Notes
The Vector Direction Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.
Teaching Ideas and Suggestions
A vector is a quantity that has both magnitude and direction. Displacement, velocity, acceleration, force, and momentum are a few examples of vectors commonly used in the mechanics portion of a physics course. A mathematical treatment of vectors will naturally include a discussion of the direction of a vector. A vector's direction is often expressed as some angle of rotation from the traditional north-south-east-west compass directions. There are numerous conventions for expressing such directions. The two most commonly used conventions at The Physics Classroom include:
- Expressing the direction of a vector as the counter-clockwise angle of rotation that the vector makes with due East.
- Expressing the direction of a vector as the angle of rotation that the vector makes with one of the two nearest axis directions.
This Concept Builder is intended to provide students with practice and feedback with respect to the use of both conventions and with the task of converting between the two conventions.
This Concept Builder is intended as an in-class activity. After some discussion, modeling, and practice with describing vector direction, allow students an opportunity to practice one or more of the activities. Questions in this Concept Builder are grouped, with questions in the same group sharing similar traits. If a student misses a question within a group, they will eventually be presented with a different question within the same group. Teachers using the Concept Builder with their classes can preview the activity (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. We strongly recommend all three activities for any physics course that has a medium to strong reliance upon the mathematics of vectors.
Our summary of the three actvities is as follows:
Our summary of the three actvities is as follows:
- Counter-Clockwise from East: Question Groups 1-6; students are given a diagram of a vector and drag a protractor into position in order to measure an angle and express the direction of the vector as a counter-clockwise angle of rotation from due east.
- Rotation Angle from Nearest Axes: Question Groups 7-12; students are given a diagram of a vector and drag a protractor into position in order to measure an angle and express the direction of the vector as the angle of rotation from one of the two nearest axes.
- CCC: Includes six question groups - the four from the Master level plus four new ones. The new questions unique to the Wizard Level Convention Conversions: QuestionGroups 13-18; students are given the direction of a vector in one of the two conventions and must do some spatial/mathematical reasoning in order to express the directoin in the other convention.
In order to complete an activity, a student must correctly answer one question from each question group for that activity. If a student's answer is incorrect, then the student will have to correctly answer the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the activity. A star is an indicator of correctly answering a question from within that question group. Once a star is earned, that question group is removed from the cue of question groups to be analyzed. Each question group is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly answer it twice before earning a star. A yellow box is an indicator that the situation must be correctly answered one time in order to earn a star. Once every question group within an level activity been answered, the student earns a medal which is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned activities.
The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.
The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.
Related Resources
There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Vector Direction Concept Builder. These include:
Additional resources and ideas for incorporating Vector Direction into an instructional unit on Vectors and Projectiles can be found at the Teacher Toolkits section of The Physics Classroom website. Visit Teacher Toolkits.
- Reading:
The first page of Lesson 1 of the Vectors - Motion and Forces in Two Dimensions Chapter at the Tutorial provides an extensive treatment of the topic of vector direction:
Vector Direction
- Minds On Physics Internet Modules:
The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignment VP1 of the Vectors and Projectiles module provide a great complement to this Concept Builder. It would best be used in the early ot middle stages of a learning cycle on vectors and vector addition. Visit the Minds On Physics Internet Modules.
Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The aforementioned assignment can be found on App#1 of the six-part app series. Visit Minds On Physics the App.
- Curriculum/Practice: There is one specific Concept Development worksheet at the Curriculum Corner that would be very useful in assisting students in cultivating their understanding of vector direction:
Vector Representation
Visit the Curriculum Corner - Vectors and Projectiles.
Additional resources and ideas for incorporating Vector Direction into an instructional unit on Vectors and Projectiles can be found at the Teacher Toolkits section of The Physics Classroom website. Visit Teacher Toolkits.