# Using Scientific Formulas

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## Objective

SWBAT use use scientific formulas and to understand how three data points can be used to determine acceleration, work, force, and power in watts.

#### Big Idea

How can we measure the energy of a wind turbine? This lesson helps students use mathmematical reasoning to calculate the power of a wind turbine by plugging data into science formulas.

## Preface

5 minutes

This lesson is intended to be used in the unit Designing for the Future: Wind Turbine. It can be modified to stand on its own but as is, it is supplementary.  Some of the science standards are implied from the entire lesson as opposed to standing alone in this lesson.  Thanks for understanding.

## Engage

5 minutes

My strategy for engaging the students is using a model of the wind turbine. I begin by asking questions about how we are going to design an investigation. I teach the parts of the wind turbine and I explain the testing procedure. I show a spool, cup, and the weights and ask, "What do you think we're going to do with these?" Students explain to me that we are going to lift the weight in the cup. I ask "Why?" "We want to see how much weight it lifts?" "Why?

The student are typically stumped at this point. I say, I'm going to show you how math makes our lives easier.

In the movie below I am introducing the presentation and working with a student who did not understand my directions. As I look at the video I realize that I should have directed the student to be aware of the units. He tried and I was rushed. Nonetheless, it shows how I teach students to "plug in" data.

## Explain

15 minutes

My next strategy is called Active Presentation. I have a power point presentation called Math and Science. I have embedded my higher level questions, some math problems, and science concepts into the presentation. I show the pages and the students will respond to the prompts on the page.

Students use scratch paper to complete the math.

The slides presentation is an overview of the science formulas used to determine watts. I explain to the students that there is a ladder of understanding in science and math makes it easier for scientists to climb the ladder.

The presentation begins with the research questions the students asked:

1. How fast does a wind turbine go?
2. How much force does a wind turbine need?
3. How much electricity can a wind turbine generate?

I explain there is a way to get all of these answers by plugging data into formulas. I begin with a review from math, I ask, "What is the following formula? D = r*t?" My students all know  Distance = rate x time.  I ask, "What is rate?"

I use a strategy called Fair Sharing. Groups of 4 students number themselves 1-4. I randomly pick a number and the person with that number stands up to share.

Using Fair Sharing the class determines that rate of change is represented in a slope.

I explain that when the concept is applied to how fast the wind turbine moves, I can use time and distance to determine speed. Velocity is speed in a given direction. By plugging velocity in the acceleration formula, and using a specific time, we can determine the acceleration of the blade. I demonstrate the initial and the final velocity of the cup using the wind turbine. A common misconception is the initial velocity. Student have a difficult time understanding that the cup is not moving so its velocity is 0 m/s.

With the acceleration, it is possible to use the number and plug it into the formula for force when we have a mass. I show my gram weights and say that we are measuring in grams. Force = mass x acceleration.

With force we can calculate work. I explain the formula, Work = Force x Distance. We are using the same distance used in our speed formula.

Once we have work, we can calculate power in watts. Work divided by time = power. I show the Work Done & Power Equation video to help reinforce the relationship between the scientific formulas and the mathematical calculations.

The video is 8 minutes long and it directs students to complete calculations. I stop it and make connections to the wind turbine. The movie shows the lifting of a book. I explain we are lifting the weights.

## Evaluate

10 minutes

After the presentation, I ask students to practice with an example on the Turbine Power Data Practice. My strategy is Practice First, Success Second. I explain this strategy is used in math.  If they practice first, their understanding of the math will help them succeed.

My intention is to integrate math and science. I ask, What three points of data do we need? Students respond, "Distance, time, and mass." I ask them to determine their own guesses for the wind turbine. Students plug in the data to practice the formulas and plug in the data to follow the ladder of math to get to the amount of electricity the wind turbine can generate. Check out the Turbine Power Data Practice.

In the movie below, my students is explaining how she used the formulas to determine the power.
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