Bowland Maths

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 can adapt for their classes, supported by a full range of video, audio and print resources.

Crash test

Pupils use computer software to explore the impact of car crashes under varying conditions. Pupils can 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.

DigiDesign [Coming soon !]

Pupils are set in the role of graphic designers to create a digital image for a hand-held electronic device for an audience of children, aged 5-7 years old. This image is created using a web-based digital drawing tool package, based upon screen pixels. Pupils need to work individually and in small groups to discuss possible designs. They need to make decisions and communicate them about planning, designing, evaluating and re-designing their product. They also need to process information that comes in via 'management' memos, and to make recommendations about their product and present their final products.

Mathematically, Digidesign 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.

Explorers

In Explorers , pupils assume the roles 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 use sonic charges to destroy asteroids blocking a space highway.

The mathematics involved includes comparing probabilities, working with different currencies, working with linear equations, 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.

Highway link design

Highway link design creates opportunities 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 bring to such a development.

The mathematical concepts include scale, speed and 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 attitudes to risk are often driven by perceptions presented 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 is 'in' or 'out' in cricket. 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 explore whether the batsman 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 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.

Mega bank [Coming soon !]

Mega Bank is a 3D learning-based game in which pupils use proportional reasoning skills, forensic techniques and investigative methods to identify the culprit(s) of a crime - a daring robbery and murder at Mega Bank. Mega Bank contains five lesson plans to show how to integrate the series of activities in the classroom.

Pupils begin with information gathering in lessons 1 and 2, where they examine the crime scene, identify the key actors in the scenario, identify key unknowns, eliminate irrelevant information and determine the forensic and investigative methods they can use to progress and test unknowns. In lessons 3 and 4, pupils move on to analysis and interpretation, where they test, analyse and interpret samples and apply forensic testing and mathematical modelling to assess the evidence. They then use their results to explain, illustrate and draw conclusions.

My music

My music uses the interest pupils have in music as an opportunity for mathematical investigations, using their 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

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.

Outbreak

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. The learner works 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

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 roles 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.

Product wars

Pupils are asked to create a new range of 'smoothie' drinks. They use proportional reasoning to analyse their nutritional value and geometry to design their 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, to develop mixes for some 'smoothies' and then to 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 several 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 cameras

Speed cameras are 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. Lower probabilities do not invariably lead to fewer accidents, and the occurrence of more accidents in one year is not necessarily evidence of a higher probability. Pupils learn that random variation can obscure the underlying probability. These are difficult but fundamental concepts for pupils to understand, and the combination of ICT and continual referral to the 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

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 and repairs 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!

Velletri scrolls [Coming soon !]

Velletri scrolls is a 3D learning-based game where pupils assemble clues, unravel codes and solve problems to understand the meaning of the scrolls and to find the riches of the Emperor Augustus. In phase one, pupils gather evidence and tools to interpret maps and papers and to decipher mathematical problems. In phase two, pupils use the elements gathered in phase one, as well as analytical thinking and algebraic skills, to solve problems that progress the scenario.

Velletri scrolls supports different levels of difficulty, with the maths problems containing different solutions and more reward being given for more sophisticated solutions. This means that pupils can follow a path on their own terms and are not precluded from progressing. Any areas of difficulty are recorded which provides feedback to the pupil and to the teacher.

Water availability

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 available, 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.

You reckon?

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.