Scaling your World
Project Description
Throughout this project, we have gone over many topics including congruence, similarity, and dilation.Our goal was to create a scaled model of an object in our everyday lives using our understanding of dilation and the relationship between similarity and congruency. To start we dug into what we knew already about similarity. As we progressed our understanding grew and we were told the mathematical terms for what we were learning, dilation, congruence, and similar shapes. Them in teams we created posters about the concept assigned to us. Now with a better understanding of our task, We choose groups and began to formulate a plan for the object we would scale up or down. To end our project after we created our final products, we dove deeper into dilation and perfected our artifacts what will be shown at a winter exhibition.
Mathematical Concepts
The 6 main mathematical concepts we focussed on can be described as the following: Congruence and Triangle Congruence is two shapes being congruent if every side and every angle is equal. Due to how a triangle's sides and angle affect each-other, you can determine if two triangles are congruent using only 3 traits from each triangle. Two shapes are described as similar if they are the same shape, but not the same size. Two shapes are described as similar if they are the same shape, but not the same size. Ratios and Proportions are used to relate two similar shapes. For example, you could describe two triangles using ratio, of 2:4 if both triangles were similar you could get the sides of one triangle by dividing the sides of the other triangle by 2, then multiplying by 4. Similarity can be proved by comparing two shapes angles: if the angles are the same, then the shapes are similar. Dilation is another way of explaining about similar shapes, a scale factor is used to relate two dilated objects so that multiplying every side of the original shape by the scale factor will give you the dilated version. This means, if the scale factor is a negative number, the shape can be reflected with respect to the center of dilation. Dilation effects on the length of sides and the area of the shape. For a scale factor of 2, the relationship between two sides can be described as the New Side equals 2 times the Old Side.
Exhibition
For our first benchmark in the project, we had to submit a project plan with what we were planning to dilate, Who else we were working with, What it would be made of, and how we would present it. Next came the second benchmark, We had to sketch two similar diagrams of the object we were going to scale. Within the diagram, we labeled all the significant dimensions of the original object that we planned on scaling. For my group, this was a pretty long process since we decided to scale my hand down by 1/2. We had to scale down each of my fingers and from the base of my palm to where the measurement for each finger. This was a total of 10 measurements we had to scale down. In the end, we ended up with a to scale tracing of my hand and also a sketch of my hand half its original size.Finally, The third benchmark, The final product, we made our final draft out of clay so the audience could get a good visual. For our clay hand, we made each finger a different color and the palm a different color so you can see how small your hand would be if it was half the size. Finally, we filled out a peer and self-assessment to get our grades for the project.
Reflection
This project was both challenging and fun. The major challenge my group came across in this project was that we were not able to use the 3D printer. We originally thought it would be really cool to have the hand 3D printed, but we complications we decided to make it out of clay. I really enjoyed this project because it was hands on so I felt like I retained the information more. Looking back at the challenges I faced during this project the only thing I would of done differently was make sure we could of used the 3D printer because when we found out we could not use it we were at a bit of a loss for what to make the hand out of. As far as the Habits of a Mathematician I think I used "Be Confident, Patient, and Persistent" because when we had the issue with the 3D printer we stayed confident and were able to come up with a solution. I think I could of done better when it came to "Be Organized" because if we were organized the 3D printer issue would of never come up in the first place. Overall my groups members and I got along really well in the project. And finally, I think this project really benefited me in the sense that it was hands not the the final product was not a huge project so I feel like it was more out the project than the product.