Overview

The Case Study uses the interest that pupils have in music as a basis for mathematical investigations, using their own favourite music tracks as the raw data. Working in small groups, pupils listen to different tracks and analyse the similarities and differences between types of track and genres of music. They measure the tempos of the tracks and then consider other variables such as track length, album sales and the highest position or number of weeks in the charts. Pupils then interpret and present their results. They can also investigate trends in music over the years.

The work can be used as an introduction to statistical work, including: the collection of numerical data, performing basic statistical calculations, forming and testing hypotheses, making inferences about a population, and identifying potential sources of error in data collection and calculations. Although not essential, this project would work well as a cross-curricular project with the music department.

Mathematical content

Describe the characteristics of different genres of music. Use the tempo of music and other variables to illustrate compound measures, eg beats per minute.

Specific Key Stage 3 National Curriculum areas covered include:

• Key processes - identify the mathematical aspects of a situation; simplify a situation in order to represent it mathematically, using appropriate variables; identify and classify patterns; interpret and analyse results, reflect on and communicate them.
• Number and algebra - calculate and manipulate rational numbers; use and apply ratio and proportion.
• Geometry and measures - scale; units, compound measures and conversions.
• Statistics - apply the handling data cycle; measures of central tendency and spread.
• Curriculum opportunities - work on problems that arise in other subjects; work collaboratively as well as independently in a range of contexts.

Organisation and pedagogy

The Case Study supports four hour-long lessons of classroom activity for Part 1. Computers or external audio devices (CD players, iPods, etc) with headphones are needed, at least one set between two pupils. An optional Part 2 requires one period of two hours and a greater use of ICT - pupils need to use audio editing software. A mixture of class, group and individual work is involved with some homework tasks. In the first lesson, teachers play music tracks to the class; in subsequent lessons, pupils listen to music in groups.

Resources provided

The Case Study includes:

• Teacher's Guide (PDF): A 31 page document that gives a detailed overview, lesson plans and worksheets. There are seven Student Sheets that can be printed in black and white to support pupil activities.
• Starter rhythm tracks (MP3).
• BPM data for various music tracks in Excel and OpenDorument formats.
• Audacity software: free software to play and edit audio files- versions for PC, Apple Mac (Intel) and Apple Mac (PPC) are included.

Resource requirements

(including hardware & software)

• The documents and data files are supplied in both Microsoft Office (.doc, .xls) and OpenDocument (.odt, .ods) formats - the latter can be used with free office software such as OpenOffice, available from http://www.openoffice.org.
• For Part 1 of the Case Study, pupils will need headphones and the means to play music CDs and/or mp3 music files. The teacher will also need a loudspeaker. Computers may be the easiest solution - but personal audio players could also be used.
• For Part 2 of the Case Study (optional), each pair or small group will need a computer with sound output and headphones, loaded with audio playing software such as Audacity.