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