Let's See How Multiplying a Vector by a Scalar Works!

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This learning activity will be used to introduce multiplying a vector by a scalar and is intended for an introduction activity. The students will watch the Scalar and Vector 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 compute the magnitude of a scalar multiple.

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

Phase

Before/Engage

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

MA19.PRE.13
Multiply a vector by a scalar.

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

Given a vector, 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 Scalar and Vector video to be introduced to the multiplication of a vector by a scalar (this can be done as a whole group or assigned through Google Classroom).
After the completion of the video, the teacher should display the Scalar and Vector Practice and have the students work 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 compute the magnitude of a scalar multiple.

Assessment Strategies

The students should write their answers to the 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 Scalar and Vector video and Scalar and Vector Practice could be assigned through Google Classroom.

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 Scalar and Vector 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.

Let's See How Multiplying A Vector By A Scalar Works! Google Doc/YouTube Video

https://docs.google.com/presentation/d/1lT7O_mdtGLxUwH2pBCK2-IwZ9ID6vXk4ePWXtGm…

Approved Date

2020-07-16

Owner (Author)

yvetteakridge

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