Geometry and Measurement

Scholar Year: 2017/2018 - 1S

Courses

Head Teacher Responsability Maria de Fátima Pista Calado Mendes Head

Weekly workload Hours/week T TP P PL L TC E OT OT/PL TPL O S Type of classes Lectures Type Teacher Classes Hours Contact hours Totals 2 8,00 Maria de Fátima Mendes   8,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

- Understand, mobilize and support concepts and procedures relating to the topics Geometry and Measurement;
- Solve problems using visualization and spatial reasoning, the geometric models and the knowledge of shapes, their characteristics and properties, specifically using dynamic geometry environments;
- Use concepts, tools and formulas properly to determine measurements, by mobilizing knowledge about units, systems and processes of measurement;
- Communicate clearly and consistently by mobilizing knowledge about the topics Geometry and Measurement;
- Demonstrate skills of inquiry and knowledge;
- To show the ability to connect ideas, concepts and mathematical procedures;
- Develop and evaluate mathematical arguments related to the subject matter using different methods of reasoning and evidence;
- Reveal autonomy to formulate and solve mathematical problems;
- Understand the learning process of geometry.

Syllabus

Geometry of plane and space
Historical perspective
Three-dimensional geometric shapes
Nets, construction and representation of views of geometric solids
Lines, planes and its positions
Plane shapes
Vectors
Transformations of the plane, isometries and similarities
Polygons and tessellations
Coordinate geometry
Physical quantities and measures
Concepts of magnitude and measure
Physical quantities and procedures for measuring physical quantities
Length and area
Length and length measuring
Perimeter of plane shapes
Surface, area and areas measurement
Area of plane shapes
To determine areas by framing or decomposition
Range of angles and amplitude measurements
Volume and capacity
Measurement of volumes and capacities
Volume of three-dimensional shapes
Estimation of measurement

Demonstration of the syllabus coherence with the UC intended learning outcomes

This course aims at understanding and mobilizing concepts and procedures relating to subjects Geometry and Measurement, hence deepening aspects associated with these two issues. Once you want students to use properly, concepts, tools and formulas to determine measurements, mobilizing knowledge units, systems and processes of measurement situations are provided them to help achieve these goals. The work around the syllabus also contributes to students to develop their ability to communicate clearly and consistently mobilizing knowledge on the subjects Geometry and Measurement.

Teaching methodologies

The work will focus on active students’ participation, either individually or in group, aiming to in depth the knowledge of the mathematical topics.
The sessions are organized in the context of problem solving. This process includes problem solving and reporting; presentation of topics; elaboration and discussion in small groups of short written tasks.The tutorial support, individual support or group support, consists in the orientation and organization of the student study to deepen the themes and answering questions posed by students and can be done in person or distance.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

It is expected that at the end of UC students: (a) mobilize concepts related to geometry and measurement, particularly in problem solving; (B) carry out activities related to geometry and measurement, involving in particular technological tools; (C) present a critical attitude in the interpretation and resolution of mathematical tasks; (D) use judiciously and critically the acquired knowledge; and (e) substantiating ideas and positions using mathematical arguments, including test methods; (F) demonstrate some knowledge of geometry as it learns. Thus, to achieve the goals of UC students involved will be in diversified activities, individually or in groups, such as problem solving on the various topics and the corresponding production of reports and the preparation and presentation of papers related the various contents to deepen. The use of dynamic geometry programs will also contribute to the development of the learning objectives of this course. The realization of works and their presentation and discussion contribute to students to develop the ability to communicate clearly and consistently mobilizing knowledge on the subjects Geometry and Measurement.

Assessment methodologies and evidences

The evaluation will focus on the work developed throughout the CU. Attendance and participation in classes and work sessions will be taken into account (5%), (ii) written work on participation in a seminar (15%); (iii) written report on the resolution of a problem (20%); (iv) the performance of a written test (60%).
The test covers all contents of the course. In order to complete the UC in the continuous assessment mode, a minimum of 70 points (in a total of 200) must be required in the test.

Attendance system

To take advantage of the form of continuous assessment, each student has to attend 75% (50% for working students) of classroom sessions. If this does not occur the students have to perform an examination.

Assement and Attendance registers

Bibliography

Breda, A.; Serrazina, L.; Menezes, L.; Sousa, H. & Oliveira, P. (2011). Geometria e Medida no Ensino Básico. Lisboa: ME-DGIDC, disponível em http://area.dgidc.min-edu.pt/materiais_NPMEB/070_Brochura_Geometria.pdf.
Caraça, B. J. (2000). Conceitos fundamentais da Matemática. Lisboa: Gradiva.
Davis, P. & Hersh, R. (1995). A Experiência Matemática Lisboa: Gradiva.
Haylock, D. (2010). Mathematics explained for primary teachers. London: Sage.
Jacobs, H. (2003). Geometry. New York: W. H. Freeman and Company.
Jacobs, H. (1994). Mathematics: a human endeavor. San Francisco: Freeman.
Mendes, F. & Delgado, C. (2008). Geometria - Textos de Apoio para. Educadores de Infância. Lisboa: ME-DGIDC.
Musser, G.; Burger, W. & Peterson, B. (2009). Mathematics for elementary teachers. A Contemporary Approach. USA: Prentice-Hall.
NCTM (2007). Princípios e normas para a Matemática escolar. Lisboa: APM.
Oliveira, A. Franco de (1997). Geometria euclidiana. Lisboa: Universidade Aberta.
Palhares, P. (coord.) (2004). Elementos de Matemática. Lisboa: Lidel.
Palhares, P.; Gomes, A. & Amaral, E. (coord.) (2011). Complementos de Matemática para professores do Ensino Básico. Lisboa: Lidel.
Ponte, J. & Serrazina, L. (2000). Didáctica da matemática do 1.º ciclo. Lisboa: Universidade Aberta.
Serra, M. (2002). Discovering geometry: An inductive approach: Berkeley: Key curriculum Press.
Veloso, E. (1998). Geometria: temas actuais: materiais para professores. Lisboa: Instituto de Inovação Educacional.
Veloso, E. (2012). Simetria e transformações geométricas. Lisboa: Associação de Professores de Matemática.

Sites de referência
http://nctm.org/ (National Council of Teachers of Mathematics)
http://www.fi.uu.nl/en/ (Instituto Freudhental)
http://www.atractor.pt/ (Matemática Interativa)
http://nrich.maths.org/public/index.php (Universidade de Cambridge)
http://www.geogebra.org (acesso ao Geogebra)