Contextualization

Notable products are algebraic expressions with standardized forms and results. They are remarkable precisely because they frequently appear in mathematical exercises and problems and because they facilitate the solution of these problems. The distributive property is fundamental to understanding notable products. This property establishes that the product of a number by a sum is equal to the sum of the products of that number by each of the terms.

Specifically, in mathematics, there is no escape from notable products in algebra! Whether in calculating areas, volumes, studying quadratic functions, or Newton's binomial. Mastery of this knowledge is essential to successfully advance in the discipline's studies.

For example, when we look at the world around us, many objects have geometric shapes that require the use of notable products to calculate their area or volume. Engineers, for example, when designing the construction of buildings, roads, bridges, and complex systems, use mathematical concepts, including notable products, to make these calculations.

That said, you might be wondering, "But how exactly are notable products applied in the real world?" Well, think of a company that produces box-shaped packaging for its products. Calculating the volume of these boxes involves the use of notable products. Thus, to ensure resource optimization and profit maximization, it is crucial that the company understands and correctly applies these mathematical concepts.

Practical Activity: "Exploring the Real World with Notable Products"

Project Goal

This project aims to allow students to explore and identify the application of notable products in the real world. Students will have the opportunity to integrate the theory learned in the classroom with practice by creating a project that requires the direct application of notable product concepts.

Detailed Project Description

Students, forming groups of 3 to 5 people, will design and build a three-dimensional object that involves the use of notable products to calculate its surface area and volume. Students may choose to create houses, bridge structures, product packaging, decorative objects, etc., using recyclable materials.

Students will prepare a report detailing the entire process, from project conception to completion, including an explanation of the theory of notable products and how it was applied in the project.

The project should be completed within a month, and each student should dedicate between five and ten hours to its execution.

Required Materials

• Recyclable materials such as cardboard, straws, plastic bottles, etc.
• Scissors, glue, adhesive tape.
• Drawing materials: ruler, compass, protractor, pencil, eraser, etc.
• Calculator.

Step by Step

1. Group formation and choice of object to be built: Students should organize themselves into groups and choose the object to be built. Everyone in the group must agree and be interested in the chosen project.

2. Structure design: The group should design the structure, with the measurements of all sides well defined. The structure should be designed in such a way that it enables the use of notable products to calculate its area and volume.

3. Object construction: With the designs in hand, the group should build the object using recyclable materials.

4. Area and volume calculation: Using the knowledge acquired in class about notable products, the students should calculate the surface area and volume of their object.

5. Report writing: The group should write a report detailing the entire process, from project conception to completion. The report should explain the theory of notable products and how it was applied to the project.

Project Delivery

The project should be delivered in two parts: the first is the physical object built by the students; the second is the written report containing the explanation of the theory, a detailed description of the object, the methodology used in the construction and calculation of the area and volume, and finally, the presentation and discussion of the results obtained.

The report should be structured in four main topics:

• Introduction: Description of the theme, its relevance, and application in the real world, and the objective of the project.
• Development: Explanation of the theory about notable products, detailed description of the activity, methodology used, and presentation of the results.
• Conclusion: Review of the main points of the work, explanation of the lessons learned, and conclusions drawn about the project.
• Bibliography: Indication of the reference sources for the execution of the project as books, web pages, videos, etc.

Through this project, students will be able to recognize the main notable products and apply them in a practical way, besides developing socioemotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.