TEAM Lesson Plan Template



|Light Bulbs Are Curvy! |

|Teacher: |Lauren Sanderson |

|Grade/Subject: |9-12/Algebra 2 |

|Course Unit: |Trigonometry |

|Lesson Title: |Applications of Cosine Curves |

|LESSON OVERVIEW |Summary of the task, challenge, investigation, career-related scenario, problem, or community link |

Students will have to read the assigned articles and video first to get an idea of what a power factor, watt, and the power grid is. Next, they will conduct an experiment of three different light bulbs to determine what their power factor is, the temperature, and the amount of watts being used. The students will have to learn how to use a device safely to record all of this. They will have to determine which lightbulb is the most effective for the power grid. Once the students have learned about the power factor, they should use their prior knowledge to graph a cosine function. They will learn from the experiment that the power factor will not always be one. There will be a discussion on how the graph will change. The relationship between the power factor and cosine graph should be discovered. The formula for the basic cosine graph and transformed cosine graphs should be discussed. The class will use their discoveries to discuss how this experiment would change in a real-world situation. Students will write a letter to their parents explaining which light bulb they should be using throughout their house. After the experiment, discussion, and letter, students will use a simulator for sine and cosine curves to see if the skateboarder has enough speed to get over the curve. Next, students will research how electrical engineers determine what voltage they need to put on the power grid and what could affect the power factor from not being close to one.

Students will then write a discussion board post detailing what they have learned about the power grid, the power factor, cosine equations, cosine graphs, and applications within real-world situations.

|STANDARDS |Identify what you want to teach. Reference State, Common Core, ACT College Readiness Standards and/or State |

| |Competencies. |

F-TF Functions-Trigonometric Functions

A. Extend the domain of trigonometric functions using the unit circle.

B. Interpret functions that arise in applications in terms of the context.

F-IF.B.4.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

C. Analyze functions using different representations

F-IF.C.7.e

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-BF Functions-Building Functions

B. Build a new functions from existing functions

F-BF.B.3.

Identify the effect on the graph of replacing [pic] for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

|OBJECTIVE |Clear, Specific, and Measurable – NOT ACTIVITIES |

| |Student-friendly |

Students will be able to accurately measure the temperature, watts being used, and power factor for all three light bulbs.

Students will interpret data from their findings in the experiment.

Students will make predictions about how each light will affect the power grid.

Students will make a connection between the cosine graph and graphing the power factor.

Students will research applications for the power factor in Knoxville, TN.

|INTRODUCTION |Should Include: Any prior knowledge that the students need to complete the lesson, approximately how long |

| |the lesson is predicted to take (Ex. 1 Day or 2 Days), and a short summary of the entire lesson plan. |

The students will have to know how to graph a cosine function, create a cosine equation, analyze periods and amplitudes, and determine the cycle pattern. This extension to the lesson on cosine curves should take approximately one day. However, the assigned online articles need to be read prior to the experiment, and the extensions should go into the next day after the experiment.

|MATERIALS LIST |A bullet list of materials. |

| |The materials need to be specific and include quantities |

• Computer (one per group) to watch the video, read the articles, and use the simulator

• Experiment data collection sheet (one per group)

• Infrared thermometer (one per group)

• Kill A Watt meter (one per group)

• LED light bulb (one per group)

• Incandescent light bulb (one per group)

• Compact flourescent light bulb (one per group)

• Three Lamps (per group)

• Pencil (one per group)

• Paper (two or three sheets per group)

[pic]

Figure 1: Infrared Thermometer image taken from



[pic]

Figrure 2: Kill-a-Watt image taken from wjuxd37zJvNAhXQdSYKHV9XBlIQ_AUICCgD&safe=active&ssui=on#imgrc=sdaT1bxKlq4J5M%3A

[pic]

Figure 3: Incandescent light bulb image taken from

[pic]

Figure 4: LED light bulbs taken from



[pic]

Figure 5: Compact fluorescent light bulb image taken from

|RESOURCES |Should Include: A bullet list of any links to videos, names of worksheets, names of projects, names of |

| |PowerPoints, links to online articles, links to interactive websites, names of reading materials, etc (All |

| |worksheets, PowerPoints, projects, and reading materials should be attached to the back of the lesson plan).|

| | |

| |Specify whether they will be used before, during, or after the lesson. |

Video (watch before the experiment):

How Modern Light Bulbs Work



Online Articles (read before the experiment):

Electric Power



Energy Sources



Lighting Choices That Will Save You Money



Quizzes (take before and after the experiment):

What Do You Know About Energy, Work, Power, and Simple Machines?



What do you know about Power Concepts?



Document (read before the experiment):

Understanding Power Factor and How it Affects Your Electric Bill



Power Point (read over before the experiment):

Power Grid Design



Extensions (after the experiment):

[pic]

Figure 6: Simulation of creating curves. Image taken from



Power Grid



Power Factor



Multimeter



Kill-A-Watt



|ACTIVATING STRATEGY |Motivator / Hook |

| |An Essential Question encourages students to put forth more effort when faced with complex, open-ended, |

| |challenging, meaningful and authentic questions. |

Would you like to know how efficiently you are using the power grid? We can do an experiment to test all of this out. You will determine which light bulb is the most efficient for the power grid. You will also be able to determine which light bulb is the cheapest for the consumer. Then, you will write a letter to your parents explaining which light bulb they should be using for their house. Finally, you will use a simulator to create a skateboard ramp out of sine and cosine curves. You will see if the skateboarder can get over the curves with enough velocity.

|INSTRUCTION |Step-By-Step Procedures – Sequence |

| |Discover / Explain – Direct Instruction |

| |Modeling Expectations – “I Do” |

| |Questioning / Encourages Higher Order Thinking |

| |Grouping Strategies |

| |Differentiated Instructional Strategies to Provide Intervention & Extension |

Teacher— First, the teacher will divide up the class into groups of 3-5 students. These are the groups that will work together for the experiment. Each student in the group should have a role (such as recorder who will document the data, data analyzer who will read the Kill A Watt meter and infrared thermometer, an engineer who will be in charge of setup, correspondent who will record data from other groups, etc.). The teacher should assign students the required reading the day before the experiment.

On the day of the experiment before students arrive, the teacher will setup the room so that there is a table for each group. On each table, place the three lights, an infrared thermometer, a Kill A Watt meter, and the three lamps. Once students arrive, discuss their reading materials from the day before. Go over introductory presentation. Then review classroom expectations and safety procedures for the experiment, modeling for students what to do. Be sure to go over setup of infrared thermometer, lights, and the Kill A Watt meter. Share with the students their assigned groups, roles, and stations.

Students— Once in groups at their workstation, students should begin working by following the directions found below:

1. Make a prediction for which light bulb will be the most efficient for the power grid and which light bulb will be the cheapest for the consumer.

2. Turn on the lamps.

3. Turn on the infrared thermometer and point it at the light bulb. Record the temperature from each light.

4. Plug the cord from each lamp into the Kill A Watt meter and record the power factor and how many watts are being used.

5. If time permits, explore what happens when you plug in your laptop and change the brightness. Try your cell phone.

Teacher—While students are working, circulate and assist as needed. Carefully monitor students to ensure that students are adhering to safety procedures. Once students have completed the activity, have them return to their seats for discussion. Discuss with students which light bulb is the most efficient for the power grid. Discuss how an electric bill would be adjusted based on the power factor being used and how it could affect long term things in the real world. Then, talk about how you could graph the relationship between the power factor matching up with the power grid and when it might not be. Have students write a letter to their parents explaining which light bulbs they should be using throughout their house. Next, have the students use the simulator to create a skateboarding ramp out of sine and cosine waves. Finally, have the students research how electrical engineers determine what voltage to use for the power grid at certain times of the day. If time permits, students may begin research in class. The teacher will open the discussion board for students to post for homework.

Students—Students will write a letter to their parents explaining which light bulbs they should be using throughout their house. Students will use the simulator on the computer to create a skateboarding ramp out of sine and cosine waves. They will try to have the skateboard go over as many waves as possible. Students will write a discussion board post detailing what they have learned about power factor affecting the power grid.

|GUIDED & INDEPENDENT PRACTICE |“We Do” – “ You Do” |

| |Encourage Higher Order Thinking & Problem Solving |

| |Relevance |

| |Differentiated Strategies for Practice to Provide Intervention & Extension |

Would you like to know how efficiently you are using the power grid? First, you might need to know that power is equal to current multiplied by the voltage. In order to calculate the power factor, you will just take the difference between the waves of the voltage and the waves of the current. When the power factor (PF) is very close to one, you are using the power grid most efficiently and you will be charged all of that real power on your electric bill. The farther away the power factor is from one, the less efficient the power grid is. To calculate the total power used, we will add the real power with the reactive power. When there is a resistor with the alternating current (AC), the power factor is very close to one. The power factor will stay constant when there is a good resistor. This would be represented by a cosine graph. The graph of the current will stay in alignment with the voltage when we have a resistor.

[pic]

When there is not a resistor acting with a current, you might have an inductor. The inductor would cause the graph to be shifted to the left due to magnetic field. This causes a misalignment of the two waves which causes our power factor to be less than one. This could look something like the graph below. The blue line represents our voltage and the red line represents the current that has an inductor.

[pic]

When there is a capacitor reacting with a current, the current will shift to the right. It will look similar to the graph below. The blue line represents the voltage. The red line represents the current with the capacitor.

[pic]

Sometimes, you could have an inductor and a capacitor interacting with the same current. When this happens, it shifts the graph to the left and then to the right. Therefore, the graph will be right back where it needs to be, so we would almost think that it could be a resistor and the current will stay in alignment with the voltage.

Let’s put some math behind this. We are starting off with the standard formula for a cosine curve, which is y = a cos b(x). The a value will represent our amplitude, which is how high or low the graph will go from zero. Another way to calculate amplitude is to subtract the minimum from the maximum, and then divide by two. The b variable will help us find the period. The period is the length of one cycle. To calculate the period for a cosine function, we will have to set the period equal to two times pi divided by b. You will have to cross multiply to determine what b is equal to.

When we have an inductor or capacitor, the graph will be shifted to the right or to the left. The standard formula for a transformed cosine function would be y = a cos b(x – h) + k. If the h value is positive, the graph will be shifted to the right. If the h value is negative, the graph will be shifted to the left. If the k value is positive, the graph will be shifted up. If the k value is negative, the graph will be shifted down.

We can do an experiment to test all of this out. Let’s start with three different kinds of light bulbs. We will use an incandescent, compact florescent, and LED light bulb. Determine the power factor, the temperature, and the amount of watts being used for each light bulb. What can you conclude about this? Which light is the most efficient for the power grid? Which light will be the cheapest for the consumer?

|CLOSURE |Reflection / Wrap-Up |

| |Summarizing, Reminding, Reflecting, Restating, Connecting |

There will be a discussion on how the cosine graph changes when there is a resistor, inductor, or capacitor acting with the AC. The relationship between the power factor and cosine graph should be discovered. The formula for the basic cosine graph and transformed cosine graphs should be discussed. The class will use their discoveries to discuss how this experiment would change in a real-world situation. For example, how someone’s electric bill will be affected based on the real or reactive power. Students will write a letter to their parents explaining which light bulb they should be using throughout their house. After the experiment, discussion, and letter, students will use a simulator for sine or cosine curves and see if the skateboarder has enough speed to get over the curves. Next, students will research how electrical engineers determine what voltage they need to put on the power grid and what could affect the power factor from not being close to one. Students will then write a discussion board post detailing what they have learned about the power grid, the power factor, cosine equations, cosine graphs, and applications within real-world situations.

Discussion Board Prompt:

How do electrical engineers determine what voltage they need to put on the power grid and what could affect the power factor from not being close to one? Explain in detail what you have learned about the power grid, the power factor, cosine equations, cosine graphs, and applications within real-world situations. (Your answer to this prompt should 2-3 paragraphs in length and you should address all questions.)

|CROSS-CURRICULAR CONNECTIONS |

There is cross-curricular connection between Science and Mathematics. We are using Science to determine temperatures, watts being used, and power factors. We are using Mathematics to determine the graph of voltage and current being transmitted.

|ASSESSMENT / |Students show evidence of proficiency through a variety of assessments. Aligned with the Lesson Objective |

|EVALUATION |Formative / Summative |

| |Performance-Based / Rubric |

| |Formal / Informal |

To assess the quality of student knowledge gained from this experiment, look at the data collected from each group, the letter to their parents, and the discussion posts of each individual student. Teachers might also want to hold students accountable for their discussion in class. This is a way to quickly determine the effectiveness of the experiment and clarify any misunderstandings. The discussion post should be the majority of the grade for this experiment since it is the culmination of all parts of the project.

|CITATIONS |Any websites that were used to gather information. |





























|NOTES: |Purchasing information for non-typical items |

| |Tips & Tricks that may help |

This is a data collection chart that will be helpful for the experiment.

Name(s):

|Experimental Data Collection Chart |

|Light Bulbs |Temperature |Watts |Power Factor |

|Incandescent | | | |

|Compact Fluorescent | | | |

|LED | | | |

Answers to experiment:

Start with three different kinds of light bulbs. Use an incandescent, compact florescent, and LED light bulb. For our Incandescent light bulb, the power factor is right at .99, the temperature is 170 degrees, and the watts being used is 70. The Compact Florescent light bulb had a power factor close to .55, temperature around 73 degrees, and used 22 watts. The LED light bulb has a power factor of 0.853, temperature around 73 degrees, and used 16 watts. In conclusion, the LED light should be the most efficient for the power grid since the power factor is close to one and not as many watts are being used. The cheapest light for consumers would be the compact fluorescent light because you are only using about half of the real power, which is what the utility companies charge you for and it only uses 22 watts.

Cost of Materials Needed:

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LED light bulb

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Incandescent Light Bulb:

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Compact Fluorescent Light Bulb:

[pic]

Lamp for the light bulbs:

[pic]

Kill A Watt:

[pic]

Temperature Gage:



Total Cost of Project: $48.72

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