Lesson 5: 1-8: Three-Dimensional Figures

1. What is the slant height of a pyramid?
2. How many faces does a sphere have?
3. What are examples of polyhedra?
4. What are examples of nonpolyhedral solids?

Polyhedron
Face
Edge
Vertex
Prism
Base
Pyramid
Cylinder
Cone
Sphere
Regular Polyhedron
Platonic Solid
Surface Area
Volume

G.MG.1
Use geometric shapes, their measures, and their properties to describe objects.
G.GMD.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

https://docs.google.com/document/d/1zq0M4k71wKerXCRC7RRT03j2PjfmBImlaTgUCbpHxkw/copy?usp=sharing

A solid with all flat surfaces that encloses a single region of space is called a polyhedron. Not all solids are polyhedral. A cylinder and a cone are not polyhedral because they have circular bases. A sphere, the set of points in space that are a given distance from a given point, is not a polyhedron.
Mathematically proficient students are careful about specifying units of measure, look closely to discern patterns, and can distinguish correct logic or reasoning from that which is flawed.

Architects often provide three-dimensional models of their ideas to clients. These models give their clients a better idea of what the completed structure will look like than a a two-dimensional drawing. Three-dimensional figures, or solids, are made of up of flat or curved surfaces.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections in the following way: students can use the surface area and volume formulas to determine what the radius of the sphere would have to be in order for the surface area and volume to be the same.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.