Connecting Geometry

Project List

Ch 1 Photo Project: Find a picture on the internet (or scan one from a book or magazine) that appears to contain lines, points and angles, like the bridge picture on the website in chapter 1. Paste your picture into a Geometer's Sketchpad file. Draw each of the 6 basic geometric elements on top of the picture, and label them as shown in the example on the website in chapter 1.

Ch 2 Graphics Project: Create a symmetrical geometric design, with compass and ruler, or using geometry software. Begin by constructing a simple geometric shape (a triangle, for example) and then repeat the shape in a symmetrical pattern. an example is shown on the website in chapter 2. You can experiment with colors, and create a beautiful design. If you have access to a paint program, such as SuperPaint, very beautiful effects can be created by copying and pasting a black and white line drawing from GSP (hide the points first) into the paint program, and then painting the design in the paint program where you have many color and effects options.

Ch 3 Research Project: Do some research of your own on the internet, on the History of Geometry. I would suggest you begin with the links on the website in chapter 3, to get warmed up. Then do a Net Search using Geometry as the Key Word. Write a 2 to 3 page report on what you discover. Please do not just copy and print pages off the internet. You should search, read what you find, think about it, and write a summary/discussion of what you find. You may include direct quotations (a few sentences or even a paragraph), but be sure to put these portions in quotation marks, and include the web addresses to give credit to your sources as was done on the website in chapter 3. You should include some images, but if you copy the images from the internet, you must give credit as was done on the website.

Ch 4 Tangrams Project: Design your own tangram challenge, using a ruler and compass, or geometry software. Create a second page with the solution to your challenge.

Ch 5 Origami Project: Fold a square piece of colored, good quality paper, to create an interesting Origami. It can be anything you like: an animal, a bird, or just an abstract three-dimensional shape. Then create a step-by-step set of instructions that someone else could follow. You may look at the step-by-step examples that you saw on the web pages using the links in chapter 5, but use the "cricket" example on the website for chapter 5 to guide you, using geometric terms to describe the steps. Your instructions do not have to be as complicated as the cricket example.

Ch 6 Spiral Project: Write an illustrated report 2-3 page report on any one of the Right Triangle, Sequences, or Spirals topics in chapter 6 on the website. Your report can be written using information you found on the internet and/or books. Keep in mind that this report must be your own work, and not just copied and pasted from the web. If you do use a sentence or two of someone else's work, be sure you include their name and the name of their book or web page to give them credit.

Ch 7 Drawing Project: Learn more about 3-D drawing by going to the Math Forum website and reading all the pages at http://www.forum.swarthmore.edu/workshops/sum98/participants/sanders Then do the following two things as your Project: 1) Find a picture of a building on the internet. (You might strat with a net search using the word "architecture") Be careful to choose a picture in which you can see the lines vanishing as in the examples on the forum website above, as if towards Vanishing Points. Your assignment is to use a pencil and ruler (or geometry softward) to draw a simple building or buildings, of your own design, in perspective.

Ch 8 Tessellation Project: Create a tessellation of your own, using the method described in the web pages. Start with a square or hexagon, and create an interesting shape as descrived in the web pages. Use tracing opaper to trace your shape, and create a tessellation.

Ch 9 Indirect Measurement Project: Choose a tall object to measure, using indirect measurement. This object must be something that cannot simply be measured with a ruler or tape measure; it must be something that is very tall, and inaccessible, such as a tall flagpole at school, a high-rise building, or a steep cliff. It also needs to be in a relatively flat field, park, or section of town, so that its shadow will be measurable. This may depend on the time of day that you do your measuring, so you will probably need to make some observations in different parts of town, and at different times of the day. Of course the shadows will be shortest near noon! Measure the length of your object's shadow, and measure the length of your own shadow as you stand nearby, or measure the length of the shadow of a yardstick held vertically nearby. If you use your own shadow, you may need an assistant, and you will need to know your own height. Draw careful sketches, and calculate the height of your object, using the method shown in the web page. Write a careful explanation, including any problems you encountered. Tell us where and what your object is. Show your calculations. Be sure to use accurate values in your calculations, and do not round any numbers until you get your final answer. Presentation is always important; do a nice job on the drawings and the written work, so that it shows pride in your work.

Ch 10 Graph Project: What activities make up your daily life? Collect data on this topic, and design a circle graph. To collect the data, keep a journal for one week of how much time you spend on each of your activities: you might include such categories as sleeping, doing homework, time spent in class, etc. Organize the data in groups with the hours and fractions of an hour. You might need to combine some of the smaller groups into a more general category. You should have at least 8 categories. Now you need to divide the circle into portions for the categories. For example, if you spend 8 hours sleeping, then that is eight twenty-fourths of the day, and would then be eight twenty-fourths of the 360 degrees in a circle. Some example calculations are shown below. After calculating the sizes of the sectors of the circle for each of your daily activities, draw a large circle on a nice piece of unlined paper or poster board, or use a painting program. Do not use a computer program that does all the calculations and graphs for you! Use a protractor (or the measuring system in your painting program) to carefully construct the angles. Label your graph, using the colorful graph called "Age of Users" on the website, as an example. Do your best work; make this a beautiful and informational graph!

Ch 11 Architectural Design Project: Do some research into the costs of real estate in your neighborhood. Read the real estate ads in the newspaper, visit some Open Houses on Sunday afternoons. The prices of houses depend on their location, the size of the lot, the "attractiveness" of the house, and the size of the house. Sometimes building a new house can be less expensive than buying one that has already been built and landscaped. This of course depends on the selling price of a vacant lot, and the cost of constructing the new house. Currently, for "average" quality construction in Hawaii, one can expect to pay about $100 per square foot of interior space, and $75 per square foot for lanai or deck space. Calculate the cost of building the house shown in the floor plan below. This floor plan is drawn to the scale 1/8" = 1', so you will need to print the drawing, then measure the overall lengths and width of the rooms with a ruler, and write proportions to find the lengths and widths in feet. Then find the areas of the rooms, total them, and multiply by the construction costs. Show all your work clearly and neatly on the paper with the drawing. The second part of the project is for you to design your own home! Pretend you have a budget of $215,000 for the construction, and don't spend any more than that! Use the approximate construction costs of about $100 per square foot of interior space, and $75 per square foot for lanai or deck space. Draw your home at the scale 1/8"=1', label the rooms, and show your calculations.

Ch 12 Castle Project: Do some research on the net, and find some images of castles. Read some information about the castles, and explore any aspects that interest you. Then design and create a 3-D drawing of your own castle, using geometric solids. You must have at least one each of the four solids we have studied: Prism, pyramid, cylinder, cone. Then find the volume of the solid portions of your castle. Be sure to write all formulas, and show all your work!

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