You have explored transformations you have used, observed, or imagined. You have also worked with figures that are similar and have learned how to calculate angles and side lengths to identify similarity.
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, I have chosen to model the Eiffel Tower. The scale factor I will use is 1:100, meaning that every centimeter on my model will represent 100 centimeters on the actual Eiffel Tower.
Two significant items on my model will be the height of the tower and one of the arches.
To determine the dimensions for these items, I will use the concept of similarity. Since my scale factor is 1:100, I can simply divide the actual measurements by 100 to get the corresponding measurements for my model. For example, the current height of the Eiffel Tower is 324 meters, so the height of my model will be 324/100 = 3.24 meters. Similarly, if one of the arches on the Eiffel Tower has a length of 10 meters, the length of the corresponding arch on my model will be 10/100 = 0.1 meters.
The specific mathematical skills I will need to create the design include understanding scale factors and proportions, as well as basic division and conversion of units. For example, I will need to correctly convert meters to centimeters when applying the scale factor to calculate dimensions.
To calculate some of the dimensions accurately, I may need to refer to outside sources. For instance, I may need to gather information about the actual measurements and proportions of the Eiffel Tower from reputable sources such as architectural documents, books, or reliable websites. This will ensure the accuracy of my calculations and help me create an authentic representation of the Eiffel Tower in my scale model.
Give me another example
Certainly! Another example of a scale model design could be modeling a car. Let's say I want to create a scale model of a Ferrari 458 Italia using a scale factor of 1:24.
Two significant items on my model will be the length of the car and the diameter of the wheels.
To determine the dimensions for these items, I will once again utilize the concept of similarity. Since my scale factor is 1:24, I can divide the actual measurements by 24 to obtain the corresponding measurements for my model. For instance, the overall length of a Ferrari 458 Italia is approximately 4.53 meters. Therefore, the length of my model car will be 4.53/24 = 0.18875 meters.
Similarly, if the wheels on the actual car have a diameter of 55 centimeters, the diameter of the wheels on my model will be 55/24 = 2.29 centimeters.
To create the design, I will need mathematical skills such as scaling ratios, proportions, and division. I will also need to convert units, such as converting meters to centimeters for precise measurements.
To ensure the accuracy of my calculations and dimensions, I may need to seek outside sources such as car specifications from the official Ferrari website or reputable car magazines. These sources will provide the correct measurements for the car and its components, allowing me to accurately recreate them in my scale model.