Pupils appreciate how simple mathematical estimation supports decision making in our private and public lives in real and unusual contexts.
Newspapers, television, politicians and the media regularly make claims about how long things will take, how much things will cost and other tricky problems involving large numbers. It is important to be able to judge if such claims are reasonable.
This Case Study stimulates discussion between pupils about how to think about whether a particular claim is reasonable or not. It develops pupils' ability to make estimates about unusual quantities based on only limited information. Pupils consider everyday statistical claims and judge whether they are reasonable. Using limited information, pupils use mathematical reasoning to make estimates to arrive at a conclusion and then communicate their solutions, ideas and reasoning to others. Pupils see that the problems they are asked to solve are the same as those in real life.
The Case Study helps pupils to recognise the power of even simple mathematics (together with smart thinking) when making decisions about important topics.
The Assesment Guide for You Reckon? is comprehensive guide to help teachers to assess pupils' achievement and progression as they work on the activities. It includes sample work and progression charts.
Break a problem into its component parts; combine everyday knowledge to create chains of reasoning that result in reasonable estimates of useful quantities.
Specific Key Stage 3 National Curriculum areas covered include:
- Key processes - simplify a situation from the real world and represent it mathematically, using appropriate variables, symbols, diagrams and models; work logically towards results and solutions, reason deductively and form convincing arguments.
- Number and algebra - use rational numbers, their properties and different representations; rules of arithmetic applied to calculations and manipulations; ratio and proportion; accuracy and rounding; algebra as generalised arithmetic.
- Geometry and measures - units, compound measures and conversions; perimeters, areas, surface areas and volumes.
- Curriculum opportunities - work collaboratively on sequences of tasks that involve using mathematics in increasingly difficult or unfamiliar contexts; 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.
Organisation and pedagogy
The Case Study consists of a mixture of longer and shorter tasks. There are five 'Lesson Blocks', each intended to take 30 minutes or more, five 'Sprinklers' which are shorter and four 'One Liners' which may take about 10 minutes to solve. The entire Case Study could be taught as a unit of work lasting from three to five hours; alternatively each problem can stand alone. It is suggested that pupils work in groups of three or four to encourage discussion and the sharing of ideas. Different groups could work on the same problem or could solve different ones. Most of the problems can be presented to pupils as a printed handout or orally or by using a projector (or interactive white board).
The problems are suitable for all age groups and abilities, however, lower ability groups and pupils less used to working independently may need more help by starting with the shorter problems as a whole class exercise, before moving on to the longer problems.
The materials are presented as an interactive browser for use by the teacher, containing:
- General Teaching notes.
- Lesson Block materials - tasks, teacher notes, pupil information sheets and PowerPoint presentations.
- Sprinkler materials - tasks and teacher notes.
- One Liner materials - tasks.
- Associated Software.
- Printable material - including general teacher notes, introductory materials, task notes.
(including hardware & software)
- A computer with data projector (or interactive whiteboard), sound output and speakers is useful for showing videos and presentations to the class, but not essential.
- Videos are available in a number of formats (WMV and AVI) The WMV files, if accessed from the web browser, are generally not accessible with Firefox, though some systems have been configured to handle them. Videos are also available in Shockwave format -if a Shockwave player is not available on your machine, you will be prompted to download it.
- Microsoft Office or an alternative (such as OpenOffice) is required to open some files, including documents, PowerPoint presentations and spreadsheets. OpenOffice is available from http://www.openoffice.org.
- Pupils do not require computers for this Case Study.