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

Use a Lego house as the scale model

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 Outline for a Scale Model of a Lego House

Real-World Figure and Scale Factor

For this project, I will be modeling a typical single-story house measuring 30 feet in length and 20 feet in width. The scale factor I plan to use for my Lego house model is 1:10. This means that every foot of the actual house will be represented by 1 inch on the Lego model. Thus, the model will have dimensions of 3 feet in length (36 inches) and 2 feet in width (24 inches).

Significant Items in the Model

1. Front Door

   • Real-World Dimensions: A standard front door typically measures about 3 feet tall and 2.5 feet wide.
   • Model Dimensions: At a scale of 1:10, the front door will be scaled down to 3 inches tall and 2.5 inches wide.

2. Windows

   • Real-World Dimensions: A standard house window might be approximately 4 feet wide and 3 feet tall.
   • Model Dimensions: At a scale of 1:10, each window will measure 4 inches in width and 3 inches in height.

Calculations and Dimensions for Significant Items

To create an accurate scale model, I will need to perform the following calculations:

1. Calculate Scale Dimensions:

   • For the front door: \[ \text{Model Height} = \frac{3 \text{ feet}}{10} \times 12 \text{ inches/foot} = 3 \text{ inches} \] \[ \text{Model Width} = \frac{2.5 \text{ feet}}{10} \times 12 \text{ inches/foot} = 2.5 \text{ inches} \]
   • For the window: \[ \text{Model Width} = \frac{4 \text{ feet}}{10} \times 12 \text{ inches/foot} = 4 \text{ inches} \] \[ \text{Model Height} = \frac{3 \text{ feet}}{10} \times 12 \text{ inches/foot} = 3 \text{ inches} \]

2. Ensure Mathematical Similarity: I will verify that the ratios of the dimensions of the model items are equivalent to those of the real-world counterparts. This involves ensuring that: \[ \frac{\text{Model Height}}{\text{Model Width}} \text{ for the door is the same as } \frac{\text{Real Height}}{\text{Real Width}} \text{ for the door} \] \[ \frac{3 \text{ inches}}{2.5 \text{ inches}} \approx 1.2 \text{ (same as real-world)} \]

Mathematical Skills Required

To create the design, I will need the following mathematical skills:

1. Basic Scaling Calculations: Understanding how to apply a scale factor and perform conversions between feet and inches.
2. Ratio and Proportion: Ensuring that the scaled items maintain the same proportional relationships as in the actual structure.
3. Area and Volume Calculation: Understanding how to calculate the area for the floor plan and model to ensure accurate representation in 3D.

Outside Sources for Calculations

1. Architectural Standards: Research into typical dimensions of house features (doors, windows, etc.) can be found from online architectural guidelines or design websites.
2. Lego Dimensions: I may refer to catalogs or the official Lego website to identify the dimensions of available Lego bricks to ensure I build accurately to the intended scale.
3. Math Conversion Tools: Online converters and scaling calculators can aid in determining the equivalent dimensions correctly, especially when dealing with non-standard sizes.

Conclusion

This scale model of a Lego house serves as an exciting project to apply mathematical concepts of similarity, scaling, and dimensions. By accurately modeling real-world features with careful calculations, I can create a fun and educational representation of architecture using Lego bricks.