#### Math - 2018-19

# 4.11 - Plane & Solid Figures

**The student will**

**identify, describe, compare,**and**contrast**plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations.

*Adopted: 2016*

### BIG IDEAS

So that I can recognize the perspective of different art work and different artist

So that I can see which patterns or shapes are the same and which are different

- So that I can use repeated patterns as a future fashion designer

### UNDERSTANDING THE STANDARD

- The study of geometric figures must be
active, using visual images and concrete materials (tools such as graph paper,
pattern blocks, geoboards, geometric solids, and computer software tools).
- Opportunity must be provided for building and
using geometric vocabulary to describe plane and solid figures.
- A plane figure is any closed, two-dimensional
shape.
- A solid figure is three-dimensional, having
length, width, and height.
- A face is any flat surface of a solid figure.
- An angle is formed by two rays with a common
endpoint called the
*vertex*. Angles are found wherever lines and/or line segments intersect. - An edge is the line segment where two faces
of a solid figure intersect.
- A vertex is the point at which two or more
lines, line segments, or rays meet to form an angle. In solid figures, a vertex is the point at
which three or more faces meet.
- A cube is a solid figure with six congruent,
square faces. All edges are the same
length. A cube has eight vertices and 12
edges.
- A rectangular prism is a solid figure in
which all six faces are rectangles. A
rectangular prism has eight vertices and 12 edges. A cube is a special case of a rectangular
prism.
- A sphere is a solid figure with all of its points
the same distance from its center.
- A square pyramid is a solid figure with a
square base and four faces that are triangles with a common vertex. A square pyramid has five vertices and eight
edges.
- Characteristics of solid figures included at
this grade level are defined in the chart below:

Solid Figure | # of Faces | Shape of Faces | # of Edges | # of Vertices |

Cube | 6 | Squares | 12 | 8 |

Rectangular Prism | 6 | Rectangles | 12 | 8 |

Square Pyramid | 5 | Square/Triangles | 8 | 5 |

Sphere | 0 | N/A | 0 | 0 |

### ESSENTIALS

**The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations to**

- Identify
concrete models and pictorial representations of solid figures (cube,
rectangular prism, square pyramid, sphere, cone, and cylinder).
- Identify and
describe solid figures (cube, rectangular prism, square pyramid, and sphere)
according to their characteristics (number of angles, vertices, edges, and by
the number and shape of faces).
- Compare and
contrast plane and solid figures (circle/sphere, square/cube, triangle/square
pyramid, and rectangle/ rectangular prism) according to their characteristics (number
of sides, angles, vertices, edges, and the number and shape of faces).

### KEY VOCABULARY

*Updated: Aug 22, 2018*