# Keeping the Pizza Hot

### Overview

Mathematics can get you there in time.

This case study looks at the problem of maximising the market available to a pizza shop through the ability to keep a home-delivered pizza warm for longer. Pupils use mathematical modelling to explore the issue that a pizza home delivery business faces in ensuring that the pizza arrives hot! They use mathematical modelling to explore cooling curves for pizzas in different packaging. The model is then used to address the marketing problem faced by the pizza shop.

### Getting Started

Please click here to view the presentation (pps file) and watch videos of the experiment being conducted.
Note: Please select 'open' from the file download box. Also note that the last slide in the presentation contains the following links.

- The experiment with silver foil (mp4 file). Internet Explorer users need to right click on the gold bar and select 'Allow blocked content' then choose 'yes' to view file.
- Detailed experiment graph (swf file). Internet Explorer users need to right click on the gold bar and select 'Allow blocked content' then choose 'yes' to view file.
- The taste test (mp4 file). Internet Explorer users need to right click on the gold bar and select 'Allow blocked content' then choose 'yes' to view file.
- Open a complete data set in Excel format (xls file). Please click 'open' to view the file.
- Run Equator software (jar file). Note: Internet Explorer users please click 'open' then save the file to your machine to view.

Note: You will need software to play the mp4 files. Please click here to view a list of compatible software.

### Mathematical content

Key Stage 3 National Curriculum areas covered include:

- Key processes – pupils are expected to represent and analyse the problem, including simplifying where needed. The emphasis is on interpreting and evaluating the mathematical models produced and relating 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.

### Organisation and pedagogy

This case study supports four to five lessons of activity and could be used with Years 7, 8 or 9, although 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.
An interactive whiteboard or digital projector will be required for PowerPoint and Google Maps / Earth and teachers will need access to a computer connected to a projector running graph-drawing software such as Autograph or Graph. The pupils will need access to computers.

### Resources

- Teachers guide (pdf): read and possibly print this first for a more complete overview and 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.
- Sets of data files for use in (a) Equator and (b) A graph plotter (e.g. Autograph or Graph)
- Software installer for Equator (for PC and Mac)
- If the classroom experiment is carried out (highly recommended!), you will also need a microwave oven, temperature probes and software, mini pizzas and different types of packaging

Adobe Reader is required to view the pdf files contained within this case study.