locating points & finding distances looking for pythagoras = investigation 1.1
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Locating Points & Finding Distances
Looking for Pythagoras = Investigation 1.1
4 3 2 1 0In 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.
Washington, D.C.
• The street system was designed by Pierre L’Enfant in 1791.
• 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.
Washington, D.C.
Describe the location of:
• George Washington University.
• Dupont Circle
• Benjamin Banneker Park
• The White House
• Union Station
Washington, D.C.
• How can you find the distance from Union Station to Dupont Circle?
• Find the intersection of G Street and 8th Street SE and the intersection of G Street and 8th Street NW. How are these locations related to the U.S. Capital Building?
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: http://zardz.net/Individual%20Pages/Euclid%20Trading%20Card.html
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)
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
4 blocks south
3 blocks north
6 blocks west and 1 block south
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
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?
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