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.