Knowing how to rearrange an equation can help students in determining how much interest they need to earn in order to meet their monetary goal. These skills are used in evaluating electrical circuits (e.g., how much resistance is need in a circuit) and in cost analysis as part of engineering design.

C - Engineers and electricians use Ohm’s law to identify how many volts they will have and in return how much power will be supplied or needed.

S - By creating an illuminated safety device for students, this will potentially keep a lot of students (and by extension others involved in low light activities) safer. Students can expand on their experience and create/develop other ways to keep students safe.

**Engineering Design Process (EDP)**

Challenge – Create an illuminated safety signal that lights up and can be seen from 20 feet away.

Research – Complete web quests to collect data on how light is measured and how it can be increased/decreased.

Brainstorm and Essential Questions – Look at how different locations of the lights affects brightness and how Ohm’s law can rationale their findings.

Build and test for stability – Test their design using a light sensor from Vernier.

Redesign – Improve upon the initial design, perhaps rearranging their light placements or increasing the voltage for their lights.

Final Conclusion – Videotape their findings and be able to explain what they discovered.

##### Unit Academic Standard

HAS-CED.A.4 – Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

##### Unit Activities

**Day 1 (Pretest and Hook/Lesson 1, Activity 1)**

- Give students the pretest (Lesson 1, Activity 0)
- After the student’s finish the pretest, pass out the batteries, paper clips and LED lights for the hook. As students put their lights together, have them record what they noticed with their lights. Would they consider their light to be bright? Was it brighter than the student’s around them? Whether it was brighter or dimmer, why do you think that is so?

**Day 2 (Lesson 1, Activity 1)**

- Talk about the hook from yesterday. What all did they see? Did they notice anything relating all of the items (aka variables)? What happened if the paper clip was bigger? Did the color of the light matter?
- After the hook has been discussed, introduce the idea of rearranging equations.
- Use the following link to use as notes for the students. http://serc.carleton.edu/mathyouneed/equations/index.html
- You can use the practice problems on that link as well to double check if students understand the concept of rearranging equations.
- Give students the homework (Lesson 1, Activity 1, Worksheet A)

**Day 3 (Lesson 1, Activity 2)**

- Have the student’s “trade and grade” the homework from the previous night.
- Next, you are going to play a review game called “Grudge Ball” to engage students in rearranging equations. Use the link below as the template to use for the game. The game instructions and directions can be found in Lesson 1, Activity 2.
- http://exchange.smarttech.com/details.html?id=b0ae5dda-9c80-4d0a-9fcc-05254d82b146

**Day 4 (Lesson 2, Activity 1)**

- Now it is time to introduce ohm’s law. Instead of writing the equation I = V/R on the board, present them with a few examples of data and see if the students can derive the equation.
- Present that if there is a current of 162, and the resistance is 9, then the voltage must be 1458.
- Present that if the voltage is 203 and the current is 29, than the resistance must be 7.
- Present that if the resistance is 11, and the voltage is 121, than the current is 11.
- By now, the students should be able to derive the equation I = V/R. If they cannot, keep providing examples.
- Since Ohm’s law is now discovered, pass out the Ohm’s Law Worksheet (Lesson 2, Activity 1, Worksheet B) and let them work in pairs. As pairs finish the worksheet, have them join another pair and check their answers.

**Day 5 (Lesson 2, Activity 2)**

- Present the challenge of creating an illuminated safety signal that can be seen from at least 20 feet away.
- Put students in groups of 4 and have them develop the guiding questions. Give them 10 minutes and then discuss as a class.
- As guiding questions are presented, you may choose to answer them at that time or once all of the questions are presented.
- After guiding questions are established, students are to begin designing and draw their ideas of an illuminated safety signal. There will be no actual building today.

**Day 6 (Lesson 2, Activity 2)**

- Students will continue designing and drawing their ideas.
- Once students have created a design and got it approved by the teacher, they may begin building their initial design of their illuminated safety device.

**Day 7 (Lesson 2, Activity 2)**

- Students will continue building the initial design of their illuminated safety device. Must be completed by the end of the day because tomorrow will be a test day for their device.

**Day 8 (Lesson 2, Activity 2)**

- Test their initial design using the light sensor from Vernier http://www.vernier.com/products/sensors/ls-bta/?search=light&category=autosuggest
- After their initial design is tested, they will redesign it to improve their illuminated safety device.

**Day 9 (Lesson 2, Activity 2)**

- Students will continue redesigning their illuminated safety signal.
- Remind them that today is their last full day of class to complete it.

**Day 10 (Lesson 2, Activity 2 and Presentation)**

- If not finished, give students 20 minutes maximum to finish their redesign.
- Students will present their final design they created. They will explain their engineering design process and how they created their illuminated safety signal.
- Use the following rubrics (Lesson 2, Activity 2, Worksheet C) and (Lesson 2, Activity 2, Worksheet D) to grade their final product and their group.

##### Where the CBL and EDP appear in the Unit

CBL - (Lesson 2, Activity 1)

EDP - (Lesson 2, Activity 1)

##### Misconceptions

The biggest misconceptions when rearranging equations is not dividing or multiplying the entire sides of an equation.

##### Additional Resources

##### Pre-Unit Assessment Instrument

Students will take the pre-test which is Lesson 1, Activity 0.

##### Post-Unit Assessment Instrument

To compare results and to see growth, students again will take the test from Lesson 1, Activity 0.

##### How to Make This a Hierarchical Unit

In order to make this a middle school unit, I would use this when just starting to have students rearrange equations. I would not use Ohm’s law, but just have students learn how to solve for x or y in an equation. Since you would not be using Ohm’s law, I would recommend not having student design illuminated safety signals with light bulbs. What I would do though is create homemade glow sticks. This can be accomplished with baking soda, peroxide and mountain dew. Students could solve single variable equations on how when one element is added, how that affects the brightness of their glow stick.