A Mathematical Survey of Downs Banks
Pupils were asked to undertake a survey of a piece of land made up of two ridges (about 600 metres apart) separated by a valley containing a narrow stream, about 30 metres below the ridges. They were provided with survey poles, joined by 20 metres of string, a clinometer, a compass, a 20 metre tape and clipboards. The pupils moved east to west, using the compass to keep heading in a constant direction, measuring the angle of elevation or depression between the survey poles as they crossed between the valleys. At two different points on the western ridge, they had to measure the angle of elevation of the top of a chimney and the angle of depression of the bottom of the same chimney.
Logo procedures had already been written, so that when pupils input their data into the laptop computers, they could see the cross section of the land between the ridges on the screen. They also found the height and distance away of the chimney. Once back at school the pupils made a scale drawing of the valley and of the position of the chimney. In addition they had to produce a report of their work. This report could have been word-processed.
Discipline, subject : mathématiques
Public : cycle d'orientation
Sek I, BWK
lower high school
Department of Education
Keele University, Keele
STAFFORDHIRE ST5 5BG
Tel : +44 782.583.124
Mail : firstname.lastname@example.org
Fax : +44 782.714.113
Pédagogie, pedagogy : Pupils in mathematics had to undertake a survey of a piece of land made up of two ridges separated by a valley and then produce a cross-section of the land. In addition the pupils had to find the position and height of a chimney using triangulation techniques. Pupils were required to write a report of their findings which had to include a scale diagram. A program to work out the height and position of the chimney and the Logo programming language were used.
Apprentissage, learning : Pupils collected information about the angle of a slope, estimated and then measured angles of elevation and depression, and measured bearings of a chimney. From this information they produced scale drawings, a cross section using the Logo programming language, found the height of a chimney using a short computer program, and completed a written report.
Enseignement, teaching : The aim was to provide pupils with concrete experiences of measurements and relate them to classroom work involving bearings, angles of elevation, triangulation techniques and scale drawings. Secondary aims were concerned with writing reports on work in mathematics and using
Logo to link in with pupils' work in informatics.
Technique : A short Basic program was written on an IBM PC so that it would calculate the distance and the height of the chimney, given the pupils' information. This was used to check the pupils' scale drawings. The Logo programming language was used to write a procedure to draw the cross section of the slopes. Three laptop computers were taken to the site to provide instant feedback on the slope of the land.
Société, society : Pupils had to work in groups of 4 or 5 and co-operate to take the measurements.
Institution : Survey equipment had to be borrowed from the geography department; school minibuses had to take pupils to the site (30 minutes travel), laptop computers were borrowed from local University, permission had to be obtained from pupils' parents.
Remarques, remarks :