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.
5 sentences
I have chosen to model a famous landmark - the Eiffel Tower. The scale factor I will use is 1:100, which means that every inch on my model will represent 100 inches on the actual tower.
Two significant items on my model will be the arches on the first and second levels of the Eiffel Tower. To make these arches mathematically similar to the actual arches, I will measure the angles and side lengths on the real arches and then use the scale factor to calculate the corresponding angles and side lengths on my model.
To create the design, I will need to have a good understanding of geometric transformations, specifically rotations and translations, as I will need to accurately position the arches on my model. I will also need to apply my knowledge of similar figures to calculate the dimensions of the arches on my model.
Some outside sources I may need for the calculations are measurements and blueprints of the Eiffel Tower, as well as information about the angles and side lengths of the arches. I may also need to consult architectural and engineering resources to ensure the accuracy of my design.
Effective aspects of this design include the use of a scale factor to accurately represent the proportions of the Eiffel Tower. It also demonstrates a good understanding of geometric transformations and similarity.
A potential challenge or flaw in the design could be the accuracy of the measurements and calculations. It is important to ensure that the scale factor is applied correctly and that the dimensions of the arches on the model match those of the actual arches.
An improvement to the design could be to incorporate more elements of the Eiffel Tower, such as the intricate lattice structure. This would require additional calculations and measurements, but would make the model more detailed and realistic.