Choosing a classroom project
This document serves as a quick reference and comparison guide, but is no substitute for exploring the case studies themselves. Each case study itself includes a more extensive description of its content, pedagogical aims and practicalities. These descriptions can be found in the Classroom projects section of this website.
Taking on a full 3-5 lesson project is a big initial step. Alternatively, each of the Professional Development modules incorporates two or three sample tasks and suggested lesson plans, which have similar themes to the case studies but are designed to be completed in a single lesson. You can view the PD materials to see how teachers have incorporated these tasks into lessons and how they and their pupils got on. Likewise the stand-alone assessment tasks can be completed in 20 minutes to an hour, and might provide a starting point before you commit to a multi-lesson case study.
Problem types and practicalities
This comparison chart shows the general types of problem encountered in the Case Study projects, the suitability for age and ability groups and other practical considerations, like extra resources needed.
- Type of problem
- The projects cover six broad types of problem – planning and organizing; designing and making; modelling and explaining; exploring and discovering relationships; interpreting and explaining; solving logic puzzles. A case study may have more than one of these aspects.
- Time required
- The number of (typically) 1 hour lessons suggested to cover the material
- Suitability for age and ability groups
- In terms of low, medium and high ability in UK school years 7-9 (ages 11, 12, 13)
- Resources needed
- Some Case Studies need computers or an interactive whiteboard for all or part of the project – a few case studies require other resources
Content areas, concepts and processes
One aim of the Bowland materials is to encourage pupils to choose, combine and apply mathematical tools from across the curriculum. Consequently, each project typically covers a range of mathematical topics, and a particular topic may only form a small, or optional part of a project, so sorting the projects by specific mathematical topic is not particularly useful. The table below summarises the content in terms of the three main curriculum areas of Number, Geometry and Statistics.
The table also shows the Key Concepts, Key Processes and Curriculum Opportunities from the 2008 English National Curriculum. While this language is not part of the 2014 curriculum, the framework is still useful for analysing the problem solving and mathematical thinking skills requirements of the new curriculum.
Examples of mathematical activities
This summarises the specific mathematical activities involved in some of the case studies
- Alien Invasion
- Locate spaceships using clues to estimate and calculate distances and directions. Interpret graphs and maps to plan an escape; crack a code to escape from a cell. General problem solving.
- Solve problems associated with keeping creatures in a closed environment – oxygen supply, heat, power – using proportional reasoning and linear relationships.
- Crash Test
- Control variables systematically (e.g. speeds, design of cars, barrier types). Make hypotheses and test them by observing the effects in crash test experiments. Present findings to the class.
- Devise notations to describe the moves in various styles of dance.
- Design the Mascot
- Design a toy character for a 60 by 80 pixel display. Scale proportionately for different types of display. Conduct market research into the design.
- Plan a route in space, bearing in mind fuel, food reserves and distance. Trade between planets using fantasy units of currency. Use algebraic functions to decide where explosive charges should be placed to destroy asteroids.
- Use charts and graphs to analyse buying patterns in a ficticious shop. Combine these with population data to predict sales and plan stock buying.
- Analyse players’ performances on various training exercisies to select a team. Explore the geometry and timing of passing a football. Investigate the probabilityof scoring with penalty shot aimed at different parts of the goal.
- Highway Link Design
- Propose the location of a by-pass, using data tables and graphs from the Highways Agency. Find ways to satisfy constraints (minimum radii of curvature, verge clearance, cambers etc). Cost and present proposed solutions.
- How Risky is Life?
- Compare perceptions of the causes of death with actual statistics. Interpret very large and very small probabilities. Decide what these say about behaviour and attitudes. Explore random variation.
- In or Out?
- Use photographic and slow motion evidence to decide qualitatively, then quantitatively, whether a batsman (in cricket) is ‘in’ or ‘out’. Select variables, make estimates of distances, times and speeds and use algebraic models.
- Keeping the Pizza Hot
- Choose packaging for a pizza. Measure temperatures as the pizza cools. Use data logging software. Fit a graphical model to the cooling of a pizza. Calculate the longest reasonable travel time before a pizza becomes too cold to eat.
- Mission: Rainforest
- Choose a camp location on a map using unit conversion, estimation, volume and surface area calculations and co-ordinate geometry. Apply multiple mathematical techniques to make plausible estimates about the effects of deforestation.
- My Music
- Describe the characteristics of individual genres of music. Use the tempo of music and other variables to illustrate compound measures, eg beats per minute.
- Mystery Tours
- Plan a 5-day trip to satisfy money/time constraints and to keep happy three sets of tourists with different requirements. Convert currencies, satisfy baggage allowances etc.
- Interpret the records of men’s and women’s athletics performance over the years to decide if women are set to out-perform men in the future.
- Use coordinate clues to locate infected people. Mix ingredients in proportions to create an antidote. Use resources optimally to design a vaccination programme.
- Solve number, spatial and logic puzzles to progress in an escape adventure game. Use number sequences to escape from a building. Use rotation and reflection to recreate a given pattern. Use codes and loci to escape from underground tunnels.
- Product Wars
- Design a questionnaire and conduct market research for a new drink. Mix ingredients to obtain nutritional value and taste; design packaging for the drink.
- Reducing Road Accidents
- Explore a town’s accident database. Control variables to decide on the most effective allocation of a sum of money to provide safety measures. Prepare a case and present it.
- Save a Baby Kangaroo
- Determine the age and species of a ‘Joey’ from tail and foot measurements and graphs of growth data. Devise an appropriate nutrition regime from tables of nutrient data. Present and justify this regime.
- Speed Cameras
- Explore perceptions of randomness and relate this to the perceived effectiveness of speed cameras. Simulate the effects of different sitings.
- Design, examining the maths, and then construct a sundial, using symmetry, angles, nets, origami, graphs and charts.
- Torbury Festival
- Plan how to drain a flooded site using areas, volumes and rates of change. Plan the stock for a stall, considering profit margins and limited space. Choose the optimum position for lookout towers using geometry, such as similar triangles.
- Water Availability
- Analyse a complex decision faced by a water aid agency. Devise and use a compound measure (eg per capita) to decide on a 'fair' distribution of resources.
- You Reckon?
- Break a problem into its component parts; combine everyday knowledge to create chains of reasoning that result in reasonable estimates of useful quantities.