Contextualization

Introduction

Spatial Geometry, often also referred to as solid geometry, is a fundamental area in Mathematics that deals with three-dimensional objects. In this project, we will focus on understanding the concept of "Surface Area of a Prism".

Prism, in this context, refers to a solid figure that has two parallel and congruent ends or bases, and all of its sides are rectangles. The understanding of prisms, and more specifically their surface area, is key to unlock further understanding of geometry as a whole.

The surface area of a prism can be understood as the amount of space on the outside of the figure. In simpler words, if you were to 'unwrap' the prism and lay it flat, the surface area would be the space that the 'unwrapped' figure would occupy. It is computed by adding together the areas of all the faces of the prism.

Contextualization

The concept of Surface Area, particularly in relation to prisms, is hugely significant in many fields of real-world application, such as architecture, design, construction, packaging design and even space travel.

Think of any structure or building we have constructed - each one can essentially be broken down into a combination of different prisms. The same applies to any object we design and manufacture, be it a simple cardboard box or a complex satellite. Knowing how to calculate the surface area of a prism allows us to determine how much 'material' we would need to construct such objects.

Resources

For deep learning, the following resources are recommended:

1. Khan Academy's lessons on Surface Area are very interactive and full of practical examples.
2. This article on Surface Area of a Prism on AAA Math offers a clear and concise explanation.
3. The video Surface Area of Prisms on YouTube provides a visual understanding of the concept.
4. The Spatial Geometry module on the University of Georgia's website has a comprehensive overview of solid figures, including prisms.

Practical Activity

Activity Title: "Design Your Own Prism City"

Objective

To understand and calculate the surface area of various prisms through a hands-on activity and use this knowledge to create a city model made entirely of prisms.

Description

In this activity, students will first learn to calculate the surface area of various prisms, and then apply this knowledge to design and create a city using prism-shaped buildings. Each group of students will create a unique city layout and provide a detailed report about the activity.

Materials Required

1. Cardboard or Foam Board
2. Ruler
3. Pencil and Eraser
4. Scissors
5. Glue
6. Colored Markers
7. Calculator
8. Notebook
9. Laptop with internet access

Step by Step Instructions

1. Theory Session: Begin the project with a quick theory session where each member researches different types of prisms and their surface areas and shares their findings with the group.

2. Sketching the Prisms: Each group of students should sketch several different types of prisms (at least five different types, such as rectangular prisms, triangular prisms, pentagonal prisms, etc.) on their notebook.

3. Calculating Surface Area: For each sketched prism, the students should calculate the surface area and note it down next to the corresponding prism sketch. Cross-verification within the group is encouraged to ensure accuracy of the calculation.

4. Designing the City: After the calculations, the students need to work together to design a city layout using their prism buildings. The layout should be drawn on a sheet of cardboard or foam board.

5. Creating the Buildings: The students should then create each building using cardboard, following the dimensions used in the calculations. The buildings should be colored and decorated as preferred.

6. Assembling the City: Once all buildings are ready, they should be glued to the city layout on the cardboard or foam board based on the design sketched in step 4.

7. Final Report: After the completion of the practical part of the project, students must write a report detailing the process and their learnings. This report must include sections on Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

1. A model of a city made entirely of prism-like buildings.

2. The group's notebook with sketches and surface area calculations of the prisms.

3. A final written report detailing the process and their findings.

   • Introduction: The report should begin with an explanation of the concept of surface area of prisms, its applications in real world scenarios, and the objective of the project.

   • Development: This section should contain a detailed explanation of the steps followed in the activity, from the initial brainstorming to the design process and calculation of the surface areas. Include details on the methodology used and discuss the results obtained.

   • Conclusion: The report should conclude with the students' learnings from the project, what they understood about the concept of surface area of prisms, and how they applied it in their project.

   • Bibliography: In the end, they should mention all the sources referred to during the project. These could be textbooks, websites, YouTube videos, etc.

Remember, the total duration of the project is one week, with an expected commitment of 2-4 hours per student. Make sure to manage your time well, distribute tasks among group members, and collaborate effectively to build an amazing Prism City!