Teaching Models

Plane and Solid Shapes

Basic Geometric Concepts
The study of geometry focuses on space and the figures and shapes that are a part of space. In the primary grades, geometric representations often take the form of drawing a picture. They are very useful when modeling and solving a variety of real-world problems.

The fundamental concepts of elementary geometry, sometimes called Euclidian geometry (after Euclid, who around 300 B.C.E. outlined the basic definitions and assumptions of geometry in his book Elements), are the point, the line, and the plane.

A geometric point has no dimension; that is, it has no length, height, or width. A point cannot be measured or touched, it simply is a location in space. A line is made up of a straight path of an infinite number of points and extends in two directions with no endpoints. A line segment is part of a line contained between two points on the line. These points are the endpoints of the line segment. A line segment has length, but no width. A plane is a set of points that forms a flat surface infinitely wide and infinitely long. A plane has no boundary with respect to length and width, and it has no thickness. If you imagine that the surface of the floor of your classroom continued forever in the horizontal directions, then you would be picturing a plane. A point and a line both lie in a plane.

Space is defined as the set of all points. Three-dimensional shapes that students study in elementary school are often called solid shapes, or figures. The study of geometry can be divided into two broad categories, plane geometry and solid geometry.

Plane geometry concerns itself with the study of two-dimensional shapes, or figures that lie in a plane. Common plane figures that children study in the primary grades include the rectangle, square, triangle, and circle. The square, triangle, and rectangle have line segments for sides and are all polygons. A circle is not a polygon because it is not made up of line segments.

Solid geometry concerns itself with the study of shapes of three dimensions. Common three-dimensional shapes that children study in the primary grades include the sphere, cylinder, rectangular prism, and cone. Common objects that represent these shapes are the ball, can, box, and ice-cream cone, respectively.

Young children first learn to recognize a shape in its entirety, and, using this ability, many young children will leave kindergarten able to identify a variety of plane and three-dimensional shapes. In first grade, however, the fundamental new learning should focus on the properties and relationships of these shapes. For example, students should begin to understand the ways in which a square and a rectangle are alike (they each have four sides) and how they are different. (All four sides of a square are the same length, while a rectangle has two pairs of sides that are the same length.)

A second goal of the study of geometry in the primary grades should be the gradual use of conventional terminology when students describe and discuss figures and shapes. Using appropriate language will help students develop a strong foundation for the more formal study of geometry in the intermediate and secondary grades.

Teaching Model 7.2: Plane Shapes

Houghton Mifflin Math Grade 1