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]