Notes:

The Projectile Mathematics 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 middle to latter stages of a learning cycle on the mathematics of projectiles. The projectile in this Concept Builder is one launched at an angle to the horizontal and landing at the same height as the launch height. The use of kinematic equations to solve for unknown quantities is the focus of the activity. Such unknowns include the original velocity and its components, the angle of launch, the time up to the peak, the total time in the air, the horizontal displacement, and the vertical displacement at the highest point.

There are three difficulty levels in the Concept Builder - Apprentice, Master, and Wizard. Each difficulty level includes a table of numerical data which must be accurately completed. Success involves accurately filling in the missing cells of the table. The learner can check a calculation as many times as needed. But every miss is counted and a Health Report is displayed once the table has been completed. The formula for determining a Health Rating is shown on a separate page. Students can repeat the exercise as many times as needed to improve their grade above a minimum-required level.

This Concept Builder was intended as an in-class activity or as an assigned out-of-class activity for those classrooms subscribed to Task Tracker. After some lab work, some discussion of how to analyze a series circuit, and some guided practice, allow students to try it for themselves. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in a separate file) in order to judge which difficulty levels would be most appropriate for their students. The Wizard level can be very difficult and should be reserved for use by AP Physics 1, Honors Physics, or IB Physics classes.

The Health Rating:

Students can complete as much of the table as they wish before checking their answers. And they can check their answers as many times as they wish. Feedback regarding the correctness of their answers is immediate and provided using a color-coding system. Correct answers are displayed in a table cell with a green background; these correct answers become locked and cannot be changed. Incorrect answers are displayed in a table cell with a red background. Each time students check their answers, the number of missed answers is determined. A running tally is kept of the number of misses. When a student accurately completes the table, a Health rating is displayed on the screen. The Health rating is dependent upon the number of misses. Formulas for computing the Health rating are discussed on a separate page. The Health rating is also displayed on the Main Menu screen for any completed difficulty level. A student can always repeat a difficulty level in order to improve their Health rating for that level. The best Health rating is always displayed on the Main Menu screen below the trophy for that difficulty level.

We leave it to the discretion of individual teachers as to what they wish to do with the Health rating information. We recognize that there will be some teachers who feel most comfortable with their students in simply requiring that a difficulty level be completed and  trophy be earned. Other teachers may wish to require completion of a difficulty level with a minimum Health rating. For instance, such teachers may require that each difficulty level be completed with a 70% or higher Health rating. Still other teachers may tie the Health rating into a grade or allow a homework pass for completing an activity that exceeds a 90% Health rating. Decisions as to what to do with the Health rating are best left for individual teachers who know their students the best.

Getting Help:

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 Projectile Mathematics 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 VP7, VP8, VP9, and VP10 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. The links are provided below. The Projectile Simulator serves as a suitable pre-cursor to this Concept Builder. The Turd the Target activities are good follow-ups for those courses that emphasize the mathematics of projectiles and its use in solving problems. These include the following:

Projectile Simulator

Turd the Target

Turd the Target 2

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

Projectile Motion

Visit the Curriculum Corner - Kinematics.

Additional resources and ideas for incorporating Projectile Mathematics into an instructional unit on Vectors and Projectiles can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.