Project Description:
For this project we focused on the topics of similarity, congruence, and dilation. Our goal was to take an object from our everyday lives whether it was a pencil or the Burj Khalifa, the tallest building in the world and scale it up or down. For example if you chose a pencil you would scale it up and make it 5 times the size of the original. To start off the project we got into group and chose one topic that we would further explore and put it on a poster. All of the topics revolved around dilation, similarity or congruence. We then took those posters and presented it to the class. After listening to everyone's presentations we got into different groups or we did it solo and came up with an object we wanted to scale up or down. We then would have to measure and figure out all of the dimensions that we would scale up and make an actual model. At the end of the project we would show our work at our December exhibition.
Mathematical Concepts:
All throughout this project we learned about 6 main concepts. Congruence and Triangle Congruence: When two shapes have equal size, sides, and angles. When looking at 2 congruent triangles you have to look carefully because even if one triangle is upside down and the other is opposite, if they are the same size, have equal side length and equal angles it is still congruent. (As you can see in the imagine on the right)
Definition of Similarity: When there are two of the same shape but one is larger or smaller than the other. Ratios and Proportions, including solving proportions: Ratio and proportions are used to relate two similar shapes. Proportion is an equation where the ratio of the sides of the two trianlges are the same. When the sides of the two triangles are the same its proportional. Dilation is like another way of explaining similar shapes, a scale factor is used to determine two dilated objects by multiplying every side of the original shape by the scale factor to get the dilated shape. If the scale factor is negative the shape would then be reflected. Dilation affects the lengths of sides and the area of the shape. If the scale factor is 4, the relationship between two sides can be described as the New Side equals 4 times the Old Side.
All throughout this project we learned about 6 main concepts. Congruence and Triangle Congruence: When two shapes have equal size, sides, and angles. When looking at 2 congruent triangles you have to look carefully because even if one triangle is upside down and the other is opposite, if they are the same size, have equal side length and equal angles it is still congruent. (As you can see in the imagine on the right)
Definition of Similarity: When there are two of the same shape but one is larger or smaller than the other. Ratios and Proportions, including solving proportions: Ratio and proportions are used to relate two similar shapes. Proportion is an equation where the ratio of the sides of the two trianlges are the same. When the sides of the two triangles are the same its proportional. Dilation is like another way of explaining similar shapes, a scale factor is used to determine two dilated objects by multiplying every side of the original shape by the scale factor to get the dilated shape. If the scale factor is negative the shape would then be reflected. Dilation affects the lengths of sides and the area of the shape. If the scale factor is 4, the relationship between two sides can be described as the New Side equals 4 times the Old Side.
Exhibition:
We had 3 benchmarks that we had to complete for this project. For benchmark #1 we had to submit our plan like what we wanted to dilate, who we were working with, materials we are planning to use to create the model, and what dimensions we needed to measure. We did this so we could get our plan approved. Benchmark #2 was creating 2 diagrams of what were dilating and all of the measurements we took. For example my group was creating an In-n-out cup that was 4 times the original size. We had to label and measure the circumference of the cup and then figure out what that measurement would be by multiplying it by 4 because that was our scale factor and labeling that on our second diagram. We did this so that we had a clear idea of what materials we needed and to make sure that we would be creating our model to scale and not just guessing. Benchmark #3 was creating our final draft of our model. Our final product was an In-n-out cup where the cup itself was made out of poster board with a PVC straw. |
Reflection:
This project was pretty successful for my group but we had a few obstacles throughout the process. Some challenges we faced was finding the right materials like for the lid we did not know what to use so we ended up using a clear plant saucer but it was pretty hard to find. We also had trouble finding red palm tree stickers for the design of the cup so we ended up having to draw the palm trees and the squiggly lines on the cup. We messed up with the lines on the first draft so we had to turn over the paper and start over again. The habit of a mathematician I used in this project was stay organized because when making the diagrams we had to be clear with the measurements and where they go on the diagram. I also had to be organized and make sure I didn't lose that paper and I kept track of all the measurements so I didn't forget them while we were building. I think my group did a great job of doing equal work and staying focused. I think our project was successful especially having so many things go wrong.
This project was pretty successful for my group but we had a few obstacles throughout the process. Some challenges we faced was finding the right materials like for the lid we did not know what to use so we ended up using a clear plant saucer but it was pretty hard to find. We also had trouble finding red palm tree stickers for the design of the cup so we ended up having to draw the palm trees and the squiggly lines on the cup. We messed up with the lines on the first draft so we had to turn over the paper and start over again. The habit of a mathematician I used in this project was stay organized because when making the diagrams we had to be clear with the measurements and where they go on the diagram. I also had to be organized and make sure I didn't lose that paper and I kept track of all the measurements so I didn't forget them while we were building. I think my group did a great job of doing equal work and staying focused. I think our project was successful especially having so many things go wrong.