### Notes:

The 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:

Acquisition of a skill in a Physics course is demands repeated practice with as much feedback as possible. Many teachers of Physics spend time on the skill of graphically adding vectors using the head-to-tail vector addition method in order to determine the resultant. This Concept Builder is intended to provide students multiple practice opportunities of visually rearranging the given vectors into a head-to-tail arrangement and identifying the resultant vector as extending from the tail of the first vector to the head of the last vector. Feedback is immediate and opportunities to repeat missed questions are plentiful.

This Concept Builder is intended for use near the early to middle stages of a learning cycle on vector addition. Its strength is in helping students acquire the habit of using the head-to-tail vector addition method to add 3, 4, or 5 vectors. The vectors are displayed on a background grid of adjoining squares with each vector extending from one corner to another corner of a square on the grid. While the vectors cannot be physically moved about the screen, a student can easily use a pencil or a pen cap on the screen and place it on the grid at the corner where the second, third, fourth, or fifth vector ends. They can then visually identify the length and direction of the resultant vector.

This Concept Builder is intended as an in-class activity. After some discussion, modeling, and practice with adding vectors, allow students an opportunity to practice one or more of the three levels of difficulty. Questions in this Concept Builder are grouped, with questions in the same group being nearly identical. 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 should preview the activity (or view the Questions in the separate file) in order to judge which levels would be most appropriate for their students.

Our summary of the three levels is as follows:

• Apprentice Level (easiest): Includes four question groups. Each question includes the addition of three vectors.
• Master Level (moderate difficulty): Includes eight question groups - the four from the Apprentice level plus four new ones. The new questions unique to the Master Level includes the addition of four vectors.
• Wizard Level (most difficult): Includes eight question groups - the four from the Master level plus four new ones. The new questions unique to the Wizard Level includes the addition of five vectors.

We can imagine it being profitable to allow students to make judgements as to what level to begin with and to progress from easier to more difficult levels.

In order to complete a level, a student must correctly answer one question from each question group at 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 level. 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 que 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 at a level has 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 the 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, VP3, and VP4 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 of the website includes a collection of simulations for a variety of topics. The simulatoins typically include a variable-rich environment that can be manipulated in an interactive way in order to explore a concept, principle, or physical situation. There are a couple of Interactives that would make perfect complements to this Vector Addition Concpet Builder. They are listed below:

Vector Guessing Game

• The Laboratory
Hopefully we will be one of the first to say "There is no replacement for hands-on, minds-on activities." It is our belief that Physics students should be actively involved in a physical manner with exploring their world. The Laboratory section of our website includes 150 ideas for incorporating lab experiences into the Physics curriculum. You will find a couple of excellent vector addition lab experiences in our Vectors and Projectiles section.

Map Lab

As the Crow Flies

Where Am I? Lab

Visit Vectors and Projectiles Labs

• 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 - Vectors and Projectiles.

Additional resources and ideas for incorporating 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.