Mathematics IV

Base Knowledge

N/A

Teaching Methodologies

Lectures will be of theoretical and practical nature, they try to articulate the various chapters addressing to the students to perceive the connections within mathematics, through rich tasks. Whenever appropriate, concrete and virtual manipulatives as well as dynamic geometry environments will be used.
The assessment in this CU will be performed by students in one of two ways:
a) Continuous assessment: two written tests, each one of them quoted from 0 to 5 values (50%); a group work, quoted from 0 to 5 values (25%); participation in classroom tasks, quoted, in total, from 0 to 4 values (20%); individual reflection, quoted from 0 to 1 value (5%).
b) Assessment by exam.

Learning Results

– To promote the development of geometric and visual-spatial thinking.
– To deep the knowledge of Euclidean geometry, measurement, estimation and error; to establish connections between them and between other areas of mathematics and other domains of knowledge.
– To develop mathematical arguments about geometric relationships.
– To identify measurable attributes of objects, units of mesure and processes of measurement.
– To conduct research activities that lead to discovery of geometric properties.
– To recognize the relationship between geometry and real life.

Program

-Euclidean geometry in plane and space: Primitive notions of Euclidean geometry. Axioms. Relative positions of geometric elements. Angles. Figures. Congruence. Geometric solids.
– Geometric constructions: Geometric constructions with rule and compass and with dynamic geometry software.
– Reasoning in geometry: Inductive and deductive reasoning in the conjecture and proof of figure properties.
– Geometry and cartesian coordinate system.
– Geometric transformations and symmetry: Isometries and their properties. Composition of isometries. Symmetries. Tessellations with regular polygons. Geometric transformations in a coordinate plane.
– Measurement: Systems of measure, angle, area, perimeter, volume. Estimation and error.
– Topological motions: topological mappings and topological properties.

Curricular Unit Teachers

Grading Methods

Examen
  • - Exam - 100.0%
Continuing Evaluation
  • - Individual reflexion - 5.0%
  • - Two written tests - 50.0%
  • - Individual and/or Group Work - 25.0%
  • - Attendance and Participation - 20.0%

Internship(s)

NAO

Bibliography

-Araújo, P. V. (1998). Curso de Geometria. Gradiva.
-Association of Teachers of Mathematics (2005). Moving on with Dynamic Geometry. Association of Teachers of Mathematics.
-Del Grande, J. et al (1993). Geometry and spatial sense standards. NCTM.
-Escher, M.C. (1998). Arte e Matemática. APM.
-Hilbert, D. (1952). Fundamentos da Geometria, Tradução da 7ª edição alemã por Maria Pilar Ribeiro com a colaboração de J. Silva Paulo. Instituto para a Alta Cultura.
-Jacobs, H. R. (2003). Geometry: Seeing, doing, understanding. W. H. Freeman and Company.
-Loff, D. (1991). Polígonos e pavimentações – uma abordagem elementar. SPM.
-MacMullen, C. (2019). Geometry Proofs Essential Practice Problems Workbook with Full Solutions Paperback. Zishka Publishing.
-Parker, T. H. (2008). Elementary Geometry for Teachers. Sefton – ASH Publishing.
-Serra, M. (2003). Discovering Geometry- an investigative approach. Key Curriculum Press.