TEAM Lesson Plan Template



|Keep it Frequent! |

|Teacher: |Lauren Sanderson |

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

|Course Unit: |Trigonometry |

|Lesson Title: |Applications for the Sine Curve |

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

Students will understand that there has to be exactly enough power on the grid for what is being used by consumers after watching the assigned videos and reading the assigned articles. Students will use their knowledge of how to recognize and construct sine functions to determine how frequency, amplitude, and DC offset will change what a light bulb does. They will conduct an experiment that will show the effects on two different light bulbs. The class will use their discoveries to discuss how this experiment relates to the sine function and real-life situations. They should address how our world would be affected if we had a power outage. Then, using the oscilloscope, students will see the exact sine curve that the voltage makes. After the experiment, students will research how electrical engineers use trigonometry every day. They will also use a simulator for trig functions on a graph and the unit circle. They will analyze what contributions relate to changing the efficiency of the light bulb and how it could affect the power grid. They should make the connection that if our sine waves do not stay constant on the FNET, we could have a power outage. Students will then write a discussion board post detailing what they have learned about electricity, the power grid, light bulbs, and the relevancy to trigonometry.

|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.

F-TF.A.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around 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.

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

| |Student-friendly |

Students will be able to accurately place cords and lightbulbs in the correct positions.

Students will adjust the function generator to see changes in the lightbulb.

Students will interpret data from the function generator and oscilloscope.

Students will make predictions about how adjusting the frequency, amplitude, or DC offset, changes the way the lightbulb appears.

Students will interpret how changing the lightbulb could be represented with trigonometry.

Students will research applications for the effects of frequency and amplitude on the power grid.

|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. |

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Figure 1: Image taken from

From the assigned reading and videos, students should have a grasp on the concept that there has to be exactly enough power supplied on the grid for what is being used by consumers. If there is not enough power, we will have an outage. If there is too much power, we are wasting power because power cannot be stored. Students should have prior knowledge on how to construct a sine curve, how to create a sine equation, analyze amplitudes and periods, and determine the cycle pattern. This extension to the lesson on sine 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. They will conduct an experiment that will show the effects on two different light bulbs. The class will use their discoveries to discuss how this experiment relates to the sine function. Then, the students will assess the oscilloscope on the computer to see that actual graph for the function, which is a sine curve.

|MATERIALS LIST |A bullet list of materials. |

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

• NI myDAQ equipment (one per group)

• computer (one per group)

• download NI ELVISmx Instrument Launcher (should be done by the teacher prior to the experiment)

• breadboard (one per group)

• two LED lights (per group)

• pencil (one per student)

• paper (two or three sheets per group)

• calculator (one per group)

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Figure 2: myDAQ image taken from tbm=isch&sa=X&ved=0ahUKEwi52KzIiZvNAhUHYyYKHXeQD8cQ_AUIBygC&safe=active& ssui=on#imgrc=ipa5ddFPidxqcM%3A

|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. |

Videos (watch before the experiment):

Get Started Using NI myDAQ with LabVIEW for Education



AC vs DC Explained and How to Use an Oscilloscope



Online Articles (read before the experiment):

Oscilloscope



How to Use a Function Generator



Breadboards



Quizzes (take before and after the experiment):

Sine and Cosine Graphs



Sine and Cosine Graphs



Document (read before the experiment):

Frequency, Wavelength, and Amplitude



Power Point (go through before the experiment):

AC/DC electricity



Extensions (after the experiment):

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Figure 3: Simulator for Trig Functions. Image taken from



Power Grid



Peak-to-peak Voltage



Frequency



Amplitude



|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. |

Have you ever heard of a blackout? Do you know what causes a blackout? Look at the graph below.

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Figure 4: Image taken from

A blackout occurred in Florida on February 26, 2008 a little after 6pm when everyone got home from work. What do you think is significant about 6pm? When are most Americans home and cooking? What does the chart to the left resemble? When is knowing how to graph a sine curve useful? Did you know that light bulbs involve using sine waves? We will do an experiment where we can adjust how bright we see the light bulb, how often it blinks, and when we cannot see the light at all.

|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, you will need to install the NI ELVISmx Instrument Launcher on your computer.

Next, select Function Generator. Place a NI myDAQ, breadboard, and two LED lights

at each computer. Next, have your students in groups of two. One student will be the experimenter on the computer and the other student will be recording the data

for what happened. Below is an example of the Function Generator. You will see

how you can change the frequency, amplitude, and the DC Offset.

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Figure 5: Image taken from

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Figure 6: Function Generator image taken from launcher&imgrc=QhZ8-lPEXZMxuM%3A

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Figure 7: Breadboard Diagram image take from



Students - Once in groups of two at their computer, students should begin

working by following the directions found below:

1. On the breadboard, plug in the red cord to the second hole from the top left.

Plug in the black cord to the first hole on the top left.

2. Take an LED light and put it in the fifth hole down from the left side,

to the first and second hole.

3. Once you have all of those securely fastened, on your computer, change the DC offset to 2.1 V (Volts), have the AC Voltage Amplitude at 0 Vpp (peak-to-peak Voltage), and the frequency at 100 Hz (Hertz).

4. Adjust the DC Offset to different positive and negative voltages. Record in the chart what you notice.

5. Select “Stop” and change the DC offset to 0 V. Keep the frequency at 100 Hz. Change the amplitude to no more than 5 Vpp. Record in the chart what you see.

6. Change the frequency between 1 - 10 Hz, the amplitude between 3.2 – 10 Vpp, and leave the DC offset at 0 V. What do you notice? Write it down.

7. Adjust the frequency between 10 - 30 Hz. What do you notice? Write it down.

8. Take the second LED light and put it 10 holes down on the left hand side.

Make sure the frequency is between 1-10 Hz. What happens?

9. Adjust the frequency between 10 – 30 Hz. What happens?

Teacher - While students are working, circulate and assist as needed. Carefully monitor students to ensure that students are adhering to safety procedures. Ask the students questions about what they are doing and what they observe. Once students have completed the activity, have them return to their seats for discussion. Discuss with students how this controlled experiment would affect the power grid. Ask them if they could possibly make a sine graph out of what they have observed. On the board, get them started and then see if they can lead you through the process. Next, ask them to come up with a formula for what they drew or what they have observed. Analyze how changing the a value and b value affects the graph. Now, have the students access the oscilloscope on the computer. They should remove one of the light bulbs and then adjust the frequency, DC offset, and amplitude to see how the sine curve changes. Discuss how accurate the graphs are that you drew in class compared to the ones on the oscilloscope.

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Figure 8: image take from:

Have students use the online simulator for trig functions on the unit circle. Then, have the students research how electrical engineers determine what frequency and amplitude is needed to make use of the power grid most efficiently. 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 use the simulator online to adjust the sine function on the graph or the unit circle. Then, students will write a discussion board post detailing what they observed during the experiment, how it relates to math, what could happen during a power outage, and what could have caused the power outage.

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

| |Encourage Higher Order Thinking & Problem Solving |

| |Relevance |

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

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The frequency always need to stay at 60 Hertz on the grid and the amplitude needs to be at 120 Volts. The FNET map will constantly change based on the Hertz that is being produced. FNET/GridEye measures the frequency, phase angle, and voltage of the power system. If you look at the image to the right, you will see that the Grid did not stay at 60 Hz, so it caused a blackout in Florida. Have you ever experienced a power outage?

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Next, change the frequency to 1-10 Hz, the amplitude between 3.2 – 10 Vpp, and leave the DC offset at 0 V. What do you notice? Now adjust the frequency between 10 - 35 Hz. What do you notice?

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When the voltage is between 1.6 and 3.4 or -1.6 and -3.4, we can actually see the light. So there is a gap between -1.6 to 1.6 V where you cannot see light.

You could represent the area where you cannot see the light by using asymptotes. One asymptote would be y = 1.6 (illustrated on the graph above in red) and the other one would be y = -1.6 (illustrated on the graph above in green). The area in between the two asymptotes where no light is visible would be -1.6 ( y ( 1.6.

Let’s talk about what our formula could possibly be. The standard formula for a sine curve is y = a sin bx. When you adjust the voltage under “DC offset”, you are adjusting the a value in the standard formula for sine. When you adjust the frequency, you are adjusting the period which changes the b value in the formula.

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|CLOSURE |Reflection / Wrap-Up |

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

After the experiment, students will research how electrical engineers use trigonometry every day. They will analyze what contributions relate to changing the efficiency of the lightbulb and how it could affect the power grid. Students will then write a discussion board post detailing what they have learned about electricity, light bulbs, and the relevancy to trigonometry.

Discussion Board Prompt:

How do electrical engineers use trigonometry every day? Analyze what contributions relate to changing the efficiency of the lightbulb and how it could affect the power grid. What could cause a power outage or blackout? Explain what you have learned about electricity, the power grid, light bulbs, and the relevancy to trigonometry.

|CROSS-CURRICULAR CONNECTIONS |

Mathematics is integrated into Science. There is Science behind making a light bulb come on, adjusting the brightness, and how often it blinks. There is Math that shows how the voltage of the light bulb increases and decreases. There is also Math behind the frequency of the blinking and the brightness of the light bulb. There is Science behind the FNET/GridEye and keeping the frequency at 60 Hertz and the amplitude at 120 Volts. There is Math behind the phase angle which helps us calculate the power factor and determines the difference in the voltage and current.

|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 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 will be a very useful data collection chart for the experiment.

Name:

|DC Offset

(Volts) |Amplitude

(Vpp) |Frequency

(Hz) |One LED light |Two LED lights |What happens? | |Trial 1

| | | | | | | |Trial 2

| | | | | | | |Trial 3

| | | | | | | |Trial 4

| | | | | | | |Comments

| | | | | | | |

Materials:

• 1 myDAQ - $179, Studica

• NI Elvis Software and Instrument Launcher – Free, National Instruments

• 2-4 Male Jumper Wires - $7 Jameco

• 1 Small Breadboard - $6, Jameco

• 2 Red Transparent Plastic LED - $0.15 Newark

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Once you have all of those securely fastened, on your computer, select “Function Generator” on your computer. Change the DC offset to 2.1 V (Volts), have the amplitude at 0 Vpp (Voltage from peak-to-peak), and the frequency at 100 Hz (Hertz). Start adjusting the DC offset up and down. What do you notice? Now, change the DC offset to 0 V. Change the amplitude to 3.2 Vpp. Keep the frequency at 100 Hz. What do you notice?

We need to keep things frequent, so we will do an experiment where you can adjust the amplitude and frequency of a light bulb and see what happens. This would be similar to the grid providing power to your house.

You will use the NI myDAQ, a breadboard, and two LED lights. On the breadboard, plug in the red cord to the second hole from the top left. Plug in the black cord to the first hole on the top left. Next, take an LED light and put it in the fifth hole down from the left side, to the first and second hole.

Finally, take another LED light and put it 10 holes down on the left hand side. Make sure the frequency is between 1-10 Hz. What happens? Is there ever a time where none of the lights are blinking? What happens between 11-30 Hz?

Now, let’s relate it to a graph. We will need to recall a normal sine curve.

Next, let’s look at a sine curve that uses our voltage and frequency. The voltage is represented along the y-axis and time is represented along the x-axis.

Finally, on the computer, click oscilloscope. You will be able to observe the voltage and time being used by the light bulbs. The graph will change when you adjust the amplitude and frequency. Does the graph look familiar? Write down observations you can make from the oscilloscope.

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