Subject: Mathematics V

Scientific Area:



63 Hours

Number of ECTS:




Overall objectives:

1 - Acquiring the concept of number.
2 - Understanding the numbering system in the Indo-Arabic decimal base and bases other than base 10.
3 - Knowing the history of numbers and operations, the set of natural numbers, their properties and exploring regularities.
4 - Developing skills in the teaching of mathematics and plan lessons.
5 - Solve problems in new situations and contexts wide multidisciplinary.
6 - Being able to communicate the conclusions and the knowledge and reasoning underlying them, in a clear and unambiguo
7 - Developing the ability to abstract concepts and to generalize results; distinguish the various types of mathematical objects, such as definitions, theorems, conjectures and propositions concerning single objects and case studies; be aware of the types of questions typical of Mathematics and insights about the types of responses expected, there is capacity to pose questions.
8 - Develop competence in communicating mathematics.


1 - Concept of number (Historical evolution of the concept of numbers and numerical representation).
2 - Hindu-Arabic numeral system. Decimal basis and other basis.
3 - The set of natural numbers (Properties, Exploitation of Regularities).
4 - Negative numbers and zero (brief historical reference).
5 - Pythagorean Theorem and irrational numbers.
6 - Algorithms of Arithmetic (involving natural numbers and non-negative rational numbers in decimal representation)
7 - Integers and its properties. Operations with integers.
8 - Real numbers.


D. Fernandes , 1994 , Educação matemática no 1º ciclo do ensino básico: aspectos inovadores. , Porto Editora
Anderson, M., Katz, V., & Wilson, R. , 2004 , Sherlock Holmes in Babylon and other tales of mathematical history , The Mathematical Association of America
Hodqkin, L. , 2005 , A history of mathematics: from Mesopotamis to modernity , Oxford University Press
Moreira, D., & Oliveira, I. , 2003 , Iniciação à matemática no jardim de infância , Universidade Aberta
Dantzig, Tobias , Número a linguagem das Ciências , Ed. Aster
Delgado, Mª José et al , 1988 , Matematicando Problemas , Texto Editora
Frank, Martha , 1992 , Resolução de problemas e concepções acerca da Matemática , In Educação e Matemática
Institut National de Recherche Pedágogique , 1995 , À descoberta dos números - contar, cantar e calcular , Edições Asa

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
The lectures include both theoretical-pratical moments, dedicated to the introduction or synthesis of the studied subjects, and practical, more frequent, moments. Reflection and discussion are fundamental elements of this course. Working in small groups is the most common way of working. The evaluation is continuous with emphasis on the formative aspect of the evaluation, which allows to integrate the student's practice into different moments and in response to the course's contents. In the normal evaluation season two test will be given (20 values each), as well as a work (4 values). The final grade = 0.4 * (test 1 + test 2) + work grade. To get approval in this course students need to have a final mark higher or equal to 9.5 values. At the time of grade re-examination and special season, students can choose between re-taking one or both frequencies (with the same weight as at the normal evaluation), or doing a global exam that weighs 80% in the final evaluation.