## 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 Partner

**Common 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.