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.
Then read two of your peers’ descriptions of their designs. Respond to two of your peers:
Describe what is effective about the design.
Describe the flaws or challenges you observe in the design.
Suggest some improvements in the design.
Design Description:
I have chosen to model a famous landmark, the Eiffel Tower, as my real-world figure. The scale factor I will use for my scale model is 1:100, meaning that every one unit on my model will represent 100 units on the actual Eiffel Tower.
Two significant items on my model will be the arches at the base of the tower and the intricate lattice structure on the upper levels.
To ensure that these items are mathematically similar to the actual Eiffel Tower, I will use the following calculations:
1. For the arches at the base: I will measure the height and width of the arches on the actual tower and divide them by the scale factor of 100 to determine the corresponding dimensions on my model.
For example, if the height of the arches on the actual tower is 10 meters, then the height on my model will be 10/100 = 0.1 meters.
2. For the lattice structure on the upper levels: I will measure the spacing between the horizontal and vertical beams on the actual tower and again divide them by the scale factor of 100 to determine the corresponding dimensions on my model.
For example, if the spacing between the beams on the actual tower is 5 centimeters, then the spacing on my model will be 5/100 = 0.05 centimeters.
The specific mathematical skills I will need to create this design include measurement skills, division, and scaling. I will need to accurately measure the dimensions of the real Eiffel Tower and use mathematical calculations to scale them down to the appropriate size for my model.
To perform these calculations, I may need outside sources such as architectural blueprints or detailed measurements of the Eiffel Tower. These sources will provide accurate measurements of the various elements of the tower, allowing me to create a mathematically accurate scale model.
Response to Peer 1:
I find your design of a scale model of the Taj Mahal to be effective. The choice of a famous and recognizable landmark is great, as it will capture the attention of viewers. Your use of a scale factor of 1:50 is also appropriate, as it allows for enough detail in the model without making it too large.
One improvement I would suggest is to include some of the intricate carvings and decorations on the walls of the Taj Mahal in your design. These details are a significant aspect of the real Taj Mahal and including them in your scale model would enhance its accuracy and visual appeal.
Response to Peer 2:
Your design of a scale model of the Statue of Liberty is commendable. The choice of a well-known landmark will surely attract attention. The scale factor of 1:200 seems appropriate, making the model a manageable size while still allowing for significant detail.
One improvement I would suggest is to include the crown and torch in your design. These elements are iconic features of the Statue of Liberty and adding them to your model would make it more visually appealing and accurate. Additionally, you may need to consider the challenges of replicating the intricate details of the statue's facial expression and the materials used in the real statue.