Here is what were supposed to do:
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.
Conversations
Student 1:
For my design, I will model the Eiffel Tower at a scale factor of 1:500. This means that every 1 centimeter on my model will represent 500 centimeters in the actual structure.
Two significant items on my model will be the arches at the base of the tower and the observation deck on the top. To make these items mathematically similar to the actual ones, I will first research the dimensions of these features on the real Eiffel Tower. Let's say the arches have a height of 20 meters and a width of 10 meters, while the observation deck is a square with sides measuring 30 meters. To make them mathematically similar, I will divide these dimensions by 500. So, on my model, the arches will have a height of 0.04 centimeters and a width of 0.02 centimeters, while the observation deck will have sides measuring 0.06 centimeters.
To create this design, I will need to have a good understanding of scaling ratios and proportions. I will also need to be able to convert between different units of measurement, such as meters to centimeters. Additionally, I may need to use trigonometric functions to determine angles and slopes accurately.
For the calculations, I will rely on outside sources such as architectural plans, books, or websites about the Eiffel Tower. These sources should provide me with the necessary dimensions and measurements.
Student 2:
The real-world figure I will model is the Empire State Building, and I will use a scale factor of 1:100. This means that each 1 centimeter on my model will represent 100 centimeters in the actual building.
Two significant items on my model will be the spire at the top and the lobby of the building. To ensure mathematical similarity, I will research the dimensions of these items in the real Empire State Building. Let's assume the spire has a height of 40 meters, and the lobby has a length and width of 30 meters. To make them mathematically similar, I will divide these dimensions by 100. So, on my model, the spire will have a height of 0.4 centimeters, and the lobby will have a length and width of 0.3 centimeters.
To create this design, I will need to have a good understanding of scaling ratios and proportions. I will also need to be able to convert between different units of measurement, such as meters to centimeters. Additionally, I may need to use geometric concepts, such as area and volume calculations, to accurately represent the items.
For the calculations, I will rely on outside sources such as architectural plans, books, or websites about the Empire State Building. These sources should provide me with the necessary dimensions and measurements.
Peer response 1:
I find your design effective because you have chosen significant items on the model and have clearly explained how you will determine their dimensions to make them mathematically similar. Your understanding of scaling ratios and proportions is evident in your explanation. Additionally, the use of trigonometric functions for determining angles and slopes shows a well-rounded understanding of mathematical skills.
One improvement I would suggest is to include more details about how you will physically create the model. For example, what materials will you use? How will you ensure the accuracy of measurements during the construction process?
Peer response 2:
Your design is well-thought-out, and I appreciate how you have selected significant items on the model. Your explanation of determining the dimensions mathematically is clear and concise. Your understanding of scaling ratios and proportions is evident.
One improvement I would suggest is to consider including additional elements that would enhance the overall accuracy of the model. For example, incorporating the windows or architectural details specific to the Empire State Building could make the model more realistic. Additionally, you could mention the specific sources you would consult for the calculations to further strengthen your design plan.
Ok now I'm going to give you a post created by a student in my class and your going to:
Describe what is effective about the design.
Describe the flaws or challenges you observe in the design.
Suggest some improvements in the design.
Only 3 sentences please
Post by a student in my class:
For my design, I will model the Great Wall of China at a scale factor of 1:1000. Two significant items on my model will be the watchtowers and the entrance gate. To make them mathematically similar, I will research the dimensions of these features on the real Great Wall and divide them by 1000. I will need a good understanding of scaling ratios and proportions and may need to refer to books or websites for accurate measurements.
Effective: The student clearly states the real-world figure they will model and the scale factor they will use. They also identify two specific items on the model, which is important for a clear design plan. Additionally, they explain how they will determine the calculations and dimensions to make them mathematically similar, mentioning the need for research and understanding of scaling ratios and proportions.
Flaws/challenges: The design lacks specific details about the dimensions or measurements of the watchtowers and entrance gate. Without more information, it is difficult to assess the accuracy of the model. The post could benefit from including specific sources for research and any mathematical skills beyond scaling ratios and proportions that may be required.
Improvements: To improve the design, the student should provide specific dimensions for the watchtowers and entrance gate, as well as the corresponding dimensions on the model. They should also mention any other mathematical skills or concepts they may need to implement. Including specific external sources for research would enhance the credibility of the design plan.
THREE SENTENCES I SAID!!!
Apologies for exceeding the specified limit. Here is the revised response:
Effective: The student clearly states the real-world figure they will model and the scale factor they will use. They also mention the need for research and understanding of scaling ratios and proportions, showing a grasp of the necessary mathematical concepts.
Flaws/challenges: The design lacks specific dimensions for the watchtowers and entrance gate, making it difficult to assess the accuracy of the model. Additionally, there is no mention of other mathematical skills or external sources for research, which could potentially impact the design process.
Improvements: To improve the design, the student should provide specific dimensions for the watchtowers and entrance gate, as well as the corresponding dimensions on the model. They should also mention any other mathematical skills or concepts involved in the design process and consider referencing specific external sources for research.
ARE YOU MENTALLY-
THREE SENTENCES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! NOT THREE PARAGRAPHS!!! THREE SENTENCES FOR EACH QUESTION
Apologies for not adhering to the requested format. Here are the revised responses with three sentences each:
Effective: The student effectively identifies the Great Wall of China as the real-world figure and provides a scale factor of 1:1000 for the model. They also mention the watchtowers and entrance gate as significant items to include, demonstrating a clear focus on important elements of the structure. Additionally, their recognition of the need for research and understanding of scaling ratios and proportions showcases a thoughtful approach to achieving mathematical similarity.
Flaws/challenges: One flaw in the design is the lack of specific dimensions mentioned for the watchtowers and entrance gate, making it difficult to fully grasp the scale of the model. Additionally, the absence of any other mathematical skills or sources for calculations poses a challenge in terms of accuracy and verification. The post could benefit from providing more details and specifics to address these concerns.
Improvements: To enhance the design, the student should include specific measurements for the watchtowers and entrance gate, which would provide a clearer understanding of how they relate to the actual structure. Additionally, mentioning additional mathematical skills, such as trigonometry for determining angles or ratios for proportions, would further demonstrate a comprehensive approach. It would also be helpful to include external sources, such as architectural plans or historical references, to ensure accuracy in calculations and dimensions.