Math Background

Identify Plane Shapes and Solid Shapes: Overview

Geometry and spatial relationships are a part of children's daily lives. Understanding an object's position in space and learning the vocabulary to describe position and give directions are important. Simple terms like above, below, left, right, or between, enable children to order and describe the world around them. They can apply these terms as they describe plane and solid shapes in the classroom.

Most of the objects that we encounter can be associated with basic shapes. A closed, two-dimensional or flat figure is called a plane shape. Different plane shapes have different attributes, such as the numbers of sides or corners. A side is a straight line that makes part of the shape, and a corner is where two sides meet. In this chapter, children will learn to identify, describe, sort, and classify plane shapes by these attributes.

Although children are familiar with the most common shapes, up until now they may not have been able to verbalize what distinguishes a square from a rectangle or a circle from a triangle. They will learn to describe shapes in terms of their sides and corners. A triangle is a shape with three sides and three corners. A rectangle is a shape with four sides and four corners. They may notice that opposite sides are the same length. A square is a rectangle in which all four sides are of equal length. A circle is a round shape that has no sides or corners. These attributes, as well as size, can be used to sort and classify shapes.

Circle, Square, Rectangle and Triangle

Many of the everyday objects with which children are familiar are solid shapes. For example, building blocks are often cubes or rectangular prisms. They have six faces, or flat surfaces. Other familiar solid shapes are spheres, which children might recognize as being shaped like balls; cones, like ice cream cones or traffic cones; and cylinders, which are shaped like cans. One shape that children might not immediately recognize is a pyramid, which has one rectangular face and four triangular faces.

Cube (with 'face' highlighted), Sphere, Rectangular Prism, Pyramid, Cylinder, Cone

As with plane shapes, children will learn to describe solid shapes in terms of their attributes, such as their roundness or flatness, their ability to roll or slide, and the number of sides or corners. They will also come to see how the plane shapes comprise the faces of solid shapes. Tracing around the face of solids will help a child to understand that a cube is different from a rectangular prism because all six of its faces are squares. This will enrich the ways in which they can describe and compare solids. For example, a child might see that although both a cylinder and a sphere can roll, a sphere has no faces and cannot slide. A cylinder, on the other hand, has two circular faces, so it can both roll and slide.

Once children have the ability to recognize and describe the attributes that distinguish plane and solid shapes, such as those that make a triangle different from a square or a cylinder different from a cone, they can begin to create and continue patterns. When children create or find patterns, they are using the attributes of not just one but of a series of shapes to determine the order or pattern.


Houghton Mifflin Math Grade 1