# 2.13 - Plane and Solid Figures

The student will

• identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms).

### BIG IDEAS

• So that I can draw ( 2D/plane) actual solid ( 3D) objects
• So I can use shapes to plan out picture mosaics or construction projects like dog houses, cubbies, birdfeeder,etc
• So that I can understand that the world is made of shapes

### UNDERSTANDING THE STANDARD

• A plane figure is any closed, two-dimensional shape.
• A vertex is a 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 edges meet.
• An angle is formed by two rays that share a common endpoint called the vertex.  Angles are found wherever lines or line segments intersect.
• A solid figure is a three-dimensional figure, having length, width, and height.
• A circle is the set of points in a plane that are the same distance from a point called the center.
• A sphere is a solid figure with all of its points the same distance from its center.
• A rectangle is a quadrilateral with four right angles. A square is a special type of rectangle.
• A square is a quadrilateral with four congruent (equal length) sides and four right angles.
• A right angle measures exactly 90 degrees.
• 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 solid figure with six congruent, square faces. All edges are the same length. A cube has eight vertices and 12 edges. It is a type of rectangular prism.
• The edge is the line segment where two faces of a solid figure intersect.
• A face is any flat side of a solid figure (e.g., a square is a face of a cube).
• Tracing faces of cubes and rectangular prisms and decomposing cubes and rectangular prisms along their edges helps students understand the set of plane figures related to the solid figure.
• The relationship between plane and solid figures, such as the square and the cube or the rectangle and the rectangular prism helps build the foundation for future geometric study of faces, edges, angles, and vertices.  The following chart defines the characteristics of solid figures included at this grade level:

 Solid Figure # of Faces Shape of Faces # of Edges # of Vertices Cube 6 Squares 12 8 Rectangular Prism 6 Rectangles 12 8 Sphere 0 N/A 0 0

### ESSENTIALS

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

• Determine similarities and differences between related plane and solid figures (circles/spheres, squares/cubes, rectangles/rectangular prisms), using models and cutouts.
• Trace faces of solid figures (cubes and rectangular prisms) to create the set of plane figures related to the solid figure.
• Identify and describe plane figures (circles, squares, and rectangles), according to their characteristics (number of sides, vertices, and angles).  Squares and rectangles have four right angles.
• Identify and describe solid figures (spheres, cubes, and rectangular prisms), according to the shape of their faces, number of edges, and number of vertices, using models.
• Compare and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms) according to their characteristics (number and shape of their faces, edges, vertices, and angles).

### KEY VOCABULARY

Updated: Aug 22, 2018