Geometry and Measurement

Objectives

1) To explore the properties of geometric shapes and structures.
2) To model geometric shapes, from previous planning.
3) To describe the position of geometric shapes in space.
4) To compare different lengths, areas and volumes in sequences.
5) To solve problems by mobilizing existent knowledge of lengths, areas and volumes.
6) To develop critical thinking as well as research and creative skills in problem solving.

Program

1) Plane Geometry – basic concepts, definitions and properties.
2) Polygons: general definitions, classification and properties. Congruence and similarity criteria. Circumference: relative position between a circumference and a straight line. Relationship between polygons and circumference.
3) Analytical geometry in the plane: coordinated systems vectors; straight-line equations in the plane.
4) Topological geometry in the space: relative positions between planes and straight lines.
5) Representation and planning of some solids.
6) Spatial relationships using coordinate geometry.
7) Measure and base units: international system of units; measurement of base units length; plane figure area; prism volume and time units.

Teaching Methodologies

Teaching in this course unit proceeds on the basis of lectures and practical activities, assisted by the computer whenever required. The adopted methodology encourages the active participation of students. Subject matter is presented, discussed, and developed using problems and real life situations. In order to consolidate the learning of concepts, exercises are provided on each course topic, as well as additional materials in support of lectures. The course will benefit from the use of Moodle, the learning management platform available at the University of the Azores, thus enhancing the performance of asynchronous activities. The final grade is computed as the weighted average of: midterm written tests (85%); exercise sheets and other work based on class topics, performed individually or in groups (15%). Alternatively, the students may take a finalterm written exam.

Bibliography

Pedro Palhares (Coord.), Complementos de Matemática para Professores do Ensino Básico, Lidel – Edições Técnicas, 2011.
Pedro Palhares (Coord.), Elementos de Matemática para professores do Ensino Básico, Lidel, 2004.
Eduardo Veloso, Geometria: temas actuais, Lisboa, 1998.
Paulo Araújo, Curso de Geometria, Lisboa, Gradiva 1998.
Franco de Oliveira, Geometria Euclidiana, Lisboa, Universidade Aberta, 1995.
Helena Melo e Maria do Carmo Martins, Introdução à Geometria Euclidiana, (preprint)