6.M.G.A.03: I can plot coordinates and calculate distances between vertices on a coordinate plane.

Performance Level Descriptors:

These are the possible scores a students can earn on the AzMERIT exam. We want all students to move into the Proficient or Highly Proficient category.

Highly Proficient: Solves real world multi-step geometric problems including decimal and fractional measurements, finds missing side length of a right rectangular prism given a volume and fractional side lengths, and finds a missing vertex of a polygon given other vertices

Proficient: Solves a real world context by finding the area given some measures for triangles or polygons by decomposing into rectangles and triangles, finds the volume of a right rectangular prism with fractional edges, and using coordinates for vertices of a polygon.

Partially Proficient: Finds the area given some measures for triangles or polygons by decomposing into rectangles and triangles, finds the volume of a right rectangular prism with one fractional edge, and uses coordinates to find the length of a side joining points with the same first or second coordinate.

Minimally Proficient: Finds the area given all the measurements for triangles or polygons decomposed into rectangles and triangles, finds the volume of a right rectangular prism with whole number edges, and creates polygons in the coordinate plane given coordinates for the vertices.

Key takeaway:

Points on a graph have "addresses" that describe where they are located, and we can calculate the distance between any two "addresses". If we know some of the addresses of a polygon, we can fill in the missing ones.

Vocabulary:

Origin - The exact center of a coordinate plane. Its coordinates are (0, 0).

Coordinates - The "address" for a point. Written like (3, 4). The first number is the x-value, and tells how far left or right to move. The second number is the y-value, and tells how far up or down to move. A negative x-value means to move left, while a positive x-value means to move right. A negative y-value means to move down, while a positive y-value means to move up. The address (3, 4) means to start at the origin and then move 3 spaces right and 4 spaces up.

Polygon - A shape, such as a triangle, rectangle, parallelogram, octagon, and so on. It must have all straight edges, and each edge must connect to its neighbors - no "gaps".

Vertex - The "corner" where two edges meet. If you have more than one vertex, they are called "vertices". A square has 4 vertices, a triangle has 3, an octagon has 8, and so on.

Videos:

This video shows how to find the missing vertex of a polygon: Khan Academy video

Another example, including how to plot all the vertices, then find the missing one: Khan Academy video

Another example of finding the missing vertex. Shows finding a diagonal line: YouTube video

Worksheets:

See below for a downloadable practice worksheet that covers this material.

14:37, 15 Nov 2016

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