Learning Resource Type

Learning Activity

Multiplying a Vector by a Scalar

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.

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

    MA19.PRE.13

    Multiply a vector by a scalar.

    Unpacked Content

    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.

    Phase

    Before/Engage
    Learning Objectives

    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

    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 and Preparation

    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.

    Digital Tools / Resources

    ALSDE LOGO