Ask the students to think of other uses for these representations.
When students know and fully understand the options, they will be able to choose the best tool for each task they
undertake.
Isometric Dot Paper –If students are having trouble making isometric drawings, they might benefit from the use
of isometric dot paper. The spacing of the dots allows students to make consistent lengths and angles on their
polyhedrons. After some practice with the dot paper, they should be able to make decent drawings on any paper. A
good drawing will be helpful when calculating volumes and surface areas.
Practice –Most students will need to make quite a few drawings before the result is good enough to be helpful
when making calculations. The process of making these representations provides the student with an opportunity to
contemplate three-dimensional polyhedrons. The better their concept of these solids, the easier it will be for them to
calculate surface areas and volumes in the sections to come.
Additional Exercises:
- In the next week look around you for polyhedrons. Some example may be a cereal box or a door stop. Make a
two-dimensional representation of the object. Choose four objects and use a different method of representation for
each.
These can make nice decorations for classroom walls and the assignment makes students look for way to apply what
they will learn in this chapter about surface area and volume.
Prisms
The Proper Units –Students will frequently use volume units when reporting a surface area. Because the number
describes a three-dimensional figure, the use of cubic units seems appropriate. This shows a lack of understanding
of what exactly it is that they are calculating. Provide students with some familiar applications of surface area like
wrapping a present or painting a room, to improve their understanding of the concept. Insist on the use of correct
units so the student will have to consider what exactly is being calculated in each exercise.
Review Area Formulas –Calculating the surface area and volume of polyhedrons requires the students to find the
areas of different polygons. Before starting in on the new material, take some time to review the area formulas for
the polygons that will be used in the lesson. When students are comfortable with the basic area calculations, they
can focus their attention on the new skill of working with three-dimensional solids.
A Prism Does Will Not Always Be Sitting On Its Base –When identifying prisms, calculating volumes, or using
the perimeter method for calculating surface area, it is necessary to locate the bases. Students sometimes have
trouble with this when the polyhedron in question is not sitting on its base. Remind students that the mathematical
definition of the bases of a prism is two parallel congruent polygons, not the common language definition of a base,
which is something an object sits on. Once students think they have identified the bases, they can check that any
cross-section taken parallel to the bases is congruent to the bases. Thinking about the cross-sections will also help
them understand why the volume formula works.
Additional Exercises:
- A prism has a base with area 15 cm^2 and a height of 10 cm. What is the volume of the prism?
Answer:V= 15 ∗ 10 =150 cm^3
- A triangular prism has a height of 7 cm. Its base is an equilateral triangle with side length 4 cm. What is the
volume of the prism?
Answer:V=Bh=^12 ∗ 4 ∗ 2
√
3 ∗ 7 = 28
√
3 cm^3 ≈ 48 .5 cm^3- The volume of a cube is 27 cm^3. What is the cube’s surface area?
Chapter 2. Geometry TE - Common Errors