Similar Figures Discussion
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.
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.
Post a detailed response to the Similar Figures Discussion prompt. Then respond to two classmates' posts.
Participate in the discussion to learn more about using similar figures to design a scale model.
Design:
The real-world figure I will model is a famous landmark, the Eiffel Tower. The scale factor I will use is 1:100, meaning that every unit on the scale 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 observation deck on the top.
To determine the calculations and dimensions for these items, I will first gather measurements and information about the actual Eiffel Tower. I will find the height, the width of the base, and the dimensions of the arches and observation deck.
Next, I will apply the scale factor to these measurements to determine the dimensions of the scale model. For example, if the height of the actual Eiffel Tower is 324 meters, then the height of the scale model will be 3.24 meters (324 meters divided by 100). Similarly, if the width of the base is 125 meters, then the width of the scale model will be 1.25 meters (125 meters divided by 100).
To ensure that the arches and observation deck are mathematically similar to the actual items, I will calculate the corresponding angles and side lengths. I will use the concept of corresponding angles to determine the angles of the arches and observation deck on the scale model. And I will use the concept of corresponding side lengths to ensure that the proportions of the arches and observation deck on the scale model match those of the actual items.
The specific mathematical skills needed to create this design include measuring angles, calculating scale factors, and applying the concept of corresponding angles and side lengths. For example, I will need to use trigonometry to calculate the angles of the arches and observation deck. I will also need to use proportions to ensure that the side lengths of these items on the scale model are proportional to the actual items.
For the calculations, I may need outside sources such as architectural plans of the Eiffel Tower, which provide detailed measurements and dimensions. I may also need to consult with experts or use online resources to gather accurate information about the angles and side lengths of the arches and observation deck.
Peer Response 1:
I think your design to create a scale model of the Eiffel Tower is very effective. You have clearly explained your plan and how you will determine the calculations and dimensions for the significant items. The concept of corresponding angles and side lengths is crucial in creating mathematically similar items. It seems like you have a strong understanding of the mathematical skills needed for this design, such as trigonometry and proportions. Your mention of outside sources, such as architectural plans, shows that you are considering accurate measurements and dimensions. Overall, great job!
Peer Response 2:
Your design to create a scale model of the Eiffel Tower is well thought out and effective. I like how you have chosen significant items, such as the arches and observation deck, to focus on. You have explained how you will determine the calculations and dimensions to make these items mathematically similar to the actual ones using the concept of corresponding angles and side lengths. Your understanding of the mathematical skills needed, such as trigonometry and proportions, is evident. One improvement could be to also consider the material used for the scale model, as it might affect the accuracy of the measurements. Other than that, great job!
can you do sometihng other than the eiffel tower?
Design:
The real-world figure I will model is the Great Pyramid of Giza. The scale factor I will use is 1:100, meaning that every unit on the scale model will represent 100 units on the actual pyramid.
Two significant items on my model will be the base length and the height of the pyramid.
To determine the calculations and dimensions for these items, I will first gather measurements and information about the actual Great Pyramid of Giza. I will find the base length and the height of the pyramid.
Next, I will apply the scale factor to these measurements to determine the dimensions of the scale model. For example, if the base length of the actual pyramid is 230 meters, then the base length of the scale model will be 2.3 meters (230 meters divided by 100). Similarly, if the height of the actual pyramid is 146 meters, then the height of the scale model will be 1.46 meters (146 meters divided by 100).
To ensure that the base length and height are mathematically similar to the actual pyramid, I will calculate the corresponding angles and side lengths. I will use the concept of corresponding angles to determine the slopes of the sides of the pyramid on the scale model. And I will use the concept of corresponding side lengths to ensure that the proportions of the base length and height on the scale model match those of the actual pyramid.
The specific mathematical skills needed to create this design include measuring angles, calculating scale factors, and applying the concept of corresponding angles and side lengths. I will need to use trigonometry to calculate the slope angles of the sides of the pyramid. Proportions will be used to ensure that the side lengths of the base and the height on the scale model are proportional to the actual pyramid.
For the calculations, I may need outside sources such as architectural plans or reliable sources with accurate measurements of the Great Pyramid of Giza. Consulting with experts or using online resources will be helpful in gathering the necessary information for the angles and side lengths.