Geometric Solids - Two Dimensions Vs. Three Dimensions
Lesson Plan Reference
Grade Level 2-3
Difficulty Level 3 (Developing to Mastery)
Type of Assignment Individual or PartnerCommon Core Standards
- [Math/Content/K/G/A/3] Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
In kindergarten, students learn to identify if a shape or figure is 2D or 3D, “flat” or “solid.” A picture of something will always be flat, but the actual object would be something a child could hold. Solid figures have mass and take up space, while flat figures do not. Show examples of solid figures and paper cut-outs of two-dimensional shapes and have students classify them. Then show solid figures and pictures of solid figures and lead students in a brief discussion on the difference. Introduce shape, plane, solid, and space. Depending on the level of your students, particularly if this is a review for older students, you may also want to add point, line, dimension, and perspective.
Many students will already understand the difference between 2D and 3D, but they will have a hard time grasping the “D” part and what it means. A dimension could be thought of as an extension of direction. Lacking any dimensions, a point shows position only. There are zero dimensions to the point: zero directions. We use points to show location within other dimensions. A line has one dimension. A line goes on forever in two directions, but that really means a positive and a negative direction of the same dimension. A ruler allows a pencil to move in one dimension. A train can move forward and backward along the train tracks. A painter moves up and down on a ladder. Keep in mind that a line does not actually have any thickness, so take these examples with a grain of salt.
A plane is a flat surface that does not have any thickness. It has two dimensions: length and width. Any flat surface, such as a piece of paper, tabletop, chalkboard, or screens for electronics can be considered part of a plane. Characters in side-scrolling video games move in two dimensions. Moving a pencil diagonally on a piece of paper is a combination of moving it left/right and up/down. Any drawing on a piece of paper that we make is actually only two-dimensional, despite the use of perspective. Perspective is a way to show 3D objects on a 2D surface and gives the illusion of depth.
The third dimension adds actual depth. Space is where objects physically exist. In three dimensions, everything has mass. What is different about 3D movies? A movie is a projection onto a flat screen, a plane. Sometimes people or objects seem to come toward the viewer, instead of staying flat on the screen. This is supposed to give the illusion of three dimensions; the people and objects do not actually come toward you. The physical world exists in space, but images on a screen are only two-dimensional.
Think of the claw machine you might find in an arcade. A joystick allows movement of the claw while it is still at the top. Left/right is one dimension. Left/right and forward/back are two dimensions. While the claw is still at the top of the machine, you can think of it as moving along a plane. Once you press the button or time is up, the claw descends. Left/right, forward/back and up/down are three dimensions.