Multiplying a Vector by a Scalar

Learning Resource Type

Learning Activity

Overview

This learning activity will be used to introduce multiplying a vector by a scalar and is intended as an introduction activity. The students will watch the Multiplying A Vector By A Scalar video to learn how to multiply a vector by a scalar. This activity will lead to learning how to represent scalar multiplication graphically by scaling vectors and possibly reversing their direction and computing the magnitude of a scalar multiple.

Phase

Before/Engage
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.13

Multiply a vector by a scalar.

UP:MA19.PRE.13

Vocabulary

  • Scalar Multiple
  • Scalar Multiplication
  • Scaling Vectors

Knowledge

Students know:
  • The representation of vectors graphically on the xy-plane.

Skills

Students are able to:
  • Find the components of a vector.
  • Find the magnitude and direction of a vector.

Understanding

Students understand that:
  • Scalar multiplication results in a dilation of the original vector where a scalar greater than 1 would increase the magnitude and a scalar from 0 to 1 would decrease the magnitude.
  • A negative scalar would reverse the direction of the vector.
  • The absolute value of the scalar has the resulting effect on the magnitude.

Learning Objectives

Students will be able to:

  • Perform scalar multiplication and represent it graphically.
  • Perform scalar multiplication component-wise.
  • Compute the resulting magnitude of the scaled vector and verify that the direction is the same or opposite.

Activity Details

  • This activity will be used at the beginning of a multiplying a vector by a scalar lesson.
  • The students will watch the Multiplying A Vector By A Scalar video to be introduced to the multiplication of a vector by a scalar (this can be done as a whole group or assigned through a digital platform).  
  • After the completion of the video, the teacher should display the Pre-Cal Scalar and Vector Practice and have the students work on the problems. 
  • The teacher will circulate the room to check for understanding of multiplying a vector by a scalar.
  • Once the teacher has verified students’ understanding of multiplying a vector by a scalar, he/she should teach students how to represent scalar multiplication graphically by scaling vectors and possibly reversing their direction and computing the magnitude of a scalar multiple.

Assessment Strategies

    • The students should write their answers to the Pre-Cal Scalar and Vector 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 Multiplying A Vector By A Scalar video and Pre-Cal Scalar and Vector Practice could be assigned through a digital platform.

Background / Preparation

  • Students will need to know the definition of a vector.
  • Students will need their journals or a piece of paper to complete the Pre-Cal Scalar and Vector Practice. This sheet will need to be copied.
  • 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 a digital platform.
https://docs.google.com/presentation/d/1nO6WhaDmLc0Z7vRdIg1CFI4fQ3aUoLdXSdmGGEc…

Approved Date

Owner (Author)

yvetteakridge
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