School Improvement in Maryland

Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.3 The student will apply concepts of measurement using tools and technology when appropriate.

Indicator 2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two-and three-dimensional figures and their parts.

Lesson Content

Real World Activities Involving Volume, Surface Area, and Trigonometry

Objective

Students will solve real world situations involving volumes and trigonometry.

Other Indicators Addressed

2.2.2 The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.

Approximate Time

One 45-minute lesson

Prerequisite Concepts Needed

Students will need to be able to determine the volume of a rectangular prism, cylinder and cone. Students will also need to be familiar with sine and cosine relationships in a right triangle.

Materials Needed

Homework

Worksheet: Homework

Lesson Structure

    Warm-Up/Opening Activity

    Worksheet: Warm-up

    Development of Ideas

    The students will solve problems in cooperative groups. Each group will be assigned 6 problems; the last problem is to find patterns in a trigonometry table. The theme of the assignment is to earn a camping badge. The teacher can assign points for each question a group gets right or a prize for the group that gets all of the problems correct. Each group could display or present one of their solutions.
     
    Teachers need to be aware that the answers can vary, depending on how the students round their answers. The problems can be done in class or started in class and finished for homework.
     
    Worksheet: Activity Sheet

    Closure

    1. How is the formula for volume of a pyramid different from the formula for the volume of a cylinder?
       
      Answer: The volume of a pyramid is 1/3 of the area of the base times the height while the volume of a cylinder is the area of the base times the height.
       
    2. What is the difference between the height of a cone and the slant height of a cone?
       
      Answer: The height of a cone is the perpendicular distance from the vertex of the cone to the base. The slant height is the distance from the vertex along the lateral surface to the edge of the base.
       
    3. In a triangular prism, what is the shape of the sides?
       
      Answer: In a triangular prism the sides are rectangles.

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