### Notes:

The Rocking the Boat 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:

A unit on wave mechanics typically begins with a discussion of wave properties such as wavelength, frequency, period, amplitude and speed. Both the conceptual and mathematical meaning is often emphasized. This Concept Builder targets the mathematical meaning of these five properties. It does so in the context of a problem about two boats anchored in the harbor and rocking up and down as the waves enter the harbor. The situation is described in numerical terms and students must analyze the description in order to determine the values of these five quantities. To be successful, students must understand ...
• wavelength as the distance from one crest to the next adjacent crest,
• amplitude as the distance from the resting position to a crest,
• frequency as the number of complete vibrational cycles per time,
• period as the time for one complee vibrational cycle,
• and speed, calculated as the product of frequency times wavelength.

Each question begins with a description of the waves and the boats' motion. After reading the description, students must visualize the location of the boats relative to one another and with respect to the crests and troughs of the incoming waves. They tap on a diagram to place the boats along the wave pattern. They have three chances to get the placement correct. Once the diagram has been constructed, students must then determine the numerical values of wavelength, amplitude, frequency, period and speed. They have two opportunities to get these values correct. Incorrect values are color-coded once the first attempt has been made.

There are three levels of difficulty in this Concept Builder. The difficulty levels are differentiated from one another in terms of the number of questions. The numerical information differs from problem to problem but each problem always asks for the same five quantities. There are 27 total questions grouped into Question Groups with three questions each and organized as follows:

• Apprentice Difficulty Level: Question Groups 1-2.
• Master Difficulty Level: Question Groups 3-5.
• Wizard Difficulty Level: Question Groups 6-9.

To gain a feel for the cognitive difficulty of this Concept Builder, we recommend that teachers attempt to complete one of the difficulty levels. Alternatively, the questions are provided in a separate file for preview purposes. 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. Questions in the various levels are unique to that level and are not seen in other levels.
In order to complete a level, a student must correctly analyze each question at that level. If a student's analysis is incorrect, then the student will have to correctly analyze 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 analyzing the question. Once a star is earned, that question is removed from the que of questions 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 question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question at a level has been analyzed, 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 Rocking the Boat 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 WM1-WM4 of the Waves Motion module provides a great complement to this Concept Builder. It is 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 Static Electricity module can be found on Part 5 of the six-part App series. Visit Minds On Physics the App.

Additional resources and ideas for incorporating this Rocking the Boat Concept Builder into an instructional unit on Waves can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.