Overview

Pupils examine a photograph of the position of a batsman (perhaps) being 'run out' in cricket and then construct a simple model 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, test their assumptions in detail and revisit their model and apply it to other situations. This allows them to refine their initial decisions and to understand that, sometimes, there is no single right answer! The original case arose from a controversial decision by an umpire in an 'Ashes' test match (between England and Australia) in the 1960s.

The mathematical skills and thinking that are required emerge gradually during the Case Study.

Mathematical content

Select variables, make estimates of distances, times and speeds and use algebraic models.

Specific Key Stage 3 National Curriculum areas covered include:

• Key processes - identify the mathematics needed; use mathematical procedures in combination; create convincing arguments and generalisations; consider their assumptions and the accuracy of their work; communicate their results effectively and discuss results.
• Number and algebra - rational numbers, their properties and their different representations; rules of arithmetic applied to calculations and manipulation with rational numbers; accuracy and rounding; linear equations, formulae, expressions and identities.
• Geometry and measure - similarity, scale; units, compound measures and conversions.
• Statistics - presentation and analysis of grouped and ungrouped data.
• Curriculum opportunities - use open and closed tasks in a variety of contexts; select the mathematics to use and bring together different aspects of concepts, processes and Mathematical content; tackle problems from other subjects; group and individual work.

Organisation and pedagogy

The Case Study is planned to be for five hour-long lessons - although it may take up to seven lessons to complete. Each lesson involves a combination of class discussion, group and individual work. Fieldwork may be used to assist pupils to develop a feel for the game of cricket and collect primary data. The role of the teacher is to set the broad context of the case and guide the class to generate models by posing open questions and running class discussions. Homework is provided as part of each lesson plan. Teachers may find it useful to discuss homework tasks as a starting point for the next lesson.

Resources provided

This Case Study is presented as an interactive "browser" for teachers, containing all the instructions, lesson plans, resources and supplementary materials necessary to run the Case Study, comprising:

• An overview which contains detailed advice on how the activity can be adapted for different levels of experience and preferred teaching approaches, including possible assessment strategies and a description of the mathematics that can be expected to emerge from the activities.
• Printable introduction. Teachers will need to familiarise themselves with the Case Study and prepare the appropriate materials before teaching the first lesson. All such materials are contained on the website.
• Lesson plans giving detailed notes for each lesson and detailed notes for the teacher for the whole activity including full, worked solutions or example solutions (as appropriate) and cricket knowledge. All links to photographs and videos are through the lesson plans.
• Supporting notes and materials for teachers.

Resource requirements

(including hardware & software)

• Some lessons require a computer and data projector (or an interactive whiteboard) to present videos and images to students.
• The video clips require Windows Media Player or other video media player that can play .wmv files. Users of non-Windows machines may require extra software for this (such as VLC from http://www.videolan.org/vlc/).
• Two of the lessons require students to have access to a PC with spreadsheet software. The materials assume Microsoft Excel, but alternatives such as OpenOffice could be used. OpenOffice is available from http://www.openoffice.org.
• The Case Study can be browsed using Internet Explorer, Mozilla Firefox or any web browser which supports "frames", and should be "cross-platform". Internet Explorer may warn about "Blocked Content" when opening the teacher's browser from disc. Users must choose to allow this.
• Pupils may require stopwatches for some activities.
• It might be useful to have cricket stumps, balls, bats etc. to show to the class.