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 like a bottle or a building and scale it up or down. For example if you chose a bottle you could scale it up and make it 4 times the size of the original or if you chose a building you could scale it down by 4. At the beginning of the project we talked in our table groups and chose one of the 6 topics. All of the topics were about either similarity, congruence, or dilation.We would then research about the topic more and further explore it and put it our findings on a poster then we presented 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 using our knowledge on what we just learned about dilation. We then would have to measure and figure out all of the dimensions that we would scale up or down and make an actual model of the object. At the end of the project we would show model we created at our December exhibition.
Mathematical Concepts:
During this project we learned about 6 main mathematical concepts. Congruence and Triangle congruence is when 2 shapes are equal in size, sides, and angles. Even if the shape is turned the wrong direction like triangles can be, if they have all of the same qualities it is congruent. Similarity is when there are 2 of the same shape but they are different sizes. So it is like congruent but the only difference is when shapes are similar they can be different sizes and congruency they have to be the same size. Rations and proportions is when ratio and proportions are used to relate 2 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 another way of explaining similar shapes. A scale factor is used to relate 2 dilated shapes 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 will then be reflected, dilation affects the lengths of sides and the area.
Exhibition:
For this project we had to complete 3 benchmarks that were spaced out over the course of the 2 weeks that we worked on it. Benchmark #1 we had to create and submit our project plan which included what we chose for our object, who we were planning on working with, what our object would be made out of and the materials list. Benchmark #2 we created 2 similar diagrams of the object we planned on scaling. Next to our diagram we labeled all of the dimensions that were important to creating our model. We also had to calculate all of the dimensions by multiplying it by our scale factor. For example if you were doing a bottle and the length of the bottle was 10 inches and your scale factor was 4 you would do 10 times 4 and your model would have to be 40 inches long. Benchmark #3 was our final product. My groups final product was an upscaled version of a cheeseburger. It was scaled up by 4. Our Final product is a Cheeseburger made out of styrofoam and felt.
Reflection:
Some successes I had in this project was at the beginning when we were thinking of an idea we came up with it easily. My group decided to make a burger. Another success was measuring the actual object and making our model to scale. Some challenges we faced was time management because we had a hard time getting our materials so we had to ask for an extension. Another challenge was find materials and picking what materials looked best for example we couldn't decide if we were going to paper mache or fabric. The habit of mathematician I used most in this project was describe and articulate. I used this when we were sketching diagrams and figuring out the measurements. I also used be confident, patient, and persistent because when we were having trouble with materials we had to be patient and stay confident that we will find a solution to our problem. Overall I think our project was very successful. |