Learning Activity

Adding and Subtracting Vectors in 2D Lesson

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 how to add and subtract vectors in 2D. Vectors can be represented by line segments with a specific length (magnitude) and directions. Students will use this information to help visualize vector addition and subtraction. The scope of this learning activity will only consider vectors in two dimensions; however, the methodology described can be extended to vectors in three or more dimensions. The teacher will recall that a unit vector is a vector with a magnitude equal to 1 and that the unit vectors in the 𝑥- and 𝑦-directions are denoted by  ⃑𝑖 and ⃑𝑗 respectively. This learning activity can be used as a core lesson 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

During/Explore/Explain
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 review how to express a vector in terms of components: (The teacher can skip this step if he/she used the Before Activity and/or After Activity.)

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: (20 minutes, whole group)

The teacher will use the Adding and Subtracting Lesson Presentation to teach the students how to add and subtract vectors.

(This lesson presentation has a lesson video available if the teacher would like to use the video instead of the presentation.)

Explain: (10 minutes, whole group)

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

  1. Given that vectors A = ( −2,2), B = (5,2),and C =(−3,−2), find −A + B - C.
  2. Given that vectors A = (−4,5) and  A + B = (2,7), find vector B.
  3. Given that vectors A =( 7,−1) and  B = (3,−2), find vector A + B.
  4. Given that vectors A = (3,−2), B = (−5,4), and A - B + C = (6,−1), find vector C.

(Answers to the examples)

Assessment Strategies

Assessment Strategies

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

Variation Tips

  • This lesson presentation has a lesson video available if the teacher would like to use the video instead of the presentation.
  • 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 lesson presentation or video prior to the lesson.
  • The teacher will need to decide on how they will display the lesson presentation or video and the whole group problems to check for understanding.

Digital Tools / Resources

Adding and Subtracting Vectors in 2D Lesson Nagwa Video
https://www.nagwa.com/en/presentations/403195101329/

Approved Date

Owner (Author)

yvetteakridge
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