Learning Activity

Proof I Know How to Add and Subtract Vectors

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This learning activity will be used to add and subtract vectors and is intended for an assessment activity. The students will complete the Adding and Subtracting Vectors Assessment to demonstrate mastery of 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.

This activity results from the ALEX Resource Development Summit.

Content Standards

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

MA19.PRE.12
Add and subtract vectors.

Unpacked Content

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.

Interdisciplinary Connections

Phase

After/Explain/Elaborate

Learning Objectives

Given two vectors, students will be able to:
-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

After/Explain/Elaborate Activity:

This activity will be used at the end of an Adding and Subtracting Vectors lesson.
The teacher will distribute the Adding and Subtracting Vectors Assessment.
The students will complete the Adding and Subtracting Vectors Assessment independently to demonstrate mastery of 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 (this can be done as a whole group or assigned through Google Classroom).
The teacher should circulate the room to check for understanding of adding and subtracting vectors and can correct mistakes and misunderstandings as needed.

Assessment Strategies

Adding and Subtracting Vectors Assessment will be used to assess the students.
The teacher can assess students' understanding while the students are working on the assessment.
After the assessment has been completed, the teacher should have meaningful dialogue on the process and procedures for adding and subtracting vectors.
Students should be allowed to collaborate and work problems out on the board for clarity for those who are still having trouble.

Acceleration and Intervention

Variation Tips

The Adding and Subtracting Vectors Assessment could be assigned through Google Classroom.
The teacher could assign students to work in pairs instead of individually.

Background and Preparation

Background / Preparation

The teacher will need to make copies of the Adding and Subtracting Vectors Assessment before the lesson.
Students will need prior knowledge of how to add and subtract vectors.

Digital Tools / Resources

Adding and Subtracting Vector Assessment Google Doc

https://docs.google.com/document/d/1a_jvKyX-DkqH7P8X31GJaQZzRDeHEOfeo_3Wbih8Av8…

Approved Date

2020-07-16

Author

Owner (Author)

yvetteakridge

Design by Adaptive Theme

Learning Resource Type