Learning Activity

Introduce Adding and Subtracting Vectors

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this learning activity, students will learn to add or subtract two vectors. The activity will teach the students that they simply add or subtract their components. In other words, add the x component of the first vector to the x component of the second and so on for y and z. The answers the students will get from adding or subtracting the x, y, and z components of their original vectors are the x, y, and z components of their new vector. This learning activity should be used as an introductory activity. 

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

MA19.PRE.12

Add and subtract vectors.

Unpacked Content

UP:MA19.PRE.12

Vocabulary

  • End-to-end
  • Component-wise
  • Parallelogram Rule
  • Sum of Two Vectors
  • Additive Inverse
  • Vector Subtraction

Knowledge

Students know:
  • The aspects of end-to-end, componentwise, and the parallelogram rule involving vectors.
  • The additive inverse of a vector has the same magnitude but the opposite direction.

Skills

Students are able to:
  • Draw and find the diagonal of a parallelogram.
  • Represent vectors on an xy-plane.
  • Find the components of a vector given the direction and magnitude.
  • Find the additive inverse of a vector.

Understanding

Students understand that:
  • There are multiple ways to find the sum and difference of a pair of vectors.
  • The magnitude of the sum of two vectors will not be the same as the sum of the magnitudes unless the vectors are in the same direction.
  • The vector with the larger magnitude will have the greatest effect on the result.

Phase

Before/Engage
Learning Objectives

Learning Objectives

Students will be able to:

  • add vectors in 2D, when given algebraically.
  • subtract vectors in 2D, when given algebraically.
  • perform combinations of addition and subtraction of vectors in 2D.
  • find the components of an unknown vector given the result of the addition or subtraction with a known vector.

Activity Details

Engage: (5 minutes, whole group)

The teacher will remind the students how to express a vector in terms of components. Vectors coordinate systems are expressed usually x, y, and possibly z in 2 or 3-dimensional space (higher dimensionality is possible too in some mathematical situations). These component parts are usually expressed with a notation similar to that used to describe points in a coordinate system (e.g. <x,y,z>, etc.). If these pieces are known, adding or subtracting vectors is just a simple adding or subtracting the x, y, and z components.

Explore: (10 minutes, whole group)

The teacher will use the Adding and Subtracting video to introduce adding and subtracting vectors.

Explain: (10 minutes, whole group)

Review the activity content embedded within the video using the following examples:

1. If vector a = <3,2> and vector b = <4,−1>, find vector a + b.

2. Shown on the grid of unit squares are the vectors u, v, and u + v.

Image removed.

  1. What are the components of vector u?
  2. What are the components of vector v?
  3. What are the components of vector u + v?

3. Given the vectors AB = 3i - 4j and CD = -5i - 5j, calculate AB - CD.

Assessment Strategies

Assessment Strategies

The student responses during the class discussion will be used as a formative 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 the example problems individually.

Related Learning Activities

Learning Activity (Before)

Introduce Adding and Subtracting Vectors

Learning Activity (During)

Adding and Subtracting Vectors in 2D Lesson

Learning Activity (After)

Adding and Subtracting Vectors in 2D Worksheet

Background and Preparation

Background / Preparation

    • Students should be familiar with finding the coordinates of a point on a coordinate plane and vector notation.
    • The teacher should review the teaching video prior to the lesson.
    • The teacher will need to decide on how they will display the video and the whole group's problems to check for understanding.

Digital Tools / Resources

Adding and Subtracting Vectors Varsity Tutors
https://www.varsitytutors.com/hotmath/hotmath_help/topics/adding-and-subtractin…

Approved Date

Owner (Author)

yvetteakridge
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