Numbers and Operations

Objectives

1) To consolidate the knowledge of numerical sets, arithmetic operations, and algorithms and methods.
2) To establish relationships between numerical operations.
3) To develop strategies for mental calculation.
4) To identify ways of composing and decomposing numbers.
5) To understand fractions namely the meaning of quotient, whole-and-part and operator.
6) To explore regularities and numerical patterns.

7) To be able to solve real problems, through various approaches and reasoning.
8) To develop skills in defining problems, revealing research abilities and autonomy.
9) To demonstrate transversal skills of math communication, mathematical reasoning and problem solving.
10) To reflect on the content of subject "Números e Operações" in the scientific context.

Program

1. Numeric Sets: natural numbers, non-negative integers, integers, rational, irrational, and real numbers;

2. Numerical Systems: decimal-base 10, binary-base 2, and other bases;

3. Mathematical Operations: meaning of operations and application of algorithms;

4. Numerical regularities;

5. Fractions, decimals, repeating and non-repeating decimals, percents; scientific notation;

6. Straight-oriented representation: order, Symmetry;

7. Intervals of real numbers;

8. Divisibility rules; Sieve of Eratosthenes; Prime numbers; Fundamental Theorem of Arithmetic;

9. Greatest common divisor and least common multiple;

10. The first and second degree Equations with one variable; Systems of linear equations;.

11. Inequalities of first degree;

12. Problem solving.

Teaching Methodologies

Theoretical-practical classes and tutorial sessions, in which the syllabus of the curricular unit is explored in detail, through problem solving and practical exercise sheets.

The curricular unit will benefit from the use of the Moodle learning management platform available at the University of the Azores, thus enhancing the performance of asynchronous activities.

Bibliography

Eugénio Monteiro, O corpo dos números reais, Coimbra Editora 1981.

John Walle, Matemática no ensino fundamental, Artmed Editora 2009

Ministério da Educação e Ciência, Programa e Metas Curriculares de Matemática do Ensino Básico, MEC – Direção Geral da Educação, 2013. 

Pedro Palhares (Coordenação), Elementos de Matemática para Professores do Ensino Básico, Lidel – Edições Técnicas, 2004.