| The titles of the Case Studies are listed below. Clicking on a title will provide a short description of the Case Study concerned.
Alien Invasion is a set of interactive lessons about a full-scale alien attack that coincides with a class visit to Manford City. To set the scene and support the lessons, live TV news bulletins, radio broadcasts and telephone messages help to develop the story line. The invasion leads to a series of non-routine problems for pupils to solve as the narrative unfolds. The problems are on the theme of mathematical communication and are intended to promote discussion, reasoning and creativity.
Alien Invasion is an opportunity for pupils to apply and use skills that they have previously been taught and to see connections between mathematical topics. Alternatively, it can be used to introduce or extend skills. Mathematical activities include estimating and calculating measures, interpreting graphs and maps, code breaking and problem solving.
Alien Invasion includes lesson notes which teachers are able to adapt for their own classes, supported by a full range of video, audio and print resources.
Pupils take the role of consultants called in to save the space-borne tourist attraction AstroZoo. The zoo has four bio-domes, each housing a different alien creature with its own environmental needs. Pupils are divided into groups of three or four and select one of the four bio-domes to explore in order to solve, using mathematics, some critical environmental problems the zoo is facing. There are four missions, three using the computer, the fourth paper-based and suitable for homework. Pupils must use mathematics to discover how many creatures each dome can support with the available oxygen, find the right balance between food- and oxygen-producing plants, stabilise the temperature by optimising the numbers of power-producing panels and heat shields,and, finally, solve a predator/prey problem for a new dome. The mathematics involved includes number, algebra and geometry. Pupils are expected to identify the mathematical aspects of the situation, select the tools and information to use, explore the effects of varying values using the software, work logically towards the solution and communicate their findings in the report to the zoo’s managers.
Pupils use computer software to explore the impact of car crashes under varying conditions. Pupils select a car, a crash point and a speed, then watch an animation of the crash and see the results as physical impact on a simulated dummy and as numerical data.
In Crash test , there are 3 stages to the software: researching, testing and presentation. In the research centre, pupils decide which data to collect, they collect and analyse it and test hypotheses. In the test laboratory, pupils focus on hypothesis testing; they are able to test up to 14 pre-defined hypotheses and choose 3 ‘test packages’ in each case. In the presentation suite, there are tools such as varieties of graph paper and also help to prepare a presentation of their results to share with others.
DanceStar is a case study in which pupils explore the relationship between mathematics and different styles of dance. It aims to help pupils think about how the ideas within dance are composed of mathematical constructs – such as counting, measures of turn, and directional movement.Pupils can analyse different dance forms using mathematical language and notation.
The resources comprise a collection of videos depicting dance routines and moves from seven different dance genres; they introduce the concept of written notation to help dancers to communicate dance moves. Pupils discuss what they see in the videos, explore the movements involved and work on how they could be represented on paper, describing elements of the dance using notation they have devised themselves.
Design the Mascot
Pupils take the role of graphic designers in Design the mascot to create a mascot for a fictional new primaryschool. This image is created using a web-based digital drawing tool package, based uponscreen pixels. Pupils work both individually and in small groups to discusspossible designs. They make decisions and communicate them about the
planning, designing, evaluating and re-designing their product. They also process
incoming information via ‘management’ memos, and make recommendations about their
product and present their final products.
Mathematically, Design the mascot helps pupils to learn, use and apply concepts of dimensions, proportional enlargement, ratio and linear scale factors, connecting these to area scale factors. Pupils engage in whole-class discussions about the mathematics they have used within the design process.
In Explorers , pupils assume the role of various characters scratching a living at the very edge of our galaxy in 2084. Pupils develop the skills of thinking, reasoning and problem solving as they undertake three activities in an era of reclaimed space vessels patched up beyond recognition and with barely competent crew members. Pupils have to find a safe route through a dangerous nebula, trade goods between distant planets and destroy asteroids blocking a space highway using sonic charges.
The mathematics involved includes comparing probabilities, working with different currencies and working with linear and quadratic equations. Explorers includes a series of graphically rich, engaging, exploratory applets, as well as complementary paper-based tasks, follow-ups and homework tasks. Pupils can work on these tasks in small collaborative groups or individually.
The aim of Fashionista is for pupils to investigate the mathematics behind fashion trends. Using the ‘Trendsetter’ (software that has been designed for the Case Study), pupils run simulations of buying patterns in a fictitious shop over an eight-week period and analyse these through the use of charts and graphs; they can do this either including a price variable or without it. Using census population statistics, pupils can then work out how much stock they would need to buy in order to satisfy consumer demand for a particular trend within their own town or region.
Football: the beautiful game is based around video clips of the Swanscombe Tigers youth football team as they train and prepare for a game. There are three activities: pre-match training, passing the ball and penalties. Each activity provides opportunities for pupils to demonstrate their competence in using key mathematical skills and processes, and to encounter a range of curriculum content.
Goal of the Century!
Goal of the Century opens with the story of Diago Maradona’s two goals in the 1986 FIFA World Cup quarter-final against England. The first was the infamous “hand of God” incident. The second goal, however, was voted “Goal of the Century” in a 2002 survey. The pupils investigate why this particular goal is so famous and admired. They create a simple mathematical model to explore the contention that it is best ever goal (so far!). At the conclusion of the three lessons, each pupil will have developed a personalized model for evaluating any football goal – either from the past or in the future. Pupils use their model to rate the Goal of the Century and compare it to some other famous goals, including some of their own choosing.
Highway Link Design
Highway link design is an opportunity for pupils to integrate school mathematics with wider social, economic, environmental and work-related concerns. Pupils work in groups to plan and cost a village by-pass. They engage in problem-solving to decide which solution best takes into account the variety of issues and viewpoints that different stakeholders have about such a development.
The mathematical concepts include scale, speed and the measurement of curvature, which pupils need to balance against environmental and social factors; they then need to cost their chosen route. Pupils present their solutions and assess those of others. Specialised software is included, and extension activities create further opportunities for pupils to cost real by-passes, using Google Earth.
How Risky is Life?
In How Risky is Life? , pupils explore the risk of dying unexpectedly from various causes. They start from fears they know and, by comparing them with real-life data, they recognise that their perception of risk is often driven by presentations in the media. Pupils learn how to calculate the risks involved for various activities and how these are related to the base risk of death for typical people of different ages and genders. The emphasis is on order-of-magnitude comparisons, reflecting the variations in risk level between individuals and over time.
Pupils work with real data; they deduce information about small probabilities and use measures of average and spread in real life. They also work with orders of magnitude. They learn that mathematical thinking is essential for putting risks in perspective and that the media usually focus on stories rather than on information.
In or Out?
Pupils consider the evidence from a photograph about whether a batsman in cricket is ‘in’ or ‘out’. The original case arose from a controversial decision by an umpire in an 'Ashes' test match (between England and Australia) in the 1960s.
Pupils use mathematics to examine the photograph to assess whether the batman was ‘in’ or ‘out’. Initially, pupils construct a simple mathematical model of the situation by deciding what variables they need to measure and what assumptions they need to make. Using this evidence, they decide for themselves whether the batsman was ‘in’ or ‘out’. As the work develops, pupils explore these measurements and assumptions in detail, allowing them to refine their initial decisions and to understand that, sometimes, there is no single right answer!
Pupils revisit their models, test their assumptions and apply their model to other situations. The mathematical skills and thinking that are required emerge gradually during ‘In or Out?’
Keeping the Pizza Hot
Keeping the Pizza Hot Hot involves building a mathematical model in the context of home-delivery pizza. Pizza home-delivery is dependent on being able to deliver pizzas quickly, in an edible condition. In Keeping the Pizza Hot, pupils explore ways to keep a pizza warmer for longer and the implications of doing so. Pupils are asked to help answer the questions: how long does it take a pizza to cool, how far can it travel in that time and what difference does the packaging make?
Keeping the Pizza Hot has a number of parts which include leading pupils to move from a practical problem of a cooling pizza to a mathematical representation of a cooling curve. This is a big step and is intended to induct pupils into the potential of mathematical applications. It demonstrates how mathematics can underpin scientific enquiry. The linking of the time to cool with possible distances of travel introduces further mathematics.
Although not essential, this project would work well as a cross-curricular project with the science department.
Mission: Rainforest is a set of exciting interactive lessons themed around an environmental mission to save the rainforest from deforestation. Deep in a tropical rainforest, a team of 12 undercover environmentalists is on a mission to investigate and expose the illegal activities being carried out by a multinational logging organisation, Log Inc. This company is contributing to the deforestation that is destroying the planet. It will be a dangerous mission. Once they have set up base camp, the environmentalists will work in small groups to use all their cunning and intelligence to monitor the damage while evading detection and collecting evidence for UN international inspectors. The problems are intended to promote discussion, reasoning and creativity and to encourage pupils to apply their mathematical knowledge to real life situations.
My Music uses the interest pupils have in music as an opportunity for mathematical investigations, using pupils' own favourite music tracks as the raw data. Pupils work in small groups to listen to different tracks, take measurements and then interpret and present the results. They analyse the similarities and differences between types of track, looking first at tempo and then other variables such as track length, highest position or number of weeks in the charts, and album sales; they can also investigate trends in music over the years.
My Music can work as an introduction to statistical work, including: the collection of numerical data, performing basic statistical calculations, forming and testing hypotheses, making inferences about a population, and identifying potential sources of error in data collection and calculations. Although not essential, this project would work well as a cross-curricular project with the music department.
Mystery Tours is a cartoon-based role play. Pupils take the part of the Tour Manager of a struggling tour operator; they are asked to plan a fictitious three day trip around the UK using tools and data in the software. They then lead a ‘simulation’ of the tour and write an evaluation report. There are three groups of tourists, categorised as ‘Nature Lovers’, ‘Thrill Seekers’ and ‘Culture Vultures’; data is available about the preferences of each group.
Pupils work together in small groups, or individually, to create a successful trip. In the first stages of the exercise, the most important skills are working with data such as timetables and percentages. Other areas of mathematics are brought in when the trip begins. The tourists are quite demanding, and it is up to the pupils to keep them happy by solving any problems that may arise, presented algebraically or geometrically.
One of the features of Olympic Games history is that women have had to win a series of battles to be able to compete. However, since they have been competing, there have been many cases where the women, at least for a while, have been improving faster than men.
Is this trend likely to continue until women are out-performing men?
One source of relevant data to help model the development of men’s and women’s performances is the winning performance in men’s and women’s events over successive Olympics. This data is not ‘tidy’. There are trends, but there are also many ‘outlier’ performances –a performance that is quite different from the overall trend. A feature of this case is dealing with this authentic data, recognising and dealing with outlier results and determining how well the data allows the question to be answered.
Outbreak is centred on an outbreak of a fatal virus. Pupils play the role of a scientist trying to contain the spread of the disease. Pupils have to develop a strategy which will help find the infected people, create an antidote and plan a vaccination programme to minimise the further spread of the virus. Pupils work with different experts to help with the challenges.
Completing an activity in any one of the ‘bunker areas’, unlocks a code which can then be used in the Map Room to reflect the progress that individuals or groups have made. This provides the opportunity either for the whole class to work through different activities at the same time, or for independent progression. It also promotes group work discussion and real world interaction.
PointZero is an adventure-driven puzzle game based around the central themes of survival, escape and the quest to uncover the truth. Pupils assume the role of three lead characters who have awoken trapped in strange and varying locations in an unfamiliar urban environment, following an undisclosed event. They are encouraged to use their mathematical skills to overcome problems so that each character can gain access to the ‘PointZero’ Building.
Examples of activities include exploring complicated number sequences to scale a high rise building, using loci to find the way out of a complex underground network and reproducing geometrical patterns to deactivate a museum security system. PointZero encourages pupils to reflect on how numbers, algebra and geometry influence our daily lives, albeit in ways which may not be immediately apparent.
Pupils are asked to create a new range of ‘smoothie’ drinks. They use proportional reasoning to analyse the nutritional value and geometry to design the packaging.
In Product Wars , pupils play the role of being part of a drinks company and work with other employees to research and design the ultimate range of ‘smoothie’ drinks. The Managing Director of the company, Brad King, asks pupils to carry out market research, develop mixes for some ‘smoothies’ and then design and create the packaging. Video is used at key points in the lessons to provide support and guidance.
Activities include: using enquiry-based learning to collect and analyse information from peers in developing the product; using ratio and proportion, percentages and a spreadsheet to mix the ingredients in different quantities to obtain the right nutritional value and taste for the target sector; and identifying suitable packaging designs. Pupils receive feedback via texts from members of the product team and video messages from Brad King himself.
Reducing Road Accidents
Pupils imagine that they live in a small town where, over the past year, there have been a large number of road accidents. The town council has set up an enquiry to see what could be done to improve the situation and has allocated £100,000 to spend on reducing the number of deaths and serious injuries. In Reducing road accidents , pupils choose from a wide range of possible initiatives, for example, to build new road crossings or roundabouts, to install traffic lights or to design publicity campaigns for specific groups of people.
Pupils work in small teams to plan the most effective way to allocate the money. To support this work, the police have provided data on all the road accidents. Pupils use a specially constructed computer program to analyse this data and build a convincing case for their proposal.
Save a Baby Kangaroo
Save a Baby Kangaroo is an authentic context in which the pupils find a young orphaned kangaroo just twelve centimetres long and weighing sixty grams. Different species of kangaroo have different nutrient needs at different stages of their growth. Through video clips, photographs and data such as birth to adult weights, pupils become familiar with a range of data about the different species of kangaroo. They then use the data to identify which kangaroo they have found and develop a feeding programme to save the life of their own ‘Joey’ in a simulation. Finally they communicate what they have learned in order to help someone else save a Joey by making a poster for a Vet clinic.
The mathematical content of Save a Baby Kangaroo includes creating alternative representations of data and communicating statistical information.
Speed camerasare a continuing source of controversy, and even the experts are divided on their effectiveness. This is partly because the random nature of accidents makes it difficult to draw valid conclusions, which opens up possibilities for accidental or deliberate misrepresentation of data.
Speed cameras uses video and newspaper resources to motivate discussion with and among pupils; this is combined with the use of spreadsheets to model the random occurrence of accidents over a year. Pupils realise that lower probabilities do not invariably lead to fewer accidents, and that the occurrence of more accidents in one year is not necessarily evidence of a higher probability. They learn that random variation can obscure underlying probabilities. These are difficult but fundamental concepts for pupils to understand, and the combination of ICT and continual referral to a real situation helps to bring them alive. The emphasis is on pupils interpreting and extrapolating from data and using data to support their arguments – and to examine the arguments of others.
Sundials introduces pupils to the idea of using the sun to tell the time, applying a range of mathematical skills to understand some of the theory - and to construct at least one sundial for themselves. A video about sundials provides the context, including footage explaining the history of sundials and how they work. An interview with Harriet James, a gnomonist (someone who makes sundials) shows how maths is essential to the construction of sundials.
The classroom work is differentiated into three tiers. Depending on the route followed, Sundials uses symmetry and the drawing of angles, nets, origami, circle work and comparing data. Every route includes reading information from graphs and calculating time. Sundials invites pupils to reach out to the clockwork of the heavens!
Torbury Festival iis a set of interactive lessons around the staging of a music festival. To overcome various challenges, from floods to escaped cattle to over-excited crowds storming the stage, pupils must apply their mathematical knowledge to real life situations. The problems are intended to promote discussion, reasoning and creativity in order to ensure that the festival is a success!
Pupils take the role of administrators for an international aid agency charged with providing water resources to countries in the Middle East and North Africa. Pupils examine ways to compare the availability of water fairly between the countries and then determine which country is most in need. In Water availability , pupils review documents that describe the importance of water in the region and assemble relevant data.
Pupils come to recognise that a key aspect of data handling is to determine which data it is appropriate to use to answer a particular question. In Water Availability, the analysis requires the creation of compound measures, such as per capita measures of water availability, which links to the maths of proportionality. Pupils realise that compound measures are important to enable fair comparisons to be made between countries of various sizes.
The media (and political speeches) are full of claims about how long things will take, how much things will cost and how tricky problems can be solved. The public needs to be able to judge if these claims are reasonable. You reckon? develops pupils' ability to make estimates about unusual quantities using only limited information, by posing interesting questions such as "Is it possible to provide 20% of the diesel used for road transport in the UK by growing crops on 'set aside' land?".
You Reckon? develops mathematical thinking and requires pupils to communicate their solutions. Pupils see that the problems they are asked to solve are the same problems faced by aid agencies, governments, and salesmen! You Reckon? helps pupils to recognise the power of even simple mathematics (together with smart thinking) when making decisions about important topics.
©2012 Bowland Charitable Trust