Students apply the rules of voltage, current and resistance in series and parallel circuits in order to solve unknown variables in circuits.

In a series circuit, the current remains constant and voltage-drops add together and in a parallel circuit the current adds and voltage-drops are constant.

Repetition is the path to mastery. In this lesson, students solve for the unknown variables on over a dozen circuits much like they would solve a Sudoku. They have to fill in the missing values given some initial numbers and they apply what they have learned from past lessons: Ohm on the Range and Parallel and Series Circuits. Specifically, they use Ohm's Law and the rules of simple circuits: in a series circuit, the current remains constant and voltage-drops add together and in a parallel circuit the currents add together and voltage-drops are constant. They also apply Ohm's Law.

There are rules applied to the solution of series and parallel circuits, which is an applicaiton of Science Practice 2: Developing and using models. Students use given data to find the missing values which applies Science Practice 4: Analyzing and interpreting data, Science Practice 5: Using mathematics and computational thinking and Science Practice 7: Engaging in argument from evidence. Finally, they supply multiple representations of the circuit which uses Science Practice 8: Obtaining, evaluating, and communicating information. Since voltage is an electric potential due to electric fields, the performance standards HS-PS3-5: Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.

10 minutes

I start off the class with a simple Sudoku Challenge projected on the board (pictured right). This Sudoku is from Wikipedia.

I ask if someone can tell the rest of the class the rules of a Sudoku. Several students raise their hand and I call on one of them who gives the following rules:

- You can only use one number, 1-9, for each row
- You can only use one number, 1-9, for each column
- You can only use one number, for each box of nine squares.

We solve a few of the blank values in the Sudoku and I then display the solution.

Then I inform students that today, they are to solve a series of puzzles like the Sudoku where they have a few rules to apply, a few starting values and they must fill in the blanks.

I pass out the Circuit Sudoku Challenge packet. Every student gets a packet and they are to work on it on their own.

The beginning of the packet, the students are to write down the rules for series and parallel circuits.

Before we begin, write down the rules for a **series** circuit

- Rules for the voltage: ADD
- Rules for the current: SAME
- Rules for the resistance: ADD

Write down the rules for a **parallel** circuit

- Rules for the voltage: SAME
- Rules for the current: ADD
- Rules for the resistance: Use Ohm's Law.

I give the students 5 minutes to fill in the first and second page samples. Then I have students check their own understanding by displaying the solutions to Circuit Sudoku Page 1 Solution and Circuit Sudoku Page 2 Solution. If they have those right, then they continue on with challenge 1. While the rest of the students continue with the packet, I provide some 1-on-1 support for students who need help.

35 minutes

There are 17 circuits on the Circuit Sudoku Challenge packet and the difficulty level increases as the student progress through the packet. Students work alone on their packets as this activities purpose is to increase student mastery through practice. If students work together, I find that some students spend the time not engaged and then quickly copy the answers from other students. While students work, I walk around the room and monitor their progress. I also check to make sure students do their own work. I employ the Colored Cups method which allows me to quickly scan the room and see who needs help.

If I notice any students fall behind the rest of the class, I am sure to go to them often and give them additional support. Some students struggle with this kind of problem solving and I want to make sure they are able to keep up. To help the struggling student, I don't give answers. Rather I ask leading questions to help them over the hump where they might be stuck. For instance, if I scan their work and notice that they can't move forward until they add together the resistors in the series circuit, I would ask them "What do we know about the total resistance of a series circuit?" I point the way to the next step but require them to take it.

5 minutes

Though most students do not finish the packet, if they work diligently through the period they get close to the end. Students know that if they work hard on this packet, they have less to do for homework since they have to finish the packet for homework. Minimizing homework tends to motivate students.

For the students who are especially proficient at solving puzzles, they approach me with a completed packet. I have a few copies of the Circuit Sudoku Challenge - Solutions. I hand them a copy and tell them to check their work and make corrections with a different colored pen. This is a differentiation strategy as I don't have to disturb the rest of the class. The class can continue to work while the students who finish early check their own understanding. They hand in their packets to me when they are done so that there is no sharing of the solutions.

Class ends quietly as only a few students complete the packet and check their answers. I remind the rest of the students to finish it for homework.