Contextualization

Theoretical Introduction

The parallelogram is a flat figure with four sides (quadrilateral) whose opposite sides are parallel. The word 'parallelogram' comes from the Greek 'parallelogrammon', where 'parallelos' means 'parallel' and 'gramma' means 'write'. In technical terms, a parallelogram is a specialized quadrilateral with two pairs of parallel sides. Additionally, in a parallelogram, opposite angles are equal and opposite sides also have the same length.

The study of parallelograms is important as it plays a significant role in various areas of mathematics, including Euclidean geometry, trigonometry, calculus, and many forms of applied mathematics in physics and engineering.

In this project, the main points to be addressed are: what is a parallelogram, properties of a parallelogram (including how to calculate measurements of sides and angles), and the application of parallelograms in problem-solving.

Contextualization

The concept of parallelogram is used in numerous fields of everyday and professional life. For example, in architecture and civil engineering, parallelograms are used in the design and structuring of buildings, when designing plans and calculating areas. In physics, parallelograms are used in the parallelogram law for vector addition.

Furthermore, understanding parallelograms can help in problem-solving skills and logical reasoning, which are important in many areas beyond mathematics, including computer science, engineering, and economics.

Practical Activity

Activity Title: "Building the Universe of Parallelograms"

Project Objective:

Students will explore the concept of parallelograms not only in theory but in practice, building them and taking measurements. Additionally, they will be involved in problem-solving involving parallelograms.

Detailed Project Description:

The activity will be divided into 3 distinct phases:

1. Construction and Measurement: In this phase, each group of students will build several parallelograms using everyday materials. They must then measure the sides and angles, and verify the properties of the parallelograms.

2. Problem Solving: Groups will solve a set of mathematical problems involving parallelograms.

3. Report: Finally, each group must write a project report detailing the entire learning process, construction, and problem-solving, as well as the conclusions.

Necessary Materials:

1. Materials for building parallelograms: Popsicle sticks (or straws), glue, strings.
2. Ruler and protractor for measurement.
3. Mathematical problems involving parallelograms - the teacher can provide a list.

Detailed Step-by-Step:

1. Construction and Measurement

   • Each group must build at least 3 different parallelograms using popsicle sticks (or straws) and glue. They should use the string to represent the parallel lines of the parallelograms.
   • Then, they must use the ruler and protractor to measure the sides and angles of the constructed parallelograms, respectively, and verify the properties of the parallelograms.

2. Problem Solving

   • Each group must solve the problems provided by the teacher. Solutions should be explained clearly and completely.

3. Report Writing

   • Each group must write a report detailing the entire construction, measurement, and problem-solving process.
   • The report should include an introduction, where students should contextualize the theme, consolidate the project's objective, and the application of parallelograms in the real world.
   • Next, in the development, students should explain the theory of parallelograms, detail the construction and measurements made, the methodology used for problem-solving, and the results obtained.
   • In the conclusion, students should discuss what they learned from the project, as well as their findings and difficulties encountered during the process.
   • Finally, in the bibliography, students should indicate all bibliographic sources, websites, videos, and other resources used during the project.

The project should be carried out by groups of 3 to 5 students and will have a one-month deadline for submission. Each student should dedicate 5 to 10 hours to complete it.

The evaluation will take into account both the practical part (construction, measurement, problem-solving) and the report writing.