Lesson 3
Goals
1. Students
understand what the dot product of two vectors means with the
background situation related to the concept of "work".
2. Students know the precise definition of a term " dot product of two
vectors" and can find it with the magnitudes of vectors and the angle
between them.
3. Students can find
the dot product of two vectors with their components in the component
representation.
4. Given two vectors' magnitudes and their dot product, students can
find the angle between two vectors understanding the conditions that two
vectors are parallel or perpendicular.
5. Students understand operation laws for the dot product.
Prerequisite:
1. Students are required to have basic knowledge about
trigonometry functions and cosine laws.
2. Students need sense of operation laws to be connected to the dot
product ( commutative, associative, and
distributive laws ).
Target graders: 11th
or 12th graders
Teaching procedure:
Step 1: Teachers
can start with providing real situations in order to introduce the
concept, dot product for vectors.
GSP file for teaching
Step 2: Teachers give the precise definition of the 'dot
product' and demonstrate how to find it.
GSP file for teaching
Step 3: Teachers introduce the
way to find the dot product with vectors' components in component
representation by connecting the idea of the dot product of two vectors
to their
components.
Step 4: Teacher can expand the
idea of how to find the angle between two vectors from
the way to find the dot product. GSP
file for teaching
Step 5: Teachers summarize the
operation law for the dot product in an algebraical way. GSP file for teaching
Student Activity:
Technology Connection:
1. Teachers can use GSP to show students dynamic work process, and
students can use GSP to solve problems in an easier way.