Overview

The Case Study looks at the problem of how a pizza shop can maximize its market for home delivered pizzas by keeping the pizza warm (and so edible) for longer. They use mathematical modeling to find how to ensure that the pizza arrives hot! They examine cooling curves for pizzas with different packaging and to explore ways to keep the pizza warm and the implications of doing so. Pupils then use the model to address the market problem of the pizza shop by answering the questions: how long does it take a pizza to cool, how far can the delivery travel in that time and what difference does the packaging make?

The Case Study leads pupils to move from a practical problem of a cooling pizza to a mathematical representation of a cooling curve. This draws pupils into the potential of mathematical applications and shows how mathematics can underpin scientific enquiry. The linking of the time to cool with possible distances of delivery introduces further mathematics.

Although not essential, this project would work well as a cross-curricular project with the science department.

Assessment

The Assesment Guide for Keeping the Pizza Hot 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.

Assessment Guide (PDF) Editable version (DOCX)

Mathematical content

Measure temperatures as a pizza cools and 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.

Specific Key Stage 3 National Curriculum areas covered include:

• Key processes - represent and analyse a problem, including simplifying where needed; interpret and evaluate the mathematical models produced and relate them to the original problem in order to improve upon them.
• Number and algebra - linear equations, formulae; analytical, graphical and numerical methods for solving equations; polynomial graphs.
• Geometry and measures - units, compound measures and conversions.
• Statistics - applying the handling data cycle; using an algebraic interpretation of the real data collected rather than a statistical one.
• Curriculum opportunities - work collaboratively on sequences of tasks that involve using mathematics in increasingly difficult or unfamiliar contexts; select the mathematics to use; tackle problems from other subjects.

Organisation and pedagogy

The Case Study supports four to five one hour lessons of activity and could be used with Years 7, 8 or 9, although it might be most suitable for Year 8. The activity is designed for group work (four to five pupils) interspersed with whole class plenary discussions, allowing feedback from the groups.

Resources provided

This Case Study contains a collection of lesson plans, handouts and other resources comprising:

• Teacher's Guide (PDF): read and possibly print this first for a more complete overview and for the detailed lesson plans, resources needed, four pupil worksheets and some technical support for the software and equipment.
• Overview of the Case Study (PDF): a two-page outline of the Case Study.
• A PowerPoint presentation to introduce the problem to pupils and link to the supporting video sequences, data files and software.
• Video sequences showing the pizza cooling experiment, one specific cooling example in detail, the taste test experiment and five video sequences showing the lessons in a classroom setting.
• Equator - function analysis software produced specifically for this project.
• Graph - alternative, open source graph plotter.
• Sets of data files for use in Equator, Graph or other software.

In case of difficulty in opening files from the overview/index page, the individual files can be opened from the content folder within the Case Study folder.

Resource requirements

(including hardware & software)

• The supplied graphing/function analysis software requires a PC with MS Windows. Apple Mac users can access the rest of the Case Study.
• Microsoft Office or an alternative (such as OpenOffice) is required in order to display some of the files from this Case Study. OpenOffice is available from http://www.openoffice.org.
• For some lessons, pupils will need access to computers with one of the supplied programs (Graph or Equator). Equator requires Java run time (available from www.java.com).
• For some lessons, a computer and data projector or interactive whiteboard, with sound output and speakers, internet access to Google Maps/Earth and graph plotting software are required.
• The lesson videos and the silver foil animated graph sequence require Flash Player to be present - this is a free download from http://www.adobe.com
• A sound card and speakers are required for the videos contained within the presentation. Playing the video files requires the presence of some media playing software e.g. Microsoft Media Player or Apple QuickTime (available from www.apple.com).
• The optional pizza cooling experiment requires microwave ovens, pizzas, temperature probes, data logging software and various examples of packaging materials.