ALEX Learning Activity

In this learning activity, students will learn how to find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. This learning activity can be used as a stand-alone activity or a core lesson activity. Corresponding activities can be found in the Notes or Recommendations section.

Students will be able to:

• describe a set of components in terms of the numbers of units right/left and up/down, and vice versa.
• identify the initial and terminal points of a vector.
• understand the relation between vector components and initial and terminal points.

Procedure

1. Introduction (5 minutes, whole group)
The teacher will review the component form of a vector: (The teacher can skip this step if he/she used the Before Activity.)

• Remind the students that the component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.

• Given a vector’s initial point (where it starts), (x₁, y₁), and terminal point (where it ends), (x₂, y₂) the component form can be found by subtracting the coordinates of each point: < x₂ – x₁, y₂ – y₁ >.

2. Watching the Video (10 minutes, whole group):

The teacher will show the teaching video.

3. Conclusion (10 minutes, whole group)

The teacher will display the following problems to be worked on as a whole group to check for understanding.

• 1. Find the component form of the vector with initial point <d,e> and terminal point <f,g>.
• 2. Find the component form of the vector with initial point <0,1> and terminal point <4,5>.
• 3. Find the component form of the vector with initial point <-5,-9> and terminal point <-6,-11>.
• 4. Find the component form of the vector with initial point <3,8> and terminal point <-3,-8>.

The teacher will assign additional problems to be worked on with a partner to check for understanding.

The student responses during the class discussion and additional problems will be used as a formative assessment. 

• • Students should already be familiar with finding the coordinates of a point on a coordinate plane.
  • The teacher should review the teaching video prior to the lesson.
  • The teacher will need to decide how he/she will display the video and the problems to check for understanding.

• • The teacher will need to decide how he/she wants to digitally assign the additional problems.

• For students who struggle with this activity, the teacher should provide a work buddy.
• For students who excel at this activity, the teacher could assign the example problems individually.
• The teacher can assign the additional problems to be worked on individually instead of with a partner.

This activity can stand alone or be used as a During/Explore/Explain activity for the following learning activities:

Using Initial and Terminal Points to Find the Components of a Vector Represented Graphically (Before Activity)

Components of a Vector Subtraction Practice (After Activity)