Learning Activity

Adding and Subtracting Vectors in 2D Worksheet

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this learning activity, students will practice adding and subtracting vectors in 2D. This learning activity can be used as a stand-alone activity or an assessment activity for the corresponding activities found in the Notes or Recommendations section.

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

Students will be able to:

add vectors in 2D, when given algebraically.
subtract vectors in 2D, when given algebraically.
perform combinations of addition and subtraction of vectors in 2D.
find the components of an unknown vector given the result of the addition or subtraction with a known vector.

Activity Details

Engage: (5 minutes, whole group)

The teacher will review how to express a vector in terms of components: (The teacher can skip this step if he/she used the Before Activity and/or During Activity.)
The teacher will remind the students that:
- Vector addition is the operation of adding two or more vectors together into a vector sum. The sum of two or more vectors is called the resultant. Vector subtraction is the operation of subtracting two vectors to find their difference. Given two vectors in component form, we can find their difference by subtracting the corresponding components of the vectors.

Explore: (20 minutes, whole group)

The teacher will use the Adding and Subtracting Lesson Worksheet to practice adding and subtracting vectors in 2D. (There is a video on the worksheet for each question if a student is stumped and needs to review prior to answering the question.)

Explain: (10 minutes, whole group)

At the end of class, the teacher will bring the students back to a whole-group discussion to discuss any problems the students faced while adding and subtracting vectors.

Assessment Strategies

The teacher will walk around the room as the students answer the questions on the worksheet observing as an assessment.

Acceleration and Intervention

Variation Tips

For students who struggle with this activity, the teacher should provide a work buddy.
For students who excel at this activity, the teacher could assign additional problems.

Related Learning Activities

Background and Preparation

Background / Preparation

Students should already be familiar with finding the coordinates of a point on a coordinate plane and vector notation.
The teacher should review the lesson worksheet prior to the lesson.
The teacher will need to decide on how he/she will digitally assign the worksheet to check for understanding.
Each student will need access to a digital device, such as a tablet, iPad, or laptop.

Digital Tools / Resources

Adding and Subtracting Vectors in 2D Nagwa Worksheet

https://www.nagwa.com/en/worksheets/508142396190/

Approved Date

2022-07-14

Author

Owner (Author)

yvetteakridge

Design by Adaptive Theme

Learning Resource Type