Lesson Plan | Teachy Methodology | Spatial Geometry: Deformations in Projections

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to prepare students to explore and understand the complex distortions of angles and areas in different cartographic projections. This is essential for applying spatial geometry in the real context of cartography, as well as for developing a critical understanding of the geographical representations they consume in daily life.

Main Objectives

1. Understand how cylindrical and conical cartographic projections affect the distortion of angles and areas.

2. Apply knowledge of spatial geometry to analyze distortions in maps.

Side Objectives

1. Develop critical analysis skills when comparing different types of cartographic projections.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to prepare students to explore and understand the complex distortions of angles and areas in different cartographic projections. This is essential for applying spatial geometry in the real context of cartography, as well as for developing a critical understanding of the geographical representations they consume in daily life.

Warming Up

Explain to students that cartography, the science of creating maps, uses different projections to represent the Earth's spherical surface on a flat surface. Each projection has its advantages and disadvantages, mainly regarding the distortion of angles and areas. Instruct students to use their cell phones to find an interesting fact about cartographic projections and share it with the class. For example, they might look up how the Mercator projection exaggerates the size of countries near the poles compared to those at the equator.

Initial Reflections

1. What are the main cartographic projections used in maps?

2. How does the cylindrical projection affect the representation of angles and areas?

3. What are the differences between cylindrical and conical projections in terms of distortion?

4. Why is it important to understand the distortions caused by cartographic projections?

5. How can these distortions influence the way we interpret maps?

Development

Duration: 60 - 70 minutes (+ 10 - 15 minutes of explanation)

The purpose of this stage is to actively and creatively engage students, providing a deep understanding of the distortions of angles and areas in cartographic projections. By using digital technologies and modern formats like social media and gamification, learning becomes more contextualized and aligned with students' realities.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 - Influencer Map 

> Duration: 60 - 70 minutes

- Objective: Explore the importance of cartographic projections and their distortions in a creative and accessible way, using social media as a knowledge dissemination tool.

- Description: In this activity, each group will consist of 'digital influencers'. The task will be to create a series of posts for a fictional social media platform that explains how different cartographic projections affect the perception of geographical space. Using digital tools, students will create infographics, short videos, and explanatory texts showing examples of cylindrical and conical projections and their distortions.

- Instructions:

• Form groups of up to 5 people.

• Assign a specific topic to each group, such as cylindrical projection, conical projection, and the comparison between both.

• Students must use their cell phones and laptops to research visually interesting examples of maps with different projections.

• Use image editing applications like Canva or Adobe Spark to create infographics highlighting the distortions of angles and areas in each projection.

• Record short videos (using tools like TikTok or Instagram) where the 'influencers' explain the differences between the projections and how this can impact map interpretation.

• At the end, each group will present their posts to the class, simulating a digital campaign.

Activity 2 - Virtual Escape Room ️‍♂️️‍♀️

> Duration: 60 - 70 minutes

- Objective: Encourage collaboration and critical thinking through practical problem-solving, reinforcing knowledge about distortions of cartographic projections in a playful way.

- Description: Students will participate in a 'Virtual Escape Room' where they will need to solve a series of enigmas and mathematical challenges related to cartographic projections to 'escape'. Using platforms like Google Forms or Kahoot, the challenges will be interactive and gamified, incorporating questions that involve calculations of angle and area distortion.

- Instructions:

• Form groups of up to 5 people.

• Distribute the links to the previously created 'Virtual Escape Room' on Google Forms or Kahoot.

• Students will need to solve enigmas that include distortion calculations and comparisons of different cartographic projections.

• Each correctly solved enigma will give access to the next phase of the escape room.

• The group that solves all the enigmas in the shortest time will 'escape' first.

• Discuss the correct answers and clarify doubts at the end of the activity.

Activity 3 - GeoStory: The Diary of an Explorer 

> Duration: 60 - 70 minutes

- Objective: Promote creativity and practical application of knowledge about cartographic projections and their distortions through the creation of an engaging and contextualized narrative.

- Description: Students will create a digital diary of a fictional explorer who traveled the world using different types of maps. Using text and image editing tools (such as Google Docs and Canva), they will document the explorer's adventures, highlighting how different cartographic projections impacted their journey. Each diary entry should include images of maps, descriptions of observed distortions, and reflections from the 'explorer' on the projections.

- Instructions:

• Form groups of up to 5 people.

• Each group creates a 'explorer' character and drafts a travel itinerary that passes through several continents.

• Students must research and include maps with different projections (cylindrical and conical) for each region visited.

• Use Google Docs to write diary entries and Canva to create illustrative images and infographics.

• Each entry should describe the observed distortions of angles and areas, providing a reflection on the impacts of these projections on geographical perception.

• At the end, each group will present the digital diary to the class.

Feedback

Duration: 20 - 25 minutes

The purpose of this stage is to consolidate the knowledge gained through a collective reflection on learning, providing students with the opportunity to express their conclusions, hear different perspectives, and receive constructive feedback. This contributes to the development of critical and collaborative skills, essential for continuous and applied learning.

Group Discussion

Promote a group discussion with all students, where each group will have the opportunity to share their conclusions and learnings from the proposed activities. To introduce this discussion, suggest the following script:

Introduction: Briefly explain the purpose of the discussion and the importance of sharing learnings. Group Presentations: Ask each group to present a summary of their activities and key conclusions. Open Discussion: Encourage students to ask questions and comment on their peers' presentations. Final Reflection: Lead a collective reflection on what has been learned and how this can be applied in other contexts.

Reflections

1. What were the biggest differences observed between cylindrical and conical projections? 2. How can distortions in cartographic projections influence the interpretation of geographical data? 3. What are the implications of these distortions in the real world and in our daily lives?

360° Feedback

Instruct students to carry out a 360° feedback step, where each student must receive feedback from the other members of the group they worked with. Guide the class to ensure that the feedback is constructive and respectful, using the following format:

Positive Aspects: Each student should highlight something positive about their colleagues' contributions. Areas for Improvement: Each student may suggest an area where the colleague could improve. Respect and Objectivity: Reinforce the importance of maintaining respect and being objective in observations.

Conclusion

Duration: 5 - 10 minutes

Purpose : The purpose of this stage is to consolidate learning in a playful and contextualized manner, allowing students to understand how distortions in cartographic projections affect our perception of the world. By summarizing, connecting with the current world, and discussing practical applications, we reinforce the relevance of the content learned and encourage a critical and informed view of the maps we use every day. ️

Summary

Summary 邏: Imagine the Earth is an orange and our goal is to turn that orange into a flat map without squeezing out the juice! ➡️ Today, we explored how cylindrical and conical projections help (or hinder) us in this task. We saw that each projection has its special way of distorting angles and areas, making continents look bigger or smaller than they really are. It was a true adventure of digital influencers, fictional explorers, and escape room challenges! ✨️‍♂️

World Connection

In the World : Today's lesson showed how spatial geometry influences our perception of the world around us! In a world where we use maps for almost everything - from planning trips to deciding where to meet - understanding distortions is essential. With smartphones and GPS, we have all kinds of maps at our disposal, but are they all representing the world fairly and accurately? ️

Practical Application

Applications ️: Knowing about cartographic projections is more than mastering mathematical concepts; it is understanding the power of maps in our daily lives. Whether for analyzing geographical data, planning urbanizations, or even choosing the best route on Google Maps, understanding these distortions helps in making more informed and critical decisions. ️️