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 Description:
For my scale model, I have decided to model the Eiffel Tower. The scale factor I will use is 1:100, which means that every 1 unit on my model will represent 100 units of the actual height and dimensions of the 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 make these items mathematically similar to the actual ones, I will need to calculate their dimensions and angles based on the scale factor.
To calculate the dimensions of the arches, I will start by measuring the actual dimensions of the arches on the Eiffel Tower. Let's say the height of the arch is 100 meters and the width is 50 meters. To make it mathematically similar, I will divide these dimensions by the scale factor of 100. So in my model, the height of the arch will be 1 meter and the width will be 0.5 meters.
To determine the angles of the arches, I will use the concept of similar triangles. I will measure the angle of the arch on the actual tower and use that angle to create a similar angle on my model. I can use a protractor to measure the angle accurately.
Similarly, for the observation deck, I will measure its dimensions and angles on the actual tower and scale them down using the scale factor.
The specific mathematical skills I will need to create the design include calculating ratios, using similar triangles, and measuring angles accurately. For example, when determining the dimensions and angles of the arches and observation deck, I will need to use ratios to scale down the measurements and use the concept of similar triangles to match the angles.
To ensure accuracy in my calculations, I may need to refer to outside sources such as architectural plans or blueprints of the Eiffel Tower. These sources will provide precise measurements and angles of the items I want to replicate in my scale model.
Peers' Designs:
Design 1:
I think what is effective about this design is the careful consideration of the scale factor and the use of mathematical concepts like similar triangles to determine the dimensions and angles. The reliance on outside sources for accurate measurements and angles is also a good approach.
One possible flaw or challenge in this design could be the accuracy of the measurements. Depending on the availability and precision of the outside sources, there could be small discrepancies in the dimensions and angles of the replicated items.
An improvement in the design could be to use a laser measuring device or laser levels to ensure greater accuracy in measurements. This would eliminate potential human error in measuring and give more precise results.
Design 2:
The design effectively uses the concept of similar figures and the scale factor to create a scale model of the Great Wall of China. The consideration to model the watchtowers along the wall and the inclusion of accurate dimensions and angles are commendable.
One challenge in this design could be the complexity of calculating the dimensions and angles of the watchtowers. As the Great Wall of China stretches over a vast distance, there could be variations in the dimensions and angles of the watchtowers along the different sections of the wall.
An improvement in the design could be to gather specific measurements and angles for different sections of the wall and create multiple models, each representing a particular section. This would ensure greater accuracy and attention to detail in replicating the watchtowers.
Make it simple
Design Description:
For my scale model, I have chosen to model a simple house. The scale factor I will use is 1:10, which means that every 1 unit on my model will represent 10 units of the actual dimensions of the house.
Two significant items on my model will be the windows and the door. To make these items mathematically similar to the actual ones, I will calculate their dimensions based on the scale factor.
To determine the dimensions of the windows, I will measure the actual dimensions of the windows in the house. Let's say the height of a window is 1 meter and the width is 0.5 meters. To make it mathematically similar, I will divide these dimensions by the scale factor of 10. So in my model, the height of the window will be 0.1 meters and the width will be 0.05 meters.
Similarly, for the door, I will measure its dimensions in the actual house and scale them down using the scale factor.
The specific mathematical skills I will need to create the design include calculating ratios to scale down the measurements.
To ensure accuracy in my calculations, I may need to use a measuring tape or ruler to measure the dimensions of the windows and door in the actual house. This will provide precise measurements that I can then scale down to create my model.