Project DescriptionThe scaling your world project was a long journey of math and building. We went over scaling small objects, to scaling the planet. We also went over some concepts such as congruence, dilation, and similarity. The goal of the project was to understand these concepts, and to scale and create one of our own objects. We got into teams of two or three, and combined our skills on what we knew about geometry, and chose to scale an object that's in our everyday lives.
ExhibitionBenchmark #1
In benchark one, my group and I had to simply submit a plan of what we were going to scale and how we were going to scale it. Benchmark #2 Benchmark two consisted of sketching my partner's hand to scale, and then giving the measurements of her original hand and the tinier hand we'd be creating. Our group decided to scale the hand down 1/2 smaller. We didn't even know what we'd create it out of at that point, but we still wanted to make a tiny hand. On our paper, we showed the exact proportions of each hand and what it looked like dilated. We measured the length of her palm and each finger, and her palm to each finger. It was complicated. Benchmark #3 My partner Luci and I searched the school for clay, only to end up using mine at home. We drew a scaled down version of the hand on the paper, and then I molded the hand into the drawn out version. This was harder than I thought, and I made the fingers too tiny at first. Eventually we came out with a colorful clay hand. |
Mathematical ConceptsCongruence and Triangle Congruence:
Congruence is when two shapes or objects are the same in size. Triangle congruence is when two triangles share the exact same angles and equivalent sides. Definition of Similarity: If the angles are the same and the sides of a shape are proportional then they are similar. Ratios and Proportions: Ratios are similar to fractions, because both are showing a relationship to two or more values. A fraction can look like 3/5, while a ratio is 3:5. Ratios and proportions are used to show the relationship between two different shapes. For example, you can use ratios to describe the relationship between two different triangles. Proving Similarity: Similarity between shapes can be proved by finding the relationship between two shapes' angles, and if the angles are the same then they are simliar. Dilation, including scale factors and centers of dilation: Dilation is used for scaling an object to be bigger, or smaller. When dilating an object, you use scale factors. Also known as mulitpling the proportions of a shape by any number. If the scale factor is negative, then the object appears on the other side upside down of the center of enlargement Dilation:Affect on distance and Area: Dilation affects the size and length of the shape. It effects distance because it's multiplied by the scale factor. For area, it's the area squared by itself so the relationship between the objects on a graph aren't linear. |
Project Creation and Work
Refelction
This project had some complications, but that didn't stop me from working my hardest to complete each benchmark. Some of the challenges were dealing with a partner that wouldn't work, and not being able to find the materials for our final product. I wish I dealt with the partner problem better by actually making them work. But I put my best effort into not starting anything bad. For a few days our group didn't know what to use for the final product. I kept on insisting clay until we all wanted it, and then we couldn't find any in the art room. I brought clay from my house, thank goodness I had it or else we'd be even more stuck than before. Though there were complications, there were many accomplishments. I worked really well with one of my partners on making the hand and finding the measurements for the scaled down version of our object. I used the stay organized and start small habits of a mathematician. I stayed organized with my paperwork and turned everything in on time. I also started small with proportions and scale factors when Luci and I were working on second benchmark.