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Welcome to math! Tuesday, March 27 Objective of Investigation 1.2 • Review properties of quadrilaterals • Connect properties of figures to coordinate representations • Draw shapes on a coordinate grid Fraction Problem of the day • There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? 3/8 of 24 means 3/8 times 24! Cross simplify when you multiply • There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? 3 . 24 8 1 Reduce 8 and 24 by a factor of 8 • There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? 3 . 24 3 1 8 1 Multiply across numerator and denominator • There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? 3 . 24 3 = 9 hours 1 8 1 Euclid • Nobody knows much about Euclid's life anymore - it is all forgotten. We only know that he worked at the University of Alexandria, in Egypt, for a while. There are no pictures of him. We can't even be sure he existed; Euclid could be a made-up name for a committee of mathematicians all working together. Euclid lived 2300 years ago • Either way, Euclid (or the people who called themselves Euclid) must have lived around 300 BC, in the Hellenistic period. He (or they) seems to have studied at Plato's Academy in Athens, where he learned some of the mathematics that is in his books. He probably knew Aristotle there. Use of Logic • Like Anaxagoras before him, Euclid wanted to prove that things were true by using logic and reason. We still have copies of Euclid's books today, and they begin with basic definitions of a point and a line and shapes, and then go on to use geometry to prove, for instance, that all right angles are equal, that you can draw a straight line between any two points, and that two things which are both equal to the same thing are also equal to each other. Euclid’s famous book Elements Euclid's later books teach more advanced math, including how triangles and circles work, irrational numbers, and threedimensional geometry. Euclid is considered… the Father of Geometry • Euclid is famous because his books were so easy to understand that they were used as the main math book in all schools in Europe, West Asia, and America for two thousand years, until the 20th century. There are still mathematicians working today who began studying geometry from Euclid's books. Top 5 National Parks Grand Canyon, Arizona Yellowstone, Wyoming Yellowstone Gorge Prismatic Spring Acadia, Maine Yosemite, California Denali, Alaska Things you should already know A vertex is a where to line segments meet to form a corner. Vertices is the plural form for vertex A vertex is a where to line segments meet to form a corner. What are the properties of different quadrilaterals? More quadrilateral properties Right Triangle Properties • Three sided figure • One of the angles = 90°