March 2nd, 2007 9th-10th Grade
20 students Geometry 45 min.
Surface Area and Volume
Lesson #2: Surface Area of Pyramids and Cones
Context:
The unit is over surface area and volume, so many of the sections (as is this one) are over finding surface area for different types of shapes. This section is over pyramids and cones. The previous section dealt with finding surface area of prisms and cylinders and defining some of the basic terms that will be used to describe the three-dimensional shapes we will be working with in section 12.2. Students learn about such terms as faces, edges, and bases in the first section which are important to know when dealing with pyramids and cones.
Objectives:
1. The students will understand why the surface area formula is what it is.
2. The students will be able to find the surface area of a pyramid and a cone.
Connections
-MA-HS-3.1.10
Students will describe the intersection of a plane with a three-dimensional figure.
-Objective I
-MA-HS-3.1.9:
Students will classify and apply properties of three-dimensional geometric figures.
Objective II
Assessment Plan
Objective Number Type of Assessment Description of Assessment Depth of Knowledge Level Adaptations and/or Accommodations
1. Formative I will use the interview technique and have the students guide me through the process, and then I will go around the room to answer any questions the students have as they work on their problems. DOK II None.
2. Formative I will assign the students a couple of problems and go around the room to take a look at the students work to make sure they understand how to calculate surface area. DOK II None.
Resources, Media and Technology
– 3-Dimensional Plastic Shapes
Procedures
I will start class with some bell work that reviews the area formulas for the circle and triangle since that information is essential in comprehending this lesson. Students will spend 5 minutes in looking up this information if they do not remember it. After the 5 minutes is up, I will answer the review questions with the class. I then will proceed into the lesson on surface area of pyramids and cones. I will first identify the lateral faces and base for a four-sided pyramid with a square base by displaying a 3-dimensional object for everyone to see. Then, I will show step by step how the surface area of the pyramid is calculated. I will demonstrate this by having a student measure out the dimensions of the pyramid for me and I will pose questions to the class to answer as I go along. I will start by having him measure one of the sides of the base, so that we can calculate the area of the base of the pyramid first. Then I will have them help me in calculating the area of one of the lateral faces (which is of course a triangle) and I will show them that all you have to do is multiply the area of that one triangle by 4 since there are 4 lateral faces in this particular pyramid. And then they will add the area of the base to the area of the faces. I then will show the students the actual formula for the surface area of a pyramid and explain to them the shortcut that the formula takes. The students then will do a problem #4 from the text and I will go around the room to make sure that everyone understands the material. After 5-10 minutes, I will proceed to repeat the above process in teaching them about the surface area of a cone. No assignment will be given at the end of class.
