Learning Activity

Components of a Vector by Subtracting Practice

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this learning activity, students will apply the knowledge they gained on how to find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point in order to prove they understand the learning objective. The students will work on this learning activity individually.  This learning activity can be used as a stand-alone activity or an After Activity for the associated Before and During activities.

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.9

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Unpacked Content

UP:MA19.PRE.9

Vocabulary

  • Components
  • Initial Point
  • Terminal Point

Knowledge

Students know:
  • If a vector is transposed in the xy-plane, it retains its magnitude and direction.

Skills

Students are able to:
  • Transpose a vector from one position to another position in the xy-plane.
  • Find the component form of a vector.

Understanding

Students understand that:
  • Vectors having the same magnitude and direction are equivalent regardless of where they are in the xy-plane.
  • Vectors in standard position have a terminal point that is equal to the components of the vector.

Phase

After/Explain/Elaborate
Learning Objectives

Learning Objectives

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,
  • find the components of a vector represented graphically,
  • identify the initial and terminal points of a vector,
  • understand the relation between vector components and initial and terminal points,
  • understand that equivalent vectors have equal corresponding components.

Activity Details

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 and/or During 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. Assignment (20 minutes, individual activity)

  • After the students have proven they understand how to find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point, the teacher will instruct the students to complete the Components of a Vector by Subtracting Practice.

3. Conclusion (10 minutes, whole group)

  • At the end of class, the teacher will bring the students back to a whole-group discussion to determine any problems they faced finding the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Assessment Strategies

Assessment Strategies

The teacher will walk around the room as the students answer the questions on the Components of a Vector by Subtracting Practice and taking up the practice as an assessment.

Variation Tips

    • 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 additional problems he/she has access to assigning.

Related Learning Activities

Learning Activity (Before)

Using Initial and Terminal Points to Find the Components of a Vector Represented Graphically

Learning Activity (During)

Vector Components from Initial and Terminal Points

Learning Activity (After)

Components of a Vector by Subtracting Practice

Background and Preparation

Background / Preparation

    • Students should already be familiar with finding the coordinates of a point on a coordinate plane.
    • The teacher should review the assignment prior to the lesson.
    • The teacher will need to decide on how he/she will assign problems digitally to check for understanding.
    • Each student will need access to a digital device, such as a tablet, iPad, or laptop. 

Digital Tools / Resources

Components of a Vector by Subtracting Practice Google Doc
https://docs.google.com/presentation/d/1iyMAkVDQrpZyic2w4w1d2h_0oFAIFD7CwOI8-Dl…

Approved Date

Owner (Author)

yvetteakridge
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