The Common Core State Standards require fourth graders to list the attributes of shapes to determine their classification: whether a shape has parallel or perpendicular lines, and what kinds of angles it has. Shapes get grouped together, depending on their attributes.
Polygons - a shape with straight sides. Circles and ovals are NOT polygons.
Triangle - a polygon with three sides and three angles
Right triangle - a triangle with one right angle
Quadrilateral (or quadrangle) - a polygon with four sides and four angles
Pentagon - a polygon with five sides and five angles
Hexagon - a polygon with six sides and six angles
Heptagon - a polygon with seven sides and seven angles
Octagon - a polygon with eight sides and eight angles
Nonagon - a polygon with nine sides and nine angles
Decagon - a polygon with ten sides and ten angles
Trapezoid - a quadrilateral with exactly one set of parallel sides (its other sides are NOT parallel)
Parallelogram - a quadrilateral with opposite sides parallel (trapezoids are NOT parallelograms)
Rectangle - a parallelogram with all right angles (all perpendicular sides). Since it’s a parallelogram, its opposite sides have to be parallel, also.
Rhombus - a parallelogram with all equal sides. Since it’s a parallelogram, its opposite sides are parallel, also.
Square - a parallelogram with all right angles and all equal sides. Since it’s a parallelogram, its opposite sides are parallel, also. A square is a very special and specific kind of shape!
The Venn Diagram above shows the relationship between classifications of polygons. As you can see, every single parallelogram is a quadrilateral, but some quadrilaterals are not parallelograms. A square is both a rectangle (four right angles) and a rhombus (four equal sides). But not all rectangles are squares, and not all rhombuses are squares.
In class, we examine many different shapes to practice listing their attributes. To help students do this, we use straws (to help decide if sides are parallel, perpendicular, or neither) and straws connected by twist-ties (to help examine the angles).
Last but not least, a polygon may be classified as a regular polygon. This means that all of its sides are equal and all of its angles are equal.