3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
The first part of this standard is <a href="http://www.pogo.com/games/battleship" target="_blank"><em>Battleship</em></a> meets <a href="http://www.thisiscolossal.com/2011/07/world-record-connect-the-dots-mona-lisa-in-6239-dots/" target="_blank"><em>Connect the Dots</em></a>. Students should already know about the coordinate plane and how to plot (<em>x</em>, <em>y</em>) pairs on it. Now, they'll take the next step and draw polygons whose vertices are coordinates on the coordinate plane.
For example, we may ask the students to draw the triangle whose vertices are <em>A </em>(-2, -3), <em>B </em>(-2, 1), and <em>C </em>(4, 1). It's the difference between plotting three points and plotting three points connected by line segments. See? It's as different as night and…later that night.
The next part of the standard means that students need to figure out the length of vertical or horizontal line segments on the coordinate plane using coordinates. In other words, they need to realize that points at (2, 1) and (4, 1) are 2 units apart by finding the absolute value of the difference of the relevant coordinates (i.e., finding that the distance between the two points is |4 – 2| = 2).
Students do not—we repeat: do<em> not</em>—need to find the length of diagonal line segments! They'll do that in eighth grade with a little help from our favorite ancient Greek, Pythagoras.
Of course, it's not over until the fat lady sings—or, you know, until students have applied their understanding to solve mathematical and real-world problems. For example, the students should be able to draw a polygon whose vertices are points on the coordinate plane, find horizontal and vertical lengths through pairs of these points, and use these lengths to determine the area or the perimeter of the polygon.
As for a real-world example, students should understand that if we walk from the intersection of Halsted and 95th Street to the intersection of Halsted and 37th street, the subway was probably broken. Seriously, 58 blocks is a long way to walk.