Hierarchy of Quadrilaterals

5.G.1

“Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the O on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).”

Question 1 reads vertices as ordered pairs and uses the axes to measure the 4-unit sides of ABCD.

5.G.2

“Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.”

Questions 2 and 3 solve problems on the first-quadrant grid, locating the right angle at P and the missing vertex S(7, 6).

5.G.3

“Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.”

Question 5 rests on attribute inheritance: every square carries the four right angles that define rectangles.

5.G.4

“Classify two-dimensional figures in a hierarchy based on properties.”

Question 4's definition matching and the sometimes/never judgments in questions 6 and 7 classify figures within the hierarchy.