DUE DATE: Wednesday 09 December and Wednesday 28 April. ****NO EXCEPTIONS!!!! Directions: Each semester, you may choose one of the following projects to do. These are extra credit projects. Points will be assigned based on the quality of your work. Total possible = 100 points Use www.grammarly.com - PLEASE do your best. It will be worth it!
1. Find five examples in newspapers and magazines of advertisements that use conditional statements (if-then). Tell whether you believe they are true and defend your opinion. Write the converse of each statement and tell whether you think it is true or false. Then write your own ad for a favorite product, using an appropriate conditional. Draw a diagram of the product, and prepare the ad as if it were to appear in a magazine. Cite your resources/references.
2. Pick a sport which uses angles and distance. (Possible sports include gymnastics, ice hockey, golf, football, basketball, sailing, bowling, and soccer.) Interview a player or a coach about how angles and distance are used and their importance to playing and scoring in the sport. Draw at least 2 different diagrams that involve angles & distance in the chosen sport. Write a thorough summary of your interview. Cite your resources/references.
3. The standard staircase, according to the National Association of Home Builders, has thirteen 8.25-inch risers and twelve 9-inch treads. A 1992 proposal to increase safety on stairs by the Building Officials and Code Administrators suggested a new standard of sixteen 7-inch risers and fifteen 11-inch treads. a) On graph paper, make scale drawings of these two staircase models. b) Find the slope of each staircase c) Write a paragraph explaining why the new staircase model might increase safety. What are its advantages? disadvantages? Do you think the suggestion is a good idea?
4. Interview a lawyer and find out how arguments are constructed to win a case on a point of law. What is the given information? What is to be proved? What kinds of justifications are used for conclusions? Give at least one example of an argument in detail. Include your interview questions and answers in your report. Cite your resources/references.
5. Use cardboard or tagboard and tape to construct models of the regular polyhedra from the nets provided. The patterns shown below should be enlarged. Fold along the interior segments of each net. These polyhedra are also called Platonic Solids. Find out why they have this alternate name. Why are there only five? Investigate & write a short report on Platonic solids. Cite your resources/references.
6. Choose one of the following: a) The pyramids at Giza, Egypt, b) The pyramids near Mexico City, c) The step pyramids of ancient Babylon. Look in an encyclopedia or other books for the dimensions of at least two pyramids from the location you have chosen. Draw an accurate picture of them. Calculate the lateral area and the volumes of these pyramids. Cite your resources/references.
7. An amazing property of all quadrilaterals was discovered and proved by Pierre Varignon, a French mathematician (1654-1722): If the midpoints of consecutive sides of any quadrilateral are connected, then the quadrilateral so formed is a parallelogram.
a. Draw instances of Varignon’s Theorem using quadrilaterals with different shapes, with at least one of them nonconvex.
b. Prove the theorem for the plane using coordinate geometry.
8. A rectangle known as the golden rectangle has the following property: If the square on its short side is cut off, then the remaining rectangle is similar to the original, as shown here: The ratio of the long side to the short side is called the golden ratio and is often represented by the Greek letter φ (phi). Research the golden rectangle and golden ratio and write a report on them. What are some of their properties and applications? Include drawings of everyday items that are constructed using this property. Cite your resources/references.
Nets for Project #5 can be found in the link in the title.
The ratio of the long side to the short side is called the golden ratio and is often represented by the Greek letter φ (phi). Research the golden rectangle and golden ratio and write a report on them. What are some of their properties and applications? Include drawings of everyday items that are constructed using this property. Cite your resources/references.
Nets for Project #5 can be found in the link in the title.