Adding and Subtracting Vectors Lesson

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 Adding and Subtracting Vectors. Students will explore 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. The teacher will use the Adding and Subtracting Vectors Lesson to cover the “I DO” and “We 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.12

Add and subtract vectors.

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.

Learning Objectives

Students will be able to:
- Given two vectors 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.
- 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

During/Explain/Elaborate Activity:

This learning activity will be used during a lesson on Adding and Subtracting Vectors. Students will explore 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.

(I DO)

  • The teacher will demonstrate how to add and subtract vectors by providing examples visually and explaining verbally in detail using the Adding and Subtracting 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 various types of adding and subtracting vectors using the 'We DO' section of the Adding and Subtracting 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 hand out the "You DO" section of the Adding and Subtracting Vectors Lesson.
  • The teacher will monitor students as they complete the "You DO" section of the lesson.
  • The teacher will remind the students the "You DO" section will be graded for accuracy.

Assessment Strategies

  • The teacher will monitor students as they complete the “You DO”  section to provide timely feedback to help eliminate any misconceptions.
  • Upon completion, the teacher will take up the completed "You DO" section and ensure at least 80% mastery of the skill.

Variation Tips

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

Background / Preparation

  • The teacher will need copies of the “You DO” section of the Adding and Subtracting Vectors Lesson in advance. 
  • The teacher will provide each student with a whiteboard, a dry erase pen, and an eraser for the “We DO” section.
  • 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 Adding and Subtracting Vectors Lesson.
Adding and Subtracting Vectors Lesson Google Doc
https://docs.google.com/document/d/1r-oH2x5qYdZTQuaLJ782ushnnCV4r7lIUMrLa6w63Q8…

Approved Date

Owner (Author)

yvetteakridge
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