The Parallel Circuits - ∆V=I•R Calculations 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.

This Concept Builder is intended for use near the middle stages of a learning cycle on series and parallel circuits. Most physics courses spend considerable time using physics formulas to solve numerical word problems. Algebraic manipulation and substitution of known values into the formula is a typical activity. This Concept Builder addresses this skill for a parallel circuit analysis. 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.

The**Apprentice Difficulty Level** centers around the completion of a 5-row table of numerical data with two empty cells per row. Each row can be thought of as a separate problem. The circuit being analyzed is a simple, 1-resistor circuit. To complete the table, students must be able to use the ∆V=I•R equation and know that the current is everywhere the same in a simple circuit.

The**Master Difficulty Level** is noticeably more difficult than the **Aprrentice** level. It centers around the completion of a 5-row table with two to four empty cells per row and the analysis involves a 2-resistor, parallel circuit. To complete the table, students must be able to use the ∆V=I•R equation and be able to relate the current inside the branches to the current outside the branches.

The**Wizard Difficulty Level** centers around the completion of a 5-row table with three empty cells per row and the analysis involves a 3-resistor, parallel circuit. To complete the table, students must be able to use the ∆V=I•R equation and be able to relate the current inside the branches to the current outside the branches.

The

The

The

This Concept Builder was intended as an in-class activity. After some lab work, some discussion of how to analyze a parallel 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 levels would be most appropriate for their students.

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.

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.

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.

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Parallel Circuits Calculations Concept Builder. These include:

- Reading:

Most of Lessons 3 and 4 of the Electric Circuits Chapter of the Tutorial is a perfect accompaniment to this Concept Builder. The following pages will be particularly useful in the early stages of the learning cycle on Parallel Circuits:

Ohm's Law

Parallel Circuits

- 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 EC8 and EC10 of the Electric Circuits 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 Electric Circuits module can be found on Part 4 of the six-part App series. Visit Minds On Physics the App.

- The Calculator Pad: The Calculator Pad section of our website focuses on the use of mathematical formulas in solving Physics word problems. Each topic includes a set of 25 to 35 problems of varying difficulty level. All problems are accompanied by an audio file that describes how to go about the solution to the problem. Additionally, each problem has a link that hides and shows the answer and each problem set has a page devoted to a discussion of the fundamental formulas and their use.

Visit the Calculator Pad - Electric Circuits.

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

Electrical Resistance

Mathematical Relationships in Circuits

Visit the Curriculum Corner - Electric Circuits.

Additional resources and ideas for incorporating the Parallel Circuit Concept Builder into an instructional unit on Electric Circuits can be found at the Teacher Toolkits section of The Physics Classroom website. Visit Teacher Toolkits.