Patterns and Algebra

Ficha de unidade curricular - Ano letivo 2023/2024

Teaching language

Portuguese

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

Identify, analyze and represent different types of patterns and relationships present in mathematical situations in different phenomena or in everyday life, using for example the technological tools;
Explore sequences of numbers by recursion and looking for general expressions;
Using algebraic thinking in the exploration of numerical situations;
Represent and analyze mathematical situations and structures using different representations, namely the
algebraic symbols;
Solve problems using mathematical models to represent and understand quantitative relationships;
Understand, mobilize and substantiate concepts and procedures related to Patterns and Algebra
Show the ability to connect ideas, concepts and mathematical procedures;
Demonstrate the ability to question realities and knowledge;
Develop and evaluate mathematical arguments, using different methods of reasoning and evidence.

Syllabus

The contents are organized around for major themes:
• From Arithmetic to Algebra: develop algebraic thinking;
• Patterns
• From patterns to Functions: development of functional thinking
• Modelling and exploration of patterns and functions

From Arithmetic to Algebra: develop algebraic thinking:
- Properties of numbers and operations in different algebraic structures.
- Equalities and inequalities.
- The generalized arithmetic.
- Direct and inverse relations of proportionality.

Patterns
- Numerical and geometric patterns
- Repeating and growth, patterns. Linear and quadratic sequences.

From patterns to Functions: development of functional thinking
- Successions. Arithmetic and geometric progressions.
- Representations of functions: natural language, tables, graphics and alphanumeric language.

Modelling and exploration of patterns and functions
- Construction and exploration of mathematical models.
- The technology to support the modeling of mathematical situations and phenomena of everyday life.

Demonstration of the syllabus coherence with the UC intended learning outcomes

The development of algebraic thinking is present in situations of Mathematics, other disciplines and daily life, with roots in arithmetic and in working with numerical and geometric patterns.
The study and the generalization of the properties of numbers and operations allow you to create contexts where
different representations (numerical, graphical and symbolic) are articulated to give meaning to the algebraic work.
Modeling supported by equations and functions, and the dynamic and interactive technology, provides support for translating situations, establish conjectures, develop functional thinking and problem solving

Teaching methodologies

The teaching methods include: (a) resolution of tasks and reporting on the performed activity; (b) preparation,
presentation and discussion of written work; (c) discussion and analysis of scientific and technical papers. The
spreadsheet, DGS and applets, provide resources to value approaches to patterns and Algebra.

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

Once the goals involve capabilities to explore, represent, analyse, solve problems and reason, it is necessary to promote diverse processes and activities of study, discussion and resolution of tasks. This is what happens with moments of solving practical tasks (use of knowledge), reading and discussion of issues (synthesis and argument) and identification of core ideas (reflection in comparison with the practice).

Assessment methodologies and evidences

The evaluation will be an ongoing process which will include retroactive adjustment moments of individual work
and group activities and oral and written expression.

Continuous assessment focuses on the work done by each student in class. It involves the organization and elaboration of small reports and the resolution of tasks, either in group or individually.
There will be three moments of summative assessment:
Relational thinking and Repetitive and pictorial sequences - individual - maximum score 7.5 points
Finite Differences Method, Progressions and Functions - individual - maximum score 8.5 points
Functions and modelling - pairs - maximum score 4 points.

Students enrolled in this evaluation modality, but that don’t realize some of the tasks, may realize an individual presential test, at the end of the semester, that will include only the themes of those tasks.

Attendance system

Students who participate in activities carried out in at least 75% of classes may be included in the continuous assessment system. Students who are unable to integrate into the continuous assessment system will take a final exam.

Students with special statute, in the event that they are unable to attend classes, must negotiate with each teacher (in the first 15 days of classes) the way that will be used for their evaluation, as well as the most convenient timetable.
Students that do not meet continues assessment requirement will have a final exam.

Bibliography

Blanton, M. L. (2008). Algebra and Elementary Classroom: transforming thinking, transforming practice.
Portsmouth: NH Heinemann.
Brocardo, J. et al. (2006). Números e Álgebra: Desenvolvimento curricular. In I. Vale et al. (Orgs.), Números e
Álgebra na aprendizagem da Matemática e na formação de professores (pp. 65-92). Lisboa: SPCE.
Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher & M. Blanton (Eds.),
Algebra in the Early Grades (pp. 133-160). New York: Lawrence Erlbaum.
DGE (2021). Aprendizagens Essenciais de Matemática. https://www.dge.mec.pt/noticias/aprendizagens-essenciais-de-matematica
NCTM (2007). Princípios e Normas para a Matemática Escolar. Lisboa: APM.
Ponte, J. (2006). Números e Álgebra no currículo escolar. In I. Vale et al. (Orgs.), Números e Álgebra na
aprendizagem da Matemática e na formação de professores (pp. 5-27). Lisboa: SPCE.