Project: Creating a Miniature City

Context

Mathematics, and geometry in particular, is a rich and fascinating discipline that allows us to understand and shape the world around us. One of the capabilities that mathematics offers us is the ability to enlarge or reduce figures while preserving their shape and proportions. This ability is fundamental to various activities in everyday life and careers, such as architecture, engineering, design, art, and even medicine.

The concept of enlarging or reducing a figure refers to the process of creating a new figure that is proportionally similar in shape and size to the original figure. To do this, we need to understand and apply concepts such as ratio, scale, and similarity. Enlarging a figure occurs when we increase its size, while reduction occurs when we decrease its size.

The resulting figures are known as similar figures, as they have the same shape but different sizes. The concept of similarity is based on the idea of proportion. If two figures are similar, it means that the corresponding lengths in the two figures are in the same ratio, and the corresponding angles in the two figures are equal.

Relevance and Real-World Applications

The process of enlarging and reducing figures has practical applications in the real world. For example, it is an essential skill for architects and engineers when creating construction plans. They often create a scale drawing of the project, which is a reduced version of the object they plan to build. This drawing allows them to see how all the different elements of the project fit together without having to build a full-size model.

In medicine, enlarging medical images, such as X-rays and MRI scans, allows doctors to see tiny details that can be crucial for diagnosing and treating health conditions. In art, artists may use figure enlargement and reduction to alter perspective and create unique visual effects.

Therefore, the ability to enlarge and reduce figures is an important skill that has a wide range of applications. It is not only useful in academia but also an essential tool in many careers and everyday activities.

Hands-on Activity: Creating a Miniature City

Project Goal

The goal of this project is to apply the concepts of figure enlargement and reduction in the creation of a miniature city model. You will design and construct scaled-down buildings, parks, and roads, practicing the skills of figure enlargement and reduction while learning about proportions and scales.

Detailed Project Description

Form groups of 3 to 5 students. You will need to choose a real or fictional city and research its main architectural elements. Based on this research, you will create a scale drawing of the city and later transform it into a three-dimensional model.

Students will then present their model to the class, explaining how they used the concepts of enlargement and reduction to create the different elements of the city.

Required Materials

• Graph paper
• Pencils and erasers
• Ruler and compass
• Building materials for the model (e.g., cardboard, popsicle sticks, modeling clay, etc.)
• Glue
• Scissors

Step-by-Step Instructions

1. Choose a city and research its main landmarks and features.
2. As a group, design a sketch of the city, considering the placement of buildings, plazas, parks, etc.
3. Define the scale of the model. This means determining how much of the "real-world" size each unit in the drawing will represent.
4. Create a scale drawing on graph paper, using the scale you defined earlier.
5. Use the scale drawing to create the elements of the model using the building materials.
6. Assemble the model, staying as true to the scale drawing as possible.

Project Deliverables and Report Write-Up

Upon completion of the project, each group must produce a written report containing:

1. Introduction: In this section, provide context about the chosen city, its relevance, and the reasons for choosing it. Additionally, explain the purpose of the project and the importance of the concept of figure enlargement and reduction.

2. Development: Here, detail the steps taken to execute the project. Explain the theory of figure enlargement and reduction, the measurements you chose, the scale you defined, and how you constructed the model.

3. Conclusions: Summarize the main points of the project, highlighting the lessons learned, challenges encountered, and how they were overcome. Also, reflect on the relevance of the concepts used in the project to real-life situations.

4. Bibliography: List the sources you used to research the city and understand the mathematical concepts involved.

Remember: the report should complement the hands-on project, serving as a detailed written record of the group's work and learning process.