PISCATAWAY TOWNSHIP SCHOOLS Piscataway High School 100 Behmer Road, Piscataway, NJ 08854

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1 PISCATAWAY TOWNSHIP SCHOOLS Piscataway High School 100 Behmer Road, Piscataway, NJ Mathematics Department Daniel J. Ross, Esq. Math Department Chair (732) x2241 Fax: (732) To Geometry Students and Families: Attached is the Geometry summer project for the school year. This project was created to help you maintain the prerequisite skills necessary for success in Geometry. This project will allow you to demonstrate your creativity and apply what you know about mathematics. If you feel that you need further review or practice, we encourage you to visit or and click on a high school Algebra 1 and/or Geometry textbook, as these are the textbooks used at Piscataway High School. All Geometry summer projects are due on the first day of school, and opening day activities will be based on this project. Additional copies are available at under Curriculum & Instruction or at the Piscataway Township Central office located at 1515 Stelton Road. This project will be counted as a grade for the first marking period for all Geometry students. Scoring will be based on completeness, accuracy, organization, and explanation. The rubric for the elements of grading is attached. Have fun completing the packet and enjoy your summer! If you have any questions about the project, please call (732) x2241 and leave a detailed message. I will check my messages periodically and return your call when I have the chance. Sincerely, Daniel J. Ross, Esq. A New Jersey State Department of Education Best Practices School 1

2 3-Dimensional Enlargement Project This project is designed to get you to think about geometric enlargement in a physical context. Your task is to choose a fairly small Three Dimensional object with a logo (ie. Candy bar, Chapstick, Tooth Brush, etc.) and enlarge it by a scale factor of exactly 1:4. That means that every aspect of the new item must follow this ratio of enlargement. This includes the writing, logos, side lengths, and any other key characteristic details of the original item. Enlargements should not be completed by scanning and/or printing the logos and writing. Materials: Original object to be enlarged Poster paper (or a thicker paper so that the enlarged object won t be too weak) or any other material that would be useful (paper Mache, clay, etc.) Pencil Metric Ruler (centimeters, meters) Coloring utensils (colors should be as close to the original colors as you can). Procedure: 1. Choose a three-dimensional object to enlarge. 2. Use a formula from the Formula Sheet for the figure that matches your original object and measure the required dimensions. Please ensure that all measurements are made in metric form (centimeters, millimeters). 3. Use the measurements and the scale factor (1:4) to calculate the dimensions of your enlargement (Hint: use a proportion). 4. Use the dimensions you calculated for your enlargement to construct the actual enlargement. Make sure to preserve the proportions of all logos and writing so that the enlargement looks exactly like a larger version of the original object. 5. Complete all parts of the attached questions. 6. Review grading rubric to ensure your project has all required components and is complete. What you need to hand in: The Original Object (or photographs of all sides) The Enlarged Object Completed Additional Questions 2

3 Formula Sheet 3

4 Answer the following questions regarding your project. Remember to use the formulas provided in the packet. Please show your work in boxes provided. Each question is worth 5 points. 1. Draw the front, side, and top views for your original and enlarged item. Include all of your measurements. Original Enlargement 4

5 2. Calculate the surface area and volume for your original item. Show all work using the appropriate formulas. Surface Area: Volume: 5

6 3. Calculate the surface area and volume for your enlarged item. Show all work using the appropriate formulas. Surface Area: Volume: 6

7 4. Select a linear measurement from your original item (radius, side length, height, etc.) And find the following ratios below. Be sure to reduce all ratios. a. Linear Measurement from Original Linear Measurement from Enlargement What is the relationship between this ratio and the original scale factor? b. Surface Area of Original Surface Area of Enlargement What happened mathematically between the scale factor and the surface area ratio? c. Volume of Original Volume of Enlargement What happened mathematically between the scale factor and the volume ratio? 7

8 5. Answer the following questions using complete sentences. a. What did you learn about ratios and scale factors in completing this project? b. In what careers do you think this process would be used? Be specific. c. Explain any challenges you encountered in completing this project. 8

9 Geometry Summer Project Rubric The following rubric will be used to grade your summer project. Please reference it while you are doing your project to ensure that you obtain the highest score possible. Criteria Mathematical Similarity to the Original Item How accurate are the measurements of your enlarged item? Is your enlargement built to scale? 50 points Item is built to scale and all dimensions are accurate 40 points Item has some mistakes/ some calculation errors were made Point Value 30 points Item has many errors and is not built to scale 0 points Not completed/ No effort put in Mathematical Calculations for the Both Items Have you calculated the surface area and volume of both figures and answered all of the accompanying questions. See questions for point breakdown. Points are awarded for effort and accuracy, so make sure to show all work for partial credit. 25 points All formulas are correctly used and computations are correct 20 points Correct formulas are used and some computational errors 15 points Correct formulas are used with many computational errors or wrong formulas are used. 0 points Not completed/ No effort put in Complexity Based on the figure chosen. See level of difficulty on the right. 10 points Hard: Cones, spheres, pentagonal pyramids or prisms, or combination of different figures, etc. 6 points Medium: Triangular Prisms and pyramids or cylinders, etc. 4 points Easy: Cubes or rectangular prisms, etc. 0 points Not completed/ No effort put in Student Effort/Visual Likeness Does the enlarged item display all the features, such as, logos, writing, buttons, or pictures, of your original item? Do these features look similar to the original figure? (Note: similar figures have the same shape but different sizes). The artistry on the enlargement is neat, clean and care is taken in its construction. 15 points Student s item is neat and nicely put together. Great care has been taken in the decoration of the item 10 points Student has put some effort in, but there are parts of the item that are put together without care. The logos are not enlarged or colored 5 points Student s item is not neatly put together and minimal care seems to have been put into doing this project. Features from the original item are missing. 0 Points Not completed/ No effort put in/ Scanned or Printed Enlargement Comments: 9