# Highway Link Design

### Overview

Mathematics can provide justification for positioning a new highway.

The cost of building a village bypass cannot only be measured in financial terms. This case study challenges students to create an optimal route for a village bypass using either software or physical resources, considering social, environmental, work-related and financial issues. The pupils are challenged to design and present a plan conforming to the mathematical constraints of the Highway Agency.

### Getting Started

- Introduction and contents (pdf). Please read the introduction first for a more detailed overview.
- Lesson plans (pdf). Containing five lessons and optional homeworks.
- Map (pdf). Provides a map of the terrain in which the bypass is to be built.
- Pupil handouts (pdf). Contains nine sets of pupil materials, some need printing on card, ideally in colour, and cutting out.
- ByPass software (exe). *Please note this is an .exe file (for PC only). Please select 'run' from the File Download box or contact your ICT administrator for support.
- ByPass software guide (pdf). An introduction to the icons used in the Bypass Software.
- Calculators and converters (xls). Excel Spreadsheets.
- Pin-boards guide (pdf). Gives instructions for building a physical model using pinboards and curtain wire.
- Google Earth guide (pdf). Contains a guide to using Google Earth.

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

### Mathematical content

Key Stage 3 National Curriculum areas covered include:

- Key processes – are expected to analyse the situations described in the activities using mathematical procedures, interpret and evaluate, and communicate and reflect on their results.
- Number and algebra – rational numbers, their properties and their different representations; rules of arithmetic applied to calculations and manipulations with rational numbers; applications of ratio and proportion.
- Geometry and measures – properties of 2D and 3D shapes; constructions, loci and bearings; similarity, including the use of scale; points, lines and shapes in 2D coordinate systems; units, compound measures and conversions.
- Curriculum opportunities – work on problems that arise in other subjects; work collaboratively as well as independently in a range of contexts.

This case study has been designed to develop pupils’ skills of thinking, reasoning and problem solving. It also provides opportunities for the use of either ICT or practical work, group discussion and communicating mathematical reasoning.

### Organisation and pedagogy

This case study supports four to six hour-long lessons of classroom activity with optional homework and is suitable for all pupils in Years 8 or 9. There are opportunities for a mixture of class, group and individual work. Pupils are encouraged to role-play in order to consider opinions from different ‘stakeholders’, make decisions and solve a real-world problem.

The case study can either use the facilities provided by an ICT suite or create designs using pinboard and curtain wire. The pupils are involved in thinking, discussing and making presentations of the mathematically-based content. There are curriculum opportunities to work with design and technology, geography, drama and English subject specialist lessons.