Put transformation and similarity concepts 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.
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.
For my scale model design, I have chosen to model the Eiffel Tower in Paris, France. The scale factor I will use is 1:100, meaning that every 1 unit on my model will represent 100 units in real life.
Two significant items on my model will be the base of the Eiffel Tower and one of the arches on the first level. To determine the calculations and dimensions for these items, I will need to analyze the real-world measurements and proportions of the base and arch.
To make the base of the model mathematically similar to the actual base, I will need to ensure that the ratios of the different dimensions are preserved. For example, if the base of the actual Eiffel Tower has a length of 100 meters and a width of 50 meters, in my model, I would represent it as 1 meter by 0.5 meters. By maintaining the ratio of 1:100, I am ensuring mathematical similarity.
Similarly, for the arch on the first level, I will need to analyze its measurements, such as height, width, and curvature, and apply the scale factor to recreate the same proportions on my model.
To create this design, I will need mathematical skills such as multiplication, division, and ratio calculations. For instance, I will use multiplication to determine the dimensions of the base and arch on my model based on the real-world measurements. I will also use division to check if the ratios of different dimensions are accurately represented in the model.
In order to accurately calculate the dimensions, I will need external sources such as architectural plans, photographs with measurements, or online resources that provide detailed information about the Eiffel Tower's dimensions. These sources will help ensure the mathematical accuracy and similarity of my scale model design.