Context

Mathematics is a powerful discipline that allows us to understand and model the world around us. And within mathematics, more specifically in algebra, we find the 'Notable Products'.

Notable products are ways to simplify the multiplication of algebraic expressions, based on the identification of patterns. They are notable because they are frequently used and therefore, are known to be patterns that always repeat. It is a way to make the calculation of algebraic expressions easier.

There are three main types of notable products: the square of the sum, the square of the difference, and the product of the sum by the difference. Each of them has a standard form that facilitates the resolution of mathematical problems.

Importance and Application of Notable Products

Notable products are an essential tool in algebra, present in many areas of knowledge. They are used in solving second-degree equations, simplifying algebraic expressions, and even in expanding polynomial functions.

Furthermore, notable products are fundamental for the development of skills necessary for the study of functions, geometry, and calculus, which are advanced disciplines in mathematics.

In the real world, notable products are applied in physics, engineering, computing, economics, and even in the development of video games.

For a deeper understanding of the topic, I suggest the following reliable sources:

1. Only Mathematics - Notable Products
2. World Education - Notable Products
3. Professor Ferretto on Youtube - Notable Products
4. Book: Fundamentals of Elementary Mathematics, volume 1: sets, functions. Elementary Mathematics Fundamentals Series. Authors: Gelson Iezzi, Osvaldo Dolce, Carlos Murakami. Editora Atual, 11th edition.

Practical Activity

Activity Title: Game of Notable Products

Project Objective:

Students must develop a game, in a board game format, related to Notable Products. The game should be engaging and fun to play, as well as useful for learning about notable products.

Detailed Project Description:

Divided into groups of 3 to 5 students, the students will be challenged to create an educational board game, where the main objective is to learn the fundamentals of Notable Products. Each group must create the rules, the design of the board, the pieces, and the challenges/riddles of the game.

Each challenge/riddle of the game, for example, can be an algebraic expression that needs to be solved using one of the three types of notable products. Players will advance on the board as they solve the challenges correctly.

Necessary Materials:

1. Cardboard or other firm material for making the board
2. Colored pens, pencils, markers
3. Paper for creating challenge/riddle cards
4. Pieces for players (can be small objects or pieces from other games)
5. Scissors, glue, ruler

Detailed Step-by-Step for Carrying Out the Activity:

1. Research and Planning: First, students should research the main concepts of notable products and develop a list of algebraic expressions that can be solved using notable products. These expressions will be the questions of the game. In addition, at this stage, students should plan the layout of the game, the dynamics, the rules, and how the mechanics of notable products will be inserted into the game.

2. Board Production: Next, using cardboard and colored pens, students will draw and paint the game board, following the structure they planned.

3. Creation of Challenge/Riddle Cards: Using paper, students will create challenge cards, writing the algebraic expressions they raised in the research stage. The cards should contain, in addition to the expression, the correct answer, which should be hidden during the game.

4. Game Rules and Mechanics: After finishing the construction of the game components, students should develop an instruction manual containing the rules and mechanics of the game. The rules should be clear and objective, so that anyone can understand and play.

5. Game Testing: Finally, students should play the game they created to test and adjust any rule or component that is not working well.

The project duration is one week, based on an average of 2 to 4 hours of dedication from each student to carry out the project.

Project Delivery:

After completing the practical project, groups must produce a report including the following topics:

1. Introduction: The group must introduce the topic of notable products and explain their relevance and applications. They should also include the project's objective and the motivation for choosing the type of game created.

2. Development: Here, the group must detail the theory of notable products, explain in detail the game created, including its rules and challenges. They should also insert images of the game and talk about the creation process, highlighting the strategies used to insert notable products into the game and the challenges encountered. In this part, it is important for students to show how the concepts and skills learned in mathematics and especially in notable products were applied in the creation of the educational game.

3. Conclusion: Students must conclude the report with a discussion on the learnings obtained during the process, relating the game dynamics and the notable product concepts. Additionally, they should talk about the experience of working in a group and how they managed to apply mathematical concepts in the creation of a playful-educational game.

4. Bibliography: Indication of research sources for the project, such as books, websites, videos, etc.

The report must be delivered to the teacher along with the game created, which will be evaluated in the classroom.