### Notes:

The Position-Time Graphs - Conceptual Analysis 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:

This Concept Builder is intended for use in the earlier stages of a learning cycle on Kinematic Graphing. It makes for an exceptional formative assessment of student ability to conceptually analyze a position-time graph. The emphasis is on recognizing the connection between the features of a position-time graph and the motion of the object that it represents. The Concept Builder focuses on non-accelerated motion (the "Constant Speed Model"). Students must know that the slope of the line on a position-time graph reveals information about the velocity of an object. This involves the following ideas about the slope-velocity connection:
• A line with zero slope (horizontal line) represents an object with zero velocity (not moving).
• A line with positive slope represents an object with a positive velocity.
• A line with negative slope represents an object with a negative velocity.
• A line with small slope represents an object with a small velocity (slow moving object).
• ​A line with large slope represents an object with a large velocity (fast moving object).
• ​A line with constant slope (i.e., straight line) represents an object with a constant velocity.
• ​A line with changing slope (i.e., curved line) represents an object with a changing velocity.
• The larger the slope of the line, the faster that the object is moving.

This Concept Builder was intended as an in-class activity. The Concept Builder includes 46 Questions grouped into 14 different Question Groups and organized into three different activities. Teachers using the Concept Builder with their classes should preview the activities (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. Our summary of the three activities is as follows:

• Words and Graphs: Includes six Question Groups in which students make connections between the features of a position-time graph and the characteristics of an object's motion.
• Speed Rankings: Includes four Question Groups in which students visually inspect the relative slope of three lines on a position-time graph in order to rank the three objects in order of speed.
• Dots and Graphs: Includes four Question Groups in which students inspect a dot diagram for three different motions and associating each motion with one of six lines on a position-time graph.

In order to complete an activity, a student must correctly analyze each situation in that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar situation twice in order to successfully complete the activity. This approach provides the student extra practice on situations for which they exhibited the most 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 analyzing the situation. Once a star is earned, that situation is removed from the que of situations to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the situation and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the situation must be correctly analyzed one time in order to earn a star. Once every Question Group in an activity has been correctly answered, the student earns a medal that 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-building activity 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 Position-Time Graphs Conceptual Analysis 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 from the Kinematic Graphing module make for a great complement to this Concept Builder. We recommend any of missions KG1, KG2, KG3, and KG4. 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 Kinematic Graphing module can be found on Part 1 of the six-part App series. Visit Minds On Physics the App.

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

Describing Motion with Position-Time Graphs
Describing Motion Graphically
Graphing Summary

Visit the Curriculum Corner - Kinematics.

Additional resources and ideas for incorporating Position-Time Graphs - Conceptual Analysis into an instructional unit on Kinematics  can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.