Topic 6 - PDF

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Kelsey Berg MAT 151 Carolyn Horner Topic 6 DQ 1 What is a geoboard? How can a geoboard be used to develop geometric concepts? Give some examples of how you might use a geoboard. Is this practical to use in a classroom? Explain your answer. A geoboard is a manipulative used to explore basic concepts in plane geometry such as the perimeter, area, and other characteristics of triangles and polygons. It is a board with pegs in which you use rubber-bands to create triangles and polygons, in which you can then find measurements of the shapes on the plane. I would teach students about similarity of triangles and polygons while using a geoboard. I would have students make the same shapes, but one larger than the other and determine the scale factor that makes them different size but same shape. I do think this is a practical manipulative to use in the classroom, especially for students that learn by doing hands-on examples and projects. Provide multiple sources for learning that fit each child’s learning needs will create and effective and successful learning environment for all the students. DQ 2 What is the Pythagorean theorem? Explain how the Pythagorean theorem may be proven using squares. How can the Pythagorean theorem be used to find distances on a plane? The Pythagorean theorem addresses the sides of a right triangle, it states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. When using the Pythagorean theorem, you are finding the area of three square, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square C. Therefore, by solving to find the area of the squares, you are also solving the Pythagorean theorem. When using the Pythagorean theorem to calculate the distance on a plane can be solved by one equation: a2 +b 2=c 2 . For example, side a is 6cm long and side b is 8cm long. Plug in 6 for a and 8 for b and solve for c, the answer will be 10cm and will be the hypotenuse of the triangle on the plane....