### Notes:

The Head-to-Tail Vector Addition 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:

Vectors and vector addition is a common topic in first-year, algebra-based Physics courses. In such courses, scaled vector diagrams are often used to add vectors that are not at right angles to each other. While trigonometric methods yield more precise results, a scaled vector diagram provides a reasonably accurate answer and provides students with a feel for what is physicall happening. Even courses that avoid scaled vector diagrams and rely totally upon trigonometric methods to add vectors must have a reliance on the head-to-tail method. There are numerous student difficulties associated with the head-to-tail addition of vectors. This Concept Builder provides plenty of practice with the skill of adding vectors graphically. It makes a great pre-cursor to the actual act of creating scaled vector diagrams.

This Concept Builder is intended as an in-class activity. After some discussion, modeling, and practice with doing vector addition, allow students an opportunity to practice one or more of the activities. Questions in this Concept Builder are grouped; the grouping allows us to give students a second question from the group if the first question is missed. If a student misses a question within a group, they will eventually be presented with a different question within the same group.

There are three difficulty levels in this Concept Builder. They are referred to as the Apprentice Difficulty Level (easiest), the Master Difficulty Level, and the Wizard Difficulty Level (most difficult). Questions in the Apprentice Difficulty Level are just as difficult as those ini the Wizard Difficulty Level. But the Wizard Difficulty Level has more questions. In fact that is the only trait that makes on difficulty level different than the others. For instance, the Wizard Difficulty Level contains the same six Question Groups as the Master Difficulty Level plus three more Questiion Groups. 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 difficulty levels would be most appropriate for their students.

In order to complete a level, a student must correctly answer one question from each question group in that level. 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 level. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through a level, 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 a level 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 levels.

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 this Head-to-Tail Vector Addition Concept Builder. These include:
• 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. Assignments VP2 and VP3 of the Vectors and Projectiles module provide great complements to this Concept Builder. They are best used in the middle to later stages of the learning cycle. 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 assignments can be found on App #1 of the six-part app series. Visit Minds On Physics the App.

• Physics Interactives: Our Physics Interactives section includes a collection of interactive simulations that help students visualize concepts by interacting and observing the relationships between variables. There are three simulations in the Vectors and Projectiles section of the Physics Interactives that will coordinate with this Concept Builder. These include the following:

Name That Vector

Vector Guessing Game

• Curriculum/Practice: Several Concept Development worksheets at the Curriculum Corner will be very useful in assisting students in cultivating their understanding, most notably ...

Visit the Curriculum Corner - Kinematics.

Additional resources and ideas for incorporating Head-to-Tail Vector Addition into an instructional unit on Vectors and Projectiles can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.