Introduction

This package consists of three lesson plans for the topic, plane vectors. Lesson one includes the definition of vectors and the equality of two vectors, how to represent them in two types of representation, how to convert them into another form, how to find their magnitude, and pertinent terminology. Lesson two includes vector addition, subtraction, and scalar multiplication with operation laws. In the Lesson three, dot production of vectors are introduced.

Basically, I focused on making students feel their learning meaningful by using technology to promote their deep understanding. This package, therefore, starts with touching the ideas of why we need to learn vectors in mathematics courses and how the topic is related to our daily life. Some quantities like velocity, force, and work are directly related to real situations and can be specified with vectors. So I found that connecting the concepts of plane vectors to real life is easier compared to other topics.

I chose the Geometer's Sketchpad (GSP) as technology for developing this unit although other software or tools are available. GSP provides proper functions to represent ideas of vectors with its transformation menu, including animation effect among other tools I experienced. While teachers explain concepts effectively by using GSP, the students have the opportunity to add and subtract vectors by using vector tool which GSP provides. They don't need to worry about their drawing skill to sketch elaborate parallelograms and vectors when they add or subtract vectors. They can save their time on doing it as well. This package can be considered as an example to integrate technology into mathematics classroom with the topic, plane vectors.

* Related Georgia Performance Standards to the topic are as follows.

M6G1. Students will further develop their understanding of plane figures.

a. Determine and use lines of symmetry.

b. Investigate rotational symmetry, including degree of rotation.

c. Use the concepts of ratio, proportion and scale factor to demonstrate the relationships between

similar plane figures.

d. Interpret and sketch simple scale drawings.

e. Solve problems involving scale drawings.

M6G2. Students will further develop their understanding of solid figures.

a. Compare and contrast right prisms and pyramids.

b. Compare and contrast cylinders and cones.

c. Interpret and sketch front, back, top, bottom and side views of solid figures.

d. Construct nets for prisms, cylinders, pyramids, and cones.

M7G2. Students will demonstrate understanding of transformations.

a. Demonstrate understanding of translations, dilations, rotations, reflections, and

relate symmetry to appropriate transformations.

b. Given a figure in the coordinate plane, determine the coordinates resulting

from a translation, dilation, rotation, or reflection.

M8G2. Students will understand and use the Pythagorean theorem.

a. Apply properties of right triangles, including the Pythagorean theorem.

b. Recognize and interpret the Pythagorean theorem as a statement about areas of

squares on the sides of a right triangle.

MM1G1. Students will investigate properties of geometric figures in the coordinate

plane.

a. Determine the distance between two points.

b. Determine the distance between a point and a line.

c. Determine the midpoint of a segment.

d. Understand the distance formula as an application of the Pythagorean

theorem.

e. Use the coordinate plane to investigate properties of and verify conjectures

related to triangles and quadrilaterals.

MM4A6. Students will solve trigonometric equations both graphically and

algebraically.

a. Solve trigonometric equations over a variety of domains, using technology as

appropriate.

b. Use the coordinates of a point on the terminal side of an angle to express x as

and y as .

c. Apply the law of sines and the law of cosines.

MM4A10. Students will understand and use vectors.

a. Represent vectors algebraically and geometrically.

b. Convert between vectors expressed using rectangular coordinates and vectors

expressed using magnitude and direction.

c. Add, subtract, and compute scalar multiples of vectors.

d. Use vectors to solve realistic problems.

*Related NCTM Standards

NCTM-S.GEO.9-12.3.3.1 : understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices; [Geometry]

NCTM-S.NUM.9-12.1.1.3 : understand vectors and matrices as systems that have some of the properties of the real-number system; [Number and Operations]

NCTM-S.NUM.9-12.1.2.2 : develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices; [Number and Operations]

NCTM-S.NUM.9-12.1.3.1 : develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.

[Number and Operations]