# 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.

### 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