Students will be able to create simple mathematical representations of waves and identify characteristic properties of waves.

Students go through a series of hands-on lab stations that engage students in not only identifying the properties of waves, but in creating mathematical representations as well!

This lesson is Day 1 of a 2 day lesson designed to provide students the opportunity to travel through a series of lab stations that connect to the following NGSS and Common Core Standards:

**MS-PS4-1** Use mathematical representation to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.

**MS-PS-4-2** Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.

**CCSS.ELA Reading: Science & Technical Subjects **Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

**CCSS.Math Mathematical Practice 4** Model with mathematics.

At this point, students have had multiple experiences engaging with each of these standards in previous lessons. They have created models representing energy and amplitude and have explored the relationship between frequency, wavelength, and pitch using slinkies. Moreover, they have created models of transmission, absorption, and reflection. This series of lab stations is therefore an extremely independent activity for students providing them with more interactions with the standards. Therefore, it is also a good place to focus on students that have not been demonstrating mastery and help them make connections that they have not yet previously made.

In this lab rotation, students continue to create models that explain phenomena (**SP2**). In addition, students utilize the **Crosscutting Concept** of **Patterns**, using graphs to identify patterns and relationships between variables such as frequency and wavelength.

However, one new aspect that we begin to discuss is the mathematical representation of what a wave looks like **(MP4)**. On the first day, students are introduced to the idea of how a wave can be graphed in a coordinate plane on a Displacement vs. Time/Distance plot. In this lab, students have to create graphs that demonstrate general relationships of both transverse and longitudinal waves in order to develop their mathematical and conceptual thinking (**SP5**). On the second day of instruction, students are introduced to graphing a wave based on specific numbers instead of general relationships and begin manipulating the graphs of waves to demonstrate a proportional understanding of wave relationships.

5 minutes

Have students turn to the Unit Plan in their binder. Ask students, “*What are you going to be learning today?*”. At this point in the year, my students immediately (or should!) refer to the Essential Question that is written on the board and in their Unit Plan. The EQ I use comes from the NGSS. Students reply, “*What are the characteristic properties of waves and how can they be used?*”

Next, I explain that over the course of the next days, we will be focusing on the EQ in two important ways - written as Skill 1 and Skill 5 on the Unit Plan. Ask the students to take a moment and read the “I can...” statements for Skills 1 and 5 and identify the new key ideas that they should be connecting to. Students may share things such as “*different types of waves*”, “*different types of matter*”, “*waves interacting with matter differently*”, and “*real world examples*”.

In previous lessons, students should have already ranked themselves on a scale of 1 to 4 (4 being mastery) on each of the learning targets/”I Can” statements. One of the purposes in checking in on the EQ and Skills daily is for students to self assess their learning. I ask the students to re-assess themselves on each of these learning targets, changing the number if they feel their level of understanding has changed since the last self-reflection.

15 minutes

Provide students with the Waves Light Bulb Sheet as well as the “*How Do Satellites Work?*” excerpt. Ask the students to read the article with the purpose of underlining, highlighting, or circling words or phrases that connect to the EQ. So, as students read, they should be marking up their papers identifying properties of waves and wave behavior that they know of as well as ways that waves can be used.

After providing time to read, students share the connections that they made. Students may offer that they saw that the properties of amplitude, frequency, transmission, and reflection were all mentioned in the way that satellites work. They will also note that satellites are a great example of how waves are used in the world. This conversation should be so much more than simply listing these things, however.

Citing evidence is a critical skill for scientific literacy (**SP7**). Students need to have the ability to find information in a text when given a purpose and actually show where that information is in the text (**SP8**). It always amazes me how students take what a text says and create their own interpretation of what the text actually says. Thus, it is important as students share their examples that you ask them to show exactly where they found that information in the text. The conversation may unfold like this:

Teacher: *What connections were you able to make to the EQ? What were some properties of waves and uses of waves you can cite from the text? *

Student: In the first paragraph, 2^{nd} line, it states, “a signal is reflected, or "bounced," off the satellite”. Reflection is one way that waves often behave.

Teacher*: I noticed that you cited the exact place in the text where you found the information by giving the paragraph and line he found it in. Even more than that, I noticed a few other students take their finger and go to that place on the text when he/she said that. Both of these actions are strategies that students successful at interacting with text might do. As the next students share their examples, see if you can utilize these strategies yourself.*

Or, it may unfold like this.

Teacher: *What connections were you able to make to the EQ? What were some properties of waves and uses of waves you can cite from the text?*

Student: It says reflection.

Teacher: *You have made a great connection to the essential question. Reflection is a characteristic way that waves interact with matter. As a scientist, your arguments become more credible when you can actually cite where you got your information from. Readers and listeners will be able to trust your arguments more if you can let them know which and where in the science text you used. Could you tell us where you noticed the word "reflection" in the text?*

Student*: * In the first paragraph, 2^{nd} line, it states, “a signal is reflected, or "bounced," off the satellite”. Reflection is one way that waves often behave.

Teacher: *I noticed that you cited the exact place in the text where you found the information by giving the paragraph and line he found it in. Even more, I noticed a few other students take their finger and go to that place on the text when he/she said that. Both of these actions are strategies that students successful at interacting with text might do. As the next students share their examples, see if you can utilize these strategies yourself.*

Without asking the students to share where it is in the text, students will actually frequently offer information that was not actually stated in the text. Students often share their inferences or interpretations of what the author was saying rather than actually citing what the author said. It is important for students to distinguish the difference between citing a text and creating an opinion or inference based on prior knowledge combined with the information in the text. A conversation from a student stating an inference as opposed to a citation could unfold in this way:

Teacher: *What connections were you able to make to the EQ? What were some properties of waves and uses of waves you can cite from the text? *

Student*: *The article states that satellites use absorption. Waves being absorbed by matter is a common way that waves behave.

Teacher: *As a scientist, your arguments become more credible when you can actually cite where you got your information from. Readers and listeners will be able to trust your arguments more if you can let them know which and where in the science text you used. Could you tell us where you noticed the word absorption in the text?*

Student: Oops. I guess it doesn’t.

Teacher: *As a scientist, you have a responsibility to make inferences and connections outside of the text. It is your job as a reader to make these connections. However, be careful not to disguise your own ideas as the ideas of the author in the text. If the author does not say the word absorption, you cannot say that he/she did. However, you could cite the sentence that made you make that connection. For example, you could say, “The statement in paragraph ___, line ____ that said ______________ made me think that a wave was being absorbed because I know that ______________________________.”*

Direct the students’ attention to the light bulb page and ask them to add any examples from the text that they just read, to the light bulb. Ask them to notice that one side of the light bulb is focusing on the similarities and differences on how waves interact with matter and the other is focusing on the uses of waves in the real world. For this first day, they may only write on the light bulb page that organizes how waves are used in the world as they add satellites. Let students know that they will be adding to this each day over the next two weeks and that it is not the intent that they have the light bulbs completely filled in right now. The idea is that they add their ideas as they make connections over the next weeks.

15 minutes

Provide students with the Behavior of Waves Lab document. Let them know that while you are going to explain each lab station that there are Behavior of Waves Lab Directions. Let the students know that your verbal directions are not meant to replace following a procedure. One of the most important jobs of scientists is to follow procedures so that they can produce reliable data!

**Station 1: Slinkies**

**Materials: **

3 - 4 Slinkies

**Description for students:** *At this station, you will be using slinkies to model a variety of different types of waves as well as a variety of wave properties. For each wave example written in the first column of the chart, use the slinky to model this wave. Then, place a check or an X in the columns that correlate with what you did with your hand. You should have 2 marks per row for the 1 ^{st} 6 columns. For example, the first two columns are labeled “push hand forward softly” and “push hand forward hard”. Depending on the wave, you may have done neither of those things or only one of those things. Therefore, many boxes will be left blank. The next to last column ask you to draw what the wave looked like. In other words, what did the slinky look like? The last column asks you to draw an example of what the graph of the wave might look like. This is an important new application you will be making with waves.*

**Introduction to Graphing Waves Mini Lesson:** *Using math to show relationships is very valuable to a scientist. When studying waves, scientists are able to create graphs that represent the displacement over time or over a distance. On the board, draw a coordinate plane. Label the y axis Displacement and the x axis Distance. Explain that displacement refers to the “how out of place an object is”. Thus, the x axis is the resting position of the object or particles. (Draw a slinky at rest at the origin of the coordinate plane so that they have a visual frame of reference.) When graphing, the wave will be going above and below the x axis. Picture yourself creating a transverse slinky wave. By moving your hand side to side, you displace the wave a distance above and below the starting point or the position the wave was at rest. This is one characteristic the graph is showing. (Draw a transverse wave starting at the origin going up and down past the x axis.) This graph is representing the Disturbance vs. Distance. The measurement on the x axis is referring to distance, or “how much ground the object or wave has covered”. *

Ask the students, “*What wave properties could this type of graph help us quantify? Or put into numbers?*”. Students should respond with “*Amplitude, because that is the distance from a line through the middle of the wave to a crest.*” (A definition they were provided with in notes during an earlier lesson.) Students should also offer, “*Wavelength because that is the distance from crest to crest and this graph shows this.*”

One misconception that students might have is that they might say, “F*requency -- because it is how many waves there are.*” Frequency is actually a measure of how many waves pass a fixed point in a given time. Whether a student offers this misconception or not, bring it up! Even if they are not saying it aloud, there are students thinking it! Explain that there is another type of graph used to measure waves. This type of graph looks identical to the example previously given but the x axis is labeled Time. Only with this type of graph can you measure frequency. (The reflection included in this section provides more insight into this conversation and addressing misconceptions.)

(**Side note:** While the students just draw general relationship graphs today, students will look at quantitative graphs in a later lesson.)

Explain that in the last column of this chart, the students will create a general relationship graph (meaning they will not actually be plotting specific points, just a general line that could describe the wave) for each wave. While they do not have to plot specific points, do ask them to draw the coordinate plane, label the axes with the appropriate labels and draw the wave going above and below the x axis.

One challenging idea for students is that the graph of a transverse wave looks like the actual transverse wave while the graph of a longitudinal wave actually looks like a transverse wave. This idea that when all waves are graphed, they all appear like transverse waves causes some challenges for students.

15 minutes

**Station 2: Traveling Sound**

**Materials:**

3 hangers

1 long (3 ft or more) metal “string” or rope

1 long piece of yarn

1 long piece of fishing line

Show the students that attached to each hanger, there is a different type of string that is tied in a way that there are two ends of the string available for grabbing. Direct students to wrap one end of the string around a finger on each of their hands and place those fingers gently in their ears. Then, take the hanger and swing it so that it hits the table, taking note of the sound that they hear. Repeat this process with all of the string types.

When discussing with students at lab stations, use the words and vocabulary from the skills in your questions so that students are making clear connections to what they are supposed to be learning. In addition, encourage the students to use this vocabulary as well. In this clip, the students says that with the fishing line he couldn't "hear it very well" and then added that it was a "lower amplitude". If he had not included strong vocabulary in his response, I would have asked him to explain his thinking again to me while utilizing the characteristic properties of waves in his answer.

**Station 3: Waves and Rice**

**Materials:**

Rice

A coffee can/jar

Latex glove/balloon

Metal dish or tray (It will get ruined)

Some type of hitting instrument like a mallet or hammer

Show the students that there is a rubber/latex cover over the container. Tell the students they will place rice on the cover. They will hold the metal tray above the rice without touching the rice and bang the hammer on the tray, observing what occurs to the rice.

15 minutes

**Station 4: Bouncing Sound**

**Materials:**

2 tubes (I use old containers that held posters I have purchased for my classroom.)

Laser pointer or flashlight

Explain that the students should hold the 2 tubes at an angle pointed towards the same wall (I have also had luck using a text book). Have one student place their ear to their tube and the other whisper into their tube. Then, switch roles. After observing the sound, use the laser pointer or flashlight to shine the light into one of the tubes and determine if they can see the light through the other tube.

**Station 5: Refraction Cells/Prisms**

**Materials:**

Prisms

Laser pointers

White paper

Refraction Cells (if available)

Light Box (if available)

Explain that the students will take the laser pointer and light box (if available) to shine into the prisms and refraction cells (if available). Ask them to move the laser pointer side to side and at different angles to watch the behavior of the light.

**Safety:** Be sure to address safety with the laser pointers! Scientists use technologies and tools for the purpose addressed in the procedure. Avoid transverse waves in the eyes of classmates!

**Tips: ** I have found that the bending of the light is more evident if you set these objects on a piece of plain white paper. Also, the refraction cells and light box just provide and extra example here. If you do not have these items, prisms and laser pointers get the job done!

Allow students to rotate themselves through each of the lab stations. I typically break my classes down into 6 – 7 groups. As students rotate through the stations, be sure to ask them to connect to the specific skill that each station is about. For example, at the Bouncing Sound station in the Lab Document, make sure that students are connecting to Skill 1 and identifying how different types of waves behave differently. If students do not take the time to read the skills connected to the stations, connections will be missed. In this case, many students would only connect to the idea of reflection and would miss out on the idea that this station demonstrates that light and sound waves interact with different matter in different ways.

For more insight into student work and lab documents, see the Wave Behavior Lab Rotation Day 2 Lesson Plan.

5 minutes

With about 5 minutes left of class, ask students to clean up the lab station and complete the formative assessment/exit slip that focuses on them drawing general relationship graphs about the characteristic properties of waves.