Contextualization
Mathematics is a vast field of study that permeates all areas of our lives and human knowledge. In this project, we will deepen our studies in the field of geometry, more specifically in the so-called 'vertically opposite angles' (OPV).
To begin with, what are these angles? When two lines intersect, they form four angles. The angles that are opposite to each other - that is, they do not share any side - are called OPV angles. A fundamental property of these angles is that they are always equal. This is a geometric property that can help us solve a variety of problems, as we will see next.
It is a mistake to think that this information is only useful for mathematicians or math teachers. OPV angles have practical applications in the real world, in areas such as engineering, architecture, arts, and sports. For example, in civil engineering, when it is necessary to calculate the angle for the construction of a bridge. Or even in art, when we need to understand the perspective of a drawing so that it appears three-dimensional.
Mathematics, in this sense, is a tool that allows us to better understand the world around us and even improve the world we create. That is why the study of OPV angles is so important.
To delve deeper into the subject and prepare for the project, we suggest consulting the following materials:
Let's get started? Let's do it!
Practical Activity
Activity Title: 'Challenge of OPV Angles in the City'
Project Objective:
The objective of this project is to apply the concept of vertically opposite angles (OPV) in a real-world scenario to reinforce students' understanding of the topic. In addition, teamwork will be essential for the development and completion of the project, allowing students to also develop socio-emotional skills.
Detailed Project Description:
Students, in groups of 3 to 5, will have the challenge of identifying examples of OPV angles in buildings and structures in the city where they live. They must document these examples through photos and then draw a detailed diagram, identifying the vertically opposite angles.
Required Materials:
- Camera (cell phone camera works)
- Paper and pencil (or drawing software, if preferred)
- Ruler and protractor
- Computer with internet access for research and report preparation
Detailed Step-by-Step for Carrying Out the Activity:
- Students must form groups of 3 to 5 people.
- Each group should research and identify at least five structures (bridges, buildings, artworks, etc.) in the city that have OPV angles.
- Students must take photos of these structures and, using image editing software or printing the photos, identify the OPV angles present, using a ruler and protractor.
- On a piece of paper, students must draw a diagram of the identified structure and mark the OPV angles.
- Each group must prepare a presentation, explaining about the chosen structure, the presence of OPV angles, and their importance in the structure's construction.
- Finally, each group must write a report containing: the introduction (contextualizing the theme and explaining its relevance and real-world application); the development (explaining the theory behind the concept of OPV angle, detailing the activity, indicating the methodology used, and presenting and discussing the results obtained); the conclusion (explaining the learnings obtained and the conclusions drawn about the project); and the bibliography used.
The expectation is that each student dedicates between two to four hours to complete the project, with a one-week deadline.
Project Delivery:
The project delivery should be in two parts:
- The presentation of the diagram of the found OPV angles and an explanation of why they were chosen, which will be done in the classroom.
- The written report, which must be submitted on the school's online platform. In the document, the group should discuss the selected structures, the identified angles, the theory behind OPV angles, their importance in the structure in question, and how the group worked together to complete the project.
The report should follow the suggested structure (Introduction, Development, Conclusions, Bibliography) and be well-written and formatted. Each part should be clearly defined, with a logical flow from introduction to conclusion. References should be correctly formatted.
