#### Math - 2019-20

# 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).

*Adopted: 2016*

### 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*