Scalar Multiplication With Vectors

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This learning activity will be used during a lesson on using scalar multiplication with vectors. Students will explore how to perform scalar multiplication component-wise and represent scalar multiplication graphically. This activity will lead to learning how to compute the magnitude of a scalar multiple cv using ||cv|| = |c|v.  The teacher will use the Scalar Multiplication of Vectors Lesson to cover the “I Do,” “We Do,” and “You Do” portions of the lesson.

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

Phase

During/Explore/Explain
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 multiply a vector by a scalar.  

Students will be able to represent scalar multiplication graphically by scaling vectors and possibly reversing their direction and perform scalar multiplication component-wise.

Activity Details

I Do:

    • The teacher will demonstrate how to multiply a scalar into vectors by providing examples visually and explaining verbally in detail using the Scalar Multiplication of Vectors Lesson. 
    • Students will observe, take notes using their math journals or paper, and ask questions.
    • The teacher will have the students turn and talk about any misconceptions they may have at this point in the lesson. 

We Do:

    • The teacher will say…..We will now collaborate and discuss the scalar multiplication of vectors using the “We Do” section of the Scalar Multiplication of Vectors Lesson.  
    • The teacher will issue whiteboards, pens, and erasers to the class. 
    • The teacher will ask students to work the “We Do” problems on their whiteboards holding them up as they find each answer for the teacher to check. (This will be used as a formative assessment to see if students understand the lesson.)
    • Important: The teacher will need to verbally discuss any problems and have students explain their thinking to ensure solidification of understanding.

You Do:

    • The teacher will have the students complete the “You Do” section of the Scalar Multiplication of Vectors Lesson.
    • The students will do the “You Do” problems on their whiteboards holding them up as they find each answer for the teacher to check. (This will be used as a formative assessment to see if students understand the lesson.)
    • Once the teacher has verified the students understand how to perform scalar multiplication of vectors component-wise and represent scalar multiplication graphically, he/she will hand out the Scalar Multiplication of Vectors Worksheet.
    • The teacher will monitor students as they complete the worksheet.
    • The teacher will remind the students the worksheet will be graded for accuracy.

Assessment Strategies

    • The teacher will monitor students as they complete the Scalar Multiplication of Vectors Worksheet to provide timely feedback to help eliminate any misconceptions.
    • Upon completion, the teacher will take up the completed worksheet and ensure at least 80% mastery of the skill.

Variation Tips

The Scalar Multiplication of Vectors Lesson and Scalar Multiplication of Vectors Lesson could be assigned through Google Classroom.

Background / Preparation

    • The teacher will need copies of the worksheet Scalar Multiplication of Vectors Worksheet in advance. 
    • The teacher will provide each student with a copy of the worksheet, a whiteboard, a dry erase pen, and an eraser for the “We Do” and “You Do” sections.
    • The students will need math journals if used for notes or paper if math journals are not used.
    • The teacher will need Internet access and the required equipment to display the Scalar Multiplication of Vectors Lesson.
    • Students will need to know how to graph a vector.
Scalar Multiplication With Vectors Google Doc
https://docs.google.com/document/d/1C2nPL29oh7oAh1p8YsCrya726yZcW-pePdVtNqIEJ4s…

Approved Date

Owner (Author)

yvetteakridge
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