You have worked with figures that are similar and have learned how to calculate angles and side lengths to identify similarity. Put these skills together to plan a design for a scale model. Showing how these concepts effectively work in the real world involves clear communication and the ability to defend your conclusions to others.

Question

using an Android cell phone as a real-world figure

In your post, describe your design to your peers:

State the real-world figure you will model and the scale factor you will use.
Identify at least two different but significant items on your model.
Explain how you will determine the calculations and dimensions for these items to make them mathematically similar to the actual items.
Describe the specific mathematical skills you will need to create the design and give examples.
Describe some outside sources you may need for the calculations.

Answer 1

Design Proposal for a Scale Model of an Android Cell Phone

Real-World Figure and Scale Factor: The real-world figure I will model is a standard Android cell phone, specifically the Google Pixel 5. To create a manageable scale model, I will use a scale factor of 1:10. This means that each dimension of my model will be 1/10th the size of the corresponding dimensions of the actual phone.

Significant Items:

1. Screen
2. Camera Module

Calculations for Dimensions: To ensure the model is mathematically similar to the actual items, I will first gather the official dimensions of the Google Pixel 5.

• Screen Dimensions: The Google Pixel 5 has a screen size of approximately 6.0 inches diagonally.

  • Scale model screen size:
    • 6.0 inches ÷ 10 = 0.6 inches (diagonal)
  • For width and height calculations, the aspect ratio of the phone's screen is about 19.5:9.
    • Height: \( \frac{0.6}{\sqrt{(19.5^2 + 9^2)}} \cdot 9 = 0.27 \) inches
    • Width: \( \frac{0.6}{\sqrt{(19.5^2 + 9^2)}} \cdot 19.5 = 0.61 \) inches

• Camera Module Dimensions: The camera module is approximately 0.5 inches in height and a little over 1 inch in width for the actual pixel phone.

  • Scale model camera dimensions:
    • Height: 0.5 inches ÷ 10 = 0.05 inches
    • Width: 1 inch ÷ 10 = 0.1 inches.

By retaining the aspect ratios in the way we calculated the width and height for the screen, I ensure that both features are proportionally accurate in the scale model.

Mathematical Skills Required: To create this design, I will need to apply several mathematical skills:

1. Proportions and Ratios: Using these skills allows me to ensure that items in the model maintain the same shape ratios as their real-world counterparts.

   • Example: Keeping the aspect ratio of the screen constant during scaling.

2. Basic Arithmetic Operations: Performing division for the scale factor and working with decimal dimensions.

   • Example: Dividing actual dimensions by the scale factor (in this case, 10).

3. Geometry: Understanding properties of geometric figures will help me visualize how the dimensions of the phone and its features relate to one another.

   • Example: Calculating diagonal lengths using the Pythagorean theorem when determining the screen's dimensions based on its width and height.

Outside Sources for Calculations: To gather the necessary dimensions and detailed specifications of the Google Pixel 5, I will utilize various outside sources:

1. Manufacturers’ Website: Official specifications often provide accurate and detailed measurements.
2. Technology Review Websites: Sites like GSMArena and TechRadar often provide comprehensive specs and comparisons across various phone models.
3. 3D Modeling Tools: Software that allows for creating digital models could help visualize and calculate dimensions accurately if further precision is needed.

By effectively leveraging these mathematical skills and resources, I will be able to create a scale model of the Android cell phone that is not only aesthetically pleasing but also mathematically accurate and reflective of the real-world dimensions. I look forward to presenting this model to you all!