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Locating Points & Finding Distances Looking for Pythagoras = Investigation 1.1.

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Presentation on theme: "Locating Points & Finding Distances Looking for Pythagoras = Investigation 1.1."— Presentation transcript:

1 Locating Points & Finding Distances Looking for Pythagoras = Investigation 1.1

2 43210 In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.  Make connection with other content areas.  Explain the relationship between the Pythagorean Theorem and the distance formula. The student will understand and apply the Pythagorean Theorem.  Prove the Pythagorean Theorem and its converse.  Apply the Pythagorean Theorem to real world and mathematical situations.  Find the distance between 2 points on a coordinate plane using the Pythagorean Theorem. The student will understand the relationship between the areas of the squares of the legs and area of the square of the hypotenuse of a right triangle.  Explain the Pythagorean Theorem and its converse.  Create a right triangle on a coordinate plane, given 2 points. With help from the teacher, the student has partial success with level 2 and level 3 elements.  Plot 3 ordered pairs to make a right triangle  Identify the legs and the hypotenuse of a right triangle Find the distance between 2 points on the coordinate grid (horizontal and vertical axis). Even with help, students have no success with the unit content. Focus 5 - Learning Goal #1: Students will understand and apply the Pythagorean Theorem.

3 Washington, D.C. The street system was designed by Pierre L’Enfant in The north-south and east-west streets for grid lines. The origin is at the Capitol. The y-axis is formed by the street Capitol Street. The x-axis is formed by the Lincoln Memorial through the Mall and down East Capital Street.

4 Washington, D.C. Describe the location of: George Washington University. Dupont Circle Benjamin Banneker Park The White House Union Station

5 Washington, D.C. How can you find the distance from Union Station to Dupont Circle? Find the intersection of G Street and 8 th Street SE and the intersection of G Street and 8 th Street NW. How are these locations related to the U.S. Capital Building?

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7 The City of Euclid The founders of Euclid LOVED math! They named their city after the famous mathematician Euclid of Alexandria. They designed their street system to look like a coordinate grid. They Euclidians describe the locations of buildings and other landmarks by giving coordinates. Picture from:

8 The City of Euclid Give the coordinates for the following locations: City Hall Greenhouse Gas Station Animal Shelter Hospital (0, 0) (-6, 0) (4, 4) (6, -2) (-6, -4)

9 The City of Euclid Find the distance between: City Hall & the Police Station Greenhouse & Hospital Animal Shelter & Art Museum Gas Station & the Stadium 4 blocks south 3 blocks north 6 blocks west and 1 block south

10 The Hospital to Art Museum From the Hospital go North 5 blocks to (-6, 1). Then go East 12 blocks to (6, 1). Total distance = 17 blocks How about another path? East 5 blocks, North 2 blocks, East 3 blocks, North 2 blocks, East 3 blocks, North 1 block, then East 1 block. Total distance = 17 blocks

11 The City of Euclid Instead of taking the city streets, take a helicopter. Does this change the path you would go? City Hall & the Gas Station North 4 blocks, East 4 blocks = total 8 blocks A helicopter could go directly there. Estimate the distance the helicopter would fly? What strategies could you use?

12 The City of Euclid Take a helicopter between the two locations. Estimate the distance between: Greenhouse & Cemetery Animal Shelter & the Stadium Gas Station & the Police Station


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