Barbara Perez Lesson Plan #2 4/11/07 1. Title and Summary Pages Unit: Right Triangle Trigonometry Lesson: Vectors Author: Barbara Perez Barbara.perez@browardschools.com Grade Level: 8th Grade Geometry Classroom Layout: Part 1 (Power Point Presentation). Students will be in rows. Part 2 (GeoGebra Investigation) Option 1. Students will be in groups of two with their desks adjacent to each other. Each student will have a laptop computer. Option 2. Students will be in a computer lab and will work with a partner at an adjacent computer. Prerequisite Knowledge for students: 1. Students should be able to use a web browser to access Internet sites. 2. Students should have some prior experience with GeoGebra. 3. Students should understand trigonometric ratios (sine, cosine, tangent) as a ratio of sides in right triangles and be able to use trigonometric ratios to determine side lengths in right triangles. 4. Students should know how to graph points in the coordinate plane. Prerequisite Knowledge for teacher: 1. Teacher should be able to use a web browser to access Internet sites. 2. Teacher should have some prior experience with Power Point and GeoGebra. Objectives of the Lesson: 1. Students will use graphs to describe vectors. 2. Students will use trigonometry to find the coordinates of a vector. 3. Students will derive the method for computing the resultant of two vectors. 4. Students will solve problems that involve vector addition Time Frame: 2 50-minute periods Materials: Student Computers with web browser and java installed (free from www.java.com) GeoGebra Dynamic Worksheets o Vectors.html o Vector_Addition.html Paper Pencil Scientific Calculator Trigonometric Ratios Table Teacher Computer with web browser and java installed (free from www.java.com) Power Point Presentation – Vectors.ppt GeoGebra Dynamic Worksheets o Vectors.html o Vector_Addition.html Projector Short description of the content: In this lesson students will learn the basics about vectors, how to compute the coordinates of vectors, and how to add vectors. Students will create their own area problems involving vector addition and solve them. Sunshine State Standards: MA.A.3.4.2, MA.B.2.4.1, MA.B.2.4.2 Vocabulary/Key Words: vector, scalar, magnitude, direction, resultant 2. Lesson Plan Introduction to the lesson: The concept of trigonometry will be reviewed. At this point, students already know how to find the side lengths of right triangles using sine, cosine and tangent. Students will be given several examples of scalars and vectors and asked to compare the two. For example, 5 miles, 30 m/h East, 20 degrees, 15 degrees east of north, etc. The students should be able to see that some of the examples are quantities, and some are quantities and direction. Explanation of the math involved: The motion of objects can be described by words - words such as distance, displacement, speed, velocity, and acceleration. These mathematical quantities which are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions: Scalars are quantities which are fully described by a magnitude alone. Vectors are quantities which are fully described by both a magnitude and a direction. Vectors can be described on the coordinate plane in two ways, either by using magnitude and direction, or as a coordinate pair. If you know the magnitude and direction of a vector, you can find the coordinate pair representation by forming a right triangle with one of the axes and using trigonometric ratios. Vectors can be added by adding their coordinates. For example: a 1,5 b 7,1 a b 1 7, 5 1 a b 8,6 Instructional Methods: Whole group - lecture Whole group – discussion Small group – discovery Small group - discussion Small group – problem solving/practice Procedure: Step 1: Power Point Presentation (Whole Group) Teacher will project the Power Point Presentation “Vectors.ppt.” The teacher will do this with the whole class. The class will discuss the presentation and answer all questions together. Students will copy notes from the presentation and copy and solve the examples in their notes. Step 2: Derive the method for adding two vectors (Whole Class/Small Group) Teacher will project the worksheet “Vectors.html” to show students how the worksheet is used. This worksheet allows the points to be moved so that many examples of adding vectors can be shown. The resultant is shown. Then students will use laptops to access the same worksheet (Vectors.html). They will be paired up with another student. The students will manipulate the worksheet and try to make a conjecture about how to add two vectors. They will then discuss their conjectures with their partner. Finally, the whole group will discuss their conjectures and they will take notes on the method used to add two vectors. Step 3: Vector Addition Practice (Small Group) Students will access the worksheet “Vector_Addition.html.” This worksheet allows the vectors to be changed. The resultant is hidden so that the students can compute the sum on their own. Then the solution can be revealed. Students will create several problems and first solve them on paper, then they will check their solutions. Closure/Connections: Students will review the concepts about vectors that were learned in this lesson. Students will then be presented with the following real-world problem involving vectors: An airplane starts at (0,0) and makes three parts of a flight represented by the following vectors in this order: 7,4 , 3,2 1,6 If another airplane starts at (0,0) and flies the same three parts in a different order, will it end up at the same ending point? At this point, students should be able to use what they learned about vector addition to discover that addition of vectors is commutative. Assessments: 1. Student created exercises and solutions on practice worksheets. 2. Ability to solve closure problem. Extensions: Have students use the distance formula and the Pythagorean Theorem to find magnitude of vectors in the coordinate plane. Then have them compare how these methods are alike and how they are different. For example, if a car travels 40 miles west and 20 miles north, what is the magnitude of the vector? 3. Instructional Materials Power Point Presentation o Vectors.ppt GeoGebra Dynamic Worksheets o Vectors.html o Vector_Addition.html