Learning Activity

It's Just the Beginning...Adding And Subtracting Vectors

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This learning activity will be used to introduce adding and subtracting vectors and is intended as an introduction or engagement activity. The students will watch the Adding and Subtracting Vectors video to learn how to add and subtract vectors. This activity will lead to learning how to add vectors end-to-end, component-wise, and by the parallelogram rule, determine the direction of their sum, represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. 

This activity was created as a result of the ALEX Resource Development Summit.

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:
- Given two vectors will add or subtract them to find the magnitude and direction of the resulting vector by using all three processes: end-to-end, componentwise, and parallelogram rule.

- Will show the process involved to find the resultant vector when subtracting one vector from another by using the additive inverse using all three processes: end-to-end, componentwise, and parallelogram rule.

Activity Details

Before/Explain/Elaborate Activity:

  • This activity will be used at the beginning of an adding and subtracting vectors lesson.
  • The students will watch the Adding and Subtracting Vectors video to be introduced to adding and subtracting vectors (this can be done as a whole group or assigned through Google Classroom).  
  • After the completion of the video, the teacher should display the Adding and Subtracting Practice and have the students work the problems.  
  • The teacher will circulate the room to check for understanding of adding and subtracting vectors.
  • Once the teacher has verified students’ understanding of adding and subtracting vectors, he/she should teach students how to add vectors end-to-end, component-wise, and by the parallelogram rule, determine the magnitude and direction of their sum, and represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. 
Assessment Strategies

Assessment Strategies

  • The students should write their answers to the Adding and Subtracting Practice in their math journals or on a sheet of paper.  
  • The teacher will assess the students by checking their responses and can correct mistakes or misunderstandings.

Variation Tips

The Adding and Subtracting Vectors video and Adding and Subtracting Practice could be assigned through Google Classroom.

Background and Preparation

Background / Preparation

  • Students will need their journals or a piece of paper to complete the Adding and Subtracting Practice.
  • The teacher will need to make sure there is an Internet connection (WiFi) and devices to use if he/she chooses to assign the video and practice through Google Classroom.

Digital Tools / Resources

Adding and Subtracting Vectors Google Doc/YouTube
https://docs.google.com/presentation/d/1H9HZIt-8Hy3ihdTshdk4Uiw2SPjhGopXk6ycxqx…

Approved Date

Owner (Author)

yvetteakridge
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