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PA-GM-1-2

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.GM.1.2 Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.

In a Nutshell

Students can easily find the distance between two points when they are vertical or horizontal from each other, but when the endpoints are on a diagonal segment, students will need to use the Pythagorean Theorem to find the distance. Students can create a right triangle if they draw vertical and horizontal lines through each endpoint. The intersection of the vertical and horizontal line will produce the right angle. Finding the coordinates of the right angle vertex, then subtracting as before for finding the length of the legs, students should discover they are subtracting the x and y coordinates of the diagonal segment’s endpoints. This leads to the conversion of the Pythagorean Theorem to become the Distance Formula.

Student Actions	Teacher Actions
Develop Accurate and Procedural Understanding by plotting points on a coordinate grid and connecting the points with a line segment. Draw a right triangle with the hypotenuse their line segment created. Use the Pythagorean Theorem to find the length of the hypotenuse (original line segment). Develop Strategies for Problem Solving through exploring different situations to discover that the Pythagorean Theorem can be used to find the shortest distance between two points on a coordinate plane.	Implement tasks that promote reasoning and problem solving by giving students questions involving two points on a coordinate plane. Ask them to determine a way to accurately measure the shortest distance between the two points without measuring. Promote procedural fluency by encouraging students to draw the triangle, label the sides and hypotenuse with known lengths, and plug information into the formula to find the length
Key Understandings	Misconceptions
Students will be able to use the Pythagorean Theorem to determine the shortest distance between two points on a coordinate grid.	When finding a length of a segment drawn drawn on grid paper some students miscount the units. Students will count the unit, in which they start on, as 1 instead of 0. Students may forget to complete the Pythagorean Theorem by finding the square root in the last step.