### Notes:

The Component 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:

Many first-year Physics courses include a unit in which the addition of two or more vectors is discussed. One of the methods commonly used for adding vectors that are oriented at angles to the axes is the component addition method. Each vector is considered to have a horizontal and vertical component that can be calculated using the magnitude of the vector and its direction. These components are directed along the axes and can easily be added to determine the components of the resultants. This Concept Builder focuses on the task of using such components to determine the magnitude and direction of a resultant formed by the addition of two or more vectors.

This Concept Builder is intended for use in the early to middle stages of a learning cycle on adding vectors. Students will need to first be introduced to the concept of a vector, conventions for describing their direction, and methods of adding vectors. Some time should be spent adding right-angle vectors using the Pythagorean theorem. And students should be able to use sine-cosine-tangent functions to determine components and to determine the direction of a resultant if its components are known.

This Concept Builder was intended as an in-class activity. It includes 9 different problems organized into three different ability levels. 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. There is no redundancy between the three levels; the questions included in each level are unique to that level. Our summary of the three levels is as follows:
• Apprentice Level (easiest): Includes three problems in which two vectors are added.
• Master Level (moderate difficulty): Includes three problems in which three vectors are added.
• Wizard Level (most difficult): Includes three problems in which four vectors are added.
In order to complete a level, a student must correctly analyze each problem at that level. If any part of a student's analysis is incorrect, feedback is provided and immediate opportunity for correction is allowed. As a student progresses through a level, a system of stars are used to indicate progress on the level. A star is an indicator of correctly analyzing the problem. Once every problem at a level has been analyzed, the student earns a medal. The medal 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 difficulty levels.

The most valuable (and most overlooked) aspect of this concept-building activity is the Help Me! feature. Each question group is accompanied by a Help page that discusses the details 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 Component Addition Concept Builder. These include:
• Minds On Physics the App:
The Minds On Physics apps 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 from the Vectors and Projectiles module make for a great complement to this Concept Builder. Missions VP2, VP3, and VP4 from App #1 would be particularly useful accompaniments to this Concept Builder. They are best used in the middle to later stages of the learning cycle. Visit the Minds On Physics the App.

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 Vectors and Projectiles module can be found on Part 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 interactine and observing the relatoinships between variables. There are several simulations in the Vectors and Projectiles section of the Physics Interactives. 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 ...

Vector Components, Vector Resolution, and Vector Addition

Visit the Curriculum Corner - Vectors and Projectiles.

Additional resources and ideas for incorporating Component 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.