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

Numeric Sets: natural numbers, non-negative integers, integers, rational, irrational, and real numbers;
Numerical Systems: decimal-base 10, binary-base 2, and other bases;
Mathematical Operations: meaning of operations and application of algorithms;
Numerical regularities;
Fractions, decimals, repeating and non-repeating decimals, percents; scientific notation;
Straight-oriented representation: order, Symmetry;
Intervals of real numbers;
Cartesian product – ordered pair. Vector;
Divisibility rules; Sieve of Eratosthenes; Prime numbers; Fundamental Theorem of Arithmetic;
Greatest common divisor and least common multiple;
The first and second degree Equations with one variable; Systems of linear equations;. Inequalities of first degree;
Problem solving.

Teaching Methodologies

The student benefits from theoretic-practical lessons and orientation tutorial sessions in which the syllabus is explored in detail through problem solving and practical exercise sheets. 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 projects based on class topics, performed individually or in groups (15%); or, alternatively, a final-term written exam.

Bibliography

Ministério da Educação e Ciência, Programa e Metas Curriculares de Matemática do Ensino Básico, MEC - Direção Geral da Educação, 2013.
Pedro Palhares (Coordenação), Complementos de Matemática para Professores do Ensino Básico, Lidel – Edições Técnicas, 2011.
Joana Brocardo, Lurdes Serrazina e Isabel Rocha (Organização), O sentido do número: reflexões que entrecruzam teoria e prática, Escolar Editora, 2008.
Ron Aharoni, Aritmética para pais: um livro para adultos sobre a matemática das crianças, Gradiva, 2008.
Helena Melo, Números Especiais, Revista Interpólos, folha informativa da Universidade dos Açores, julho, 2/2007, pp 65-71
Pedro Palhares (Coordenação), Elementos de Matemática para Professores do Ensino Básico, Lidel – Edições Técnicas, 2004.
Calvin T. Long, Duane W. DeTemple, Mathematical Reasoning for Elementary Teachers, 3rd Edition, Boston, Addison-Wesley, 2003.