Contextualization

Mathematics is a discipline full of patterns, and a subject that illustrates this perfectly is sequences. Basically, a sequence is an ordered list of numbers that follows a certain pattern or rule. For example, a sequence can consist of numbers that are being added or subtracted by a constant value, or that are being multiplied or divided by a constant value.

Sequences can be classified as recursive or non-recursive. A recursive sequence is one in which the next term of the sequence depends on the previous term, while a non-recursive sequence follows a fixed rule that does not depend on the previous terms.

To better understand how sequences work and what they are used for, let's consider the idea of prediction. The more we know about the patterns that something follows, the better we can predict what will happen next. And predicting the future, based on patterns, is a fundamental skill in many fields of life, from weather forecasting to financial planning.

Furthermore, sequences have a wide range of practical applications. For example, in mathematics and science, they are used to model real-world situations and solve problems. In art, they are used to create visual patterns and even in music, where sequences of notes form melodies.

Now, to deepen your knowledge on the subject, you can use the following resources:

1. Book: "Mathematics and Logic for Beginners" by Júlio Cesar Godoy.
2. Web page: Khan Academy - Sequences.
3. Video: Canal Matemática Rio - Numerical Sequences.

Thus, by developing this project, you will be able to identify the regularity of a numerical or figural sequence, build an algorithm to indicate the next numbers or figures and much more. So, are you ready to explore the wonderful world of sequences?

Practical Activity: "The Marathon of Sequences"

Project Objective

In the project 'The Marathon of Sequences', students will explore the concept of recursive and non-recursive numerical sequences in a playful and interactive way. The work will be carried out in groups of 3 to 5 students and will have a total duration of one week.

Detailed Description of the Project

The project will be mainly divided into two parts:

1. Research and study of the theme.
2. Creation of a board game that involves the theme sequences.

Required Materials

• Cardboard for the base of the board
• Colored paper for decoration and game pieces
• Colored markers
• Books or reliable websites for research
• Computer for preparing the report
• Scissors and glue

Step-by-step

Step 1: Study of the Sequences (1h30min-2h)

• Students will research and study about the sequences, their classifications, applications and how to identify the regularity of a numerical or figural sequence.

Step 2: Creating the Game (1h30min-2h)

• With the knowledge acquired, the groups must create a board game that involves the numerical sequences and figures.
• The board must have progression spaces where each space represents a term of the sequence.
• Each group must create a mathematical sequence that will be the basis of the game.
• The objective of the game is to advance in the spaces by answering the question correctly: what is the next number or shape in the sequence?
• The game must include a final challenge related to the sequence where the players must use the sequence to solve a bigger problem.

Step 3: Activity Report (1h)

• The students will report the execution of the project in a report that must contain:
  • Introduction: The students must contextualize the sequences, their relevance and application in the real world and the objective of the project.
  • Development: The students must present the theory of sequences, explain the creation and rules of the game in detail, the creation methodology and discuss the results obtained.
  • Conclusion: The students must conclude the work by reviewing their main points, highlighting the lessons learned and the conclusions about the project.
  • Bibliography: The students must indicate the sources they used to work on the project.

Project Delivery:

• Board game.
• Activity report in written document format.

The final objective is that, with this project, the students can connect the theoretical knowledge learned with the practical activity carried out, visualizing how the numerical sequences work in a concrete way. The final report will allow them to articulate this process of learning and application of knowledge.