrams (Prior knowledge for P3, P4)

Chapter 5 Exponential Growth and Decay (SG1, SG3)

Chapter 6 Financial and Business Applications (SG1, SG2)

Chapter 12 Moving Averages (A2)

Link to zip file

Source material for comprehension

Statistics

The Economist

Nuffield Foundation: Financial graphs and charts

Topic 9: Travel

Teaching time

6–8 hours

Specification references

A1, A2, A3, A4, A5, A6, A7, A8, A9, LP1, LP2, LP3, LP5, LP6, SG3, SG4, SG8

Overview

Opportunities are available for students to compare numbers of travellers and costs of travelling by different modes of transport, as well as numbers visiting the UK and amounts spent. Students should be familiar with working out moving averages to look for seasonal trends and well as comparing the numbers travelling to different destinations, using a variety of methods for displaying and interpreting data. Students need to be familiar with the algebraic form of the equation of a straight line and be able to solve simultaneous equations both algebraically and graphically. Students can make use of the Highway Code “stopping distances” data to explore functional relationships between speed and stopping distance and to contrast the relationships between speed and “thinking distance” and “braking distance”. This work can then lead to a consideration of the concepts of velocity and acceleration as instantaneous rates of change of displacement and velocity respectively.

The Mascil Project has a number of projects which could be used as part of class discussion. Amberhavn: new bus network looks at creating a new bus network for an old European city.

Resources

Nuffield Foundation: House price moving averages (A2)

Nuffield Foundation: Rain or shine (A5)

Khan Academy: Range, variance and standard deviation as measures of dispersion (A5)

Nuffield Foundation: Plumbers prices (LP1, LP2, LP5)

Exam solutions: Simultaneous equations (LP5)

Nuffield foundation: Simultaneous equations on a graphics calculator (LP5)

Khan Academy: Linear inequalities (using set notation) (LP6)

Exam solutions: Inequalities (LP6)

Math Centre: Sigma notation (SG8)

CMSP: Population data (A1, A3, A4, A5, A6, A7, A8, A9) (not equations of regression lines nor how to calculate correlation coefficients)

CMSP: Practice time (A3, A4, A5)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 12 Moving Averages (A2)

Link to zip file

Source material for comprehension

National Travel Survey Statistics

National Travel Survey – Transport

Travel Trends

Transport Statistics

Visit Britain

Topic 10: Environment

Teaching time

10–12 hours

Specification references

A2, A5, A6, A7, A8, A9, LP2, LP3, SG1, SG2, SG3, SG4, SG5, SG6

Overview

Students need to be able interpret and construct statistical diagrams, perform statistical calculations on relevant data and interpret their results. In this topic, this could be in relation to areas such as climate change, waste disposal and the Ozone layer. Students need to use statistical diagrams to compare outcomes, for example in changes in climate over time, and be able to use mathematical modelling to make predictions. There are opportunities for exploring correlation by comparing different environmental variables and consider the extent to which correlation may be evidence for causal links.

The Mascil Project has a number of projects which could be used as part of class discussion. The Water Quality activity combines mathematics and chemistry in a project looking at the quality of water. Closed greenhouses looks at regulating temperature to keep energy costs as low as possible. Solar cells looks at the value of installing solar panels.

Resources

Pearson Mathematics in Context Waste and recycling (A6, A7, A8, A9)

CMSP: Climate change (A2)

Nuffield Foundation: Rain or shine (A5)

Nuffield Foundation: Spreadsheet graphs ( LP2, LP3, SG3)

Nuffield Foundation: Tides ( LP2, LP3, SG3, SG4)

CMSP: Horse manure (SG1)

Nuffield Foundation: Climate prediction (SG3)

Nuffield Foundation: Ozone hole (SG3)

CMSP: Wind chill (SG5)

CMSP: 100 m sprint (A6, A7, A8, A9)

CMSP: Anthropometric data (A1−A10)

CMSP: Bivariate data (A7)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 6 Financial and Business Applications (SG1, SG2)

Chapter 5 Exponential Growth and Decay (SG1, SG3)

Chapter 10 Gradient of Graphs (SG4)

Chapter 2 Quadratic Sequences (SG6)

Chapter 12 Moving Averages (A2)

Link to zip file

Source material for comprehension

Environment data

The World Bank

OECD Environmental Data

UNSD Environmental Indicators

European Environment Agency

Topic 11: Disasters

Teaching time

4–6 hours

Specification references

A1, A3, A4, A5, A6, A7, A8, A9, SG1, SG3, SG5, SG7

Overview

There is much scope within the topic area of disasters, with much of the data readily available. Natural disasters are regularly in the news and may be a good source of interest for students. Resource data and material are readily available for catastrophes such as earthquakes, tsunamis, volcanoes, hurricanes and tornadoes. Students need to be able interpret and construct statistical diagrams, perform statistical calculations on relevant data and interpret their results. They need to use statistical diagrams to compare outcomes, for example on changes in features of natural disasters over time and be able to use mathematical modelling to make predictions. Students need to be able to recognise patterns and interpret sequences.

Resources

Pearson Mathematics in Context Earthquakes (A5, A6, A9, SG5)

Edexcel GCSE Statistics 01 2ST01 June 2001 Q9 (A5)

Math Skills for Science: Earthquake power (SG1)

STEM Central: Mathematical Modelling Learning (topic intro)

CMSP: Population data (A1, A3, A4, A5, A6, A7, A8, A9) (not equations of regression lines nor how to calculate correlation coefficients)

CMSP: Practice time (A3, A4, A5)

Pearson GCSE Mathematics Linked Pair Pilot resources:

Chapter 6 Financial and Business Applications (SG1)

Chapter 5 Exponential Growth and Decay (SG1, SG3)

Link to zip file

Source material for comprehension

+plusmagazine: Tsunami

NOAA Center for Tsunami Research

Passy’s World of Mathematics: Tsunami Mathematics

GNS Science: New Zealand volcanoes

National Centers for Environmental Information: Earthquake data

+plus magazine: Modelling catastrophes

+plus magazine: El Nino

St Thomas University, School of Science: Learning about hurricanes

The maths of natural disasters

Our Earth: Natural Disasters

6 Small Math Errors That Caused Huge Disasters

Topic 12: Engineering

Teaching time

10–12 hours

Specification references

A1, A3, A4, A5, A8, P4, P6, LP1, LP2, LP7, LP8, LP9, LP10, LP11, SG3, SG4

Overview

Much of the mathematics involved in the different disciplines of Engineering is beyond the scope of this qualification, but there are still a good number of topics which provide relevant study and opportunities to study the mathematical basis of some of the key functions that are encountered in engineering situations. Students need to be familiar with techniques to compare data sets through appropriate measures of central tendency. They should be able to calculate the probability of independent and dependent events and calculate and interpret conditional probabilities. Students also need to be able to use algebra to construct arguments and formulate problems as linear programs. One important aspect of working in engineering is how functions of the same mathematical form provide useful models to explain very diverse phenomena.

Resources

Freestudy.co.uk: Mathematics for Engineers (A8)

MEI: Mathematics Resources for Level 3 Engineering (P4, P6)

Learn About O.R.: SwedeBuild – Tables and chairs (LP8, LP9, LP10, LP11)

Learn About O.R.: Linear programming (LP8, LP9, LP10, LP11)

Centre for Innovation in Mathematics Teaching (LP1, LP2, LP3, LP5, LP9, LP10)

CMSP: Maximising profit (LP1, LP2, LP7, LP9, LP10)

Pearson GCSE Mathematics Linked Pair Pilot resources

Chapter 1 Venn Diagrams (Prior knowledge for P3, P4)

Chapter 4 Probability and Venn Diagrams (P5, P6)

Chapter 9 Linear Programming (LP9, LP10, LP11)

Link to zip file

Source material for comprehension

engNRICH

IET: Faraday[pic]

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