How can a sound make something move?

This unit builds toward the following NGSS Performance Expectations (PEs): 

• MS-PS4-1. Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. [Clarification Statement: Emphasis is on describing waves with both qualitative and quantitative thinking.]
• MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. [Clarification Statement: Emphasis is on both light and mechanical waves. Examples of models could include drawings, simulations, and written descriptions.]

This unit helps develop the following elements of Disciplinary Core Ideas (DCIs):

PS4.A: Wave Properties

• A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. (MS-PS4-1)
• A sound wave needs a medium through which it is transmitted. (MS-PS4-2)

• Developing & Using Models
• Using Mathematics & Computational Thinking
• Engaging in Argument from Evidence

• Patterns
• Scale, Proportion & Quantity

This unit calls upon understandings from all three grade levels in middle school CCSS. Later lessons, in particular, ask students to apply skills and understandings from grade 8 CCSS. Since this unit falls at the beginning of the 8th grade year of the OpenSciEd Scope and Sequence, it’s important to identify which math concepts and skills students may need extra support in applying as these concepts are fundamental to students engaging in Science and Engineering Practices like analyzing and interpreting data as well as using mathematical and computational thinking. 

Mathematical concepts and skills from middle school CCSS are used in the following lessons:

• In Lesson 4, students collect and analyze data in the form of distance vs. time graphs showing the motion of a vibrating stick over time. Students characterize the shape of these graphs as wave patterns, and describe differences in properties like the vertical distance between peaks and troughs of waves when looking at graphs for louder vs. softer sounds. They will also connect the properties of these functions to the physical differences they represent using the axes of the graph to inform what the graph represents. This data analysis calls on the ability to describe the relationship between two quantities using a graph (CCSS.MATH.8.F.B.5) as well as the ability to compare two functions expressed graphically in order to determine key properties about each function (CCSS.MATH.8.F.A.2).
• In Lesson 5, students are expected to exercise these same skills and understandings to interpret differences between graphs of distance vs. time for a stick simulating higher- and lower-pitched sounds. In addition, students define the frequency as the amount of vibrations the stick goes through in a second. They calculate this frequency by finding the unit rate (vibrations per second) using the overall number of vibrations and the total time passed (CCSS.MATH.6.RP.A.2).
• In Lesson 5 and 6, students work independently to interpret graphs of time vs. distance to describe sounds in terms of pitch and loudness using qualitative properties of the functions shown on each graph (CCSS.MATH.8.F.A.2). Depending on the math understandings that students display in Lessons 4 and 5, students might need support in reading and interpreting these graphs. It may help some students to go over the axes of the graph as a class to draw attention to what the graph is showing, and students may benefit from probing questions like, “What differences do you notice between these graphs? How do those differences compare to what we saw in the graphs we made with the motion detector?”.
• In Lesson 13, students discuss and use mathematical methods of finding the average of data sets, including calculating mean and median as a way to combine results from different groups in order to improve the accuracy of the class’s data. They also work together as a class to decide how to account for or discard outliers in the class’s data in order to best represent what each group found in their investigations (CCSS.MATH.6.SP.B.5). Depending on their experience using these concepts in math classes, students may need reminders of how mean and median are calculated. You can support students in recalling these procedures by taking a sample data set (either from the investigation or a random example set) and working together as a class to describe how students could find the mean and median of the set. By doing this with the class or with small groups that could use this extra practice, you can support students with mathematical methods needed to analyze the data the class has collected to draw conclusions about the lesson question.
• Later in Lesson 13, students gather data describing how the energy of a vibration changes with changes to the frequency and amplitude of the vibration. They then use this data to describe and graph functions that represent the relationships between energy and frequency and energy and amplitude. From their numerical data and the graphs they create, students will see that there is a proportional relationship between frequency and energy transferred; when we increase the frequency of the vibrations, the energy transferred increases in proportion (CCSS.MATH.7.RP.A.2). While frequency and energy have a linear relationship, amplitude and energy have a nonlinear relationship where increasing amplitude causes much greater increases in energy compared to increasing frequency. Some students may recognize the pattern on the amplitude vs. energy graph as exponential, where increasing amplitude causes a much greater increase in energy than in a linear relationship like that between frequency and energy (CCSS.MATH.8.F.A.3). 
• By the end of Lesson 13, Students are expected to use these qualitative properties of the graphs for frequency vs. energy and amplitude vs. energy to conclude that the energy vs. amplitude function has a greater rate of change than does the energy vs. frequency function (CCSS.MATH.8.F.A.2). Depending on students’ experience with linear and nonlinear functions, students may identify these differences in different ways. Some students may only be able to state that the amplitude vs. energy graph is steeper or increases more quickly, and they may need support in connecting this observation to the idea that increasing amplitude causes a greater increase in energy compared to frequency. Further, some students may benefit from using the data tables they generate in their investigations to find numerical patterns to support their observations of the two graphs. In this numerical data, for example, they might notice that doubling the frequency doubles the energy but doubling the amplitude makes the energy increase by 4 times. These numerical patterns may be helpful to call out and emphasize for students who are still developing their skills at reading and analyzing graphs.

This is the second unit in 8th grade in the OpenSciEd Middle School Scope and Sequence. Given this placement, several modifications would need to be made if teaching this unit earlier or later in the middle school curriculum. 

• If students haven’t developed lines of evidence from previous grades (PS1 in grade 5) that air is matter and therefore air has mass, you may need to conduct additional investigations first to establish these ideas. (e.g. massing a soda bottle before and after opening it; massing a volleyball before and after adding air. )
• If students haven’t developed lines of evidence from previous grades (PS1A in MS) that (a) solids, liquids, and gases are made of particles; (b) the spacing between those particles is different for a solid and liquid versus a gas; and (c) that the particles in liquid or gas are moving, you will need to establish these ideas first. The unit rests on explaining sound as the collision of particles that transfers energy — so so students need to see matter as composed of particles and see how those particles can move, even in solids. 
• The idea that moving objects have energy and that this energy can be transferred through collisions needs to  be developed prior to this unit.  

• Renee Affolter, Unit Lead, Boston College
• Susan Kowalski, Field Test Unit Lead, BSCS Science Learning
• Gail Housman, Writer, Ideal Elementary School
• Jamie Noll, Writer, Northwestern University
• Tyler Scaletta, Writer and Pilot Teacher, North Shore Country Day School
• Michael Novak, Reviewer, Northwestern University
• Chris Newlan, Pilot Teacher,  David Wooster Middle School
• Sara Ryner, Pilot Teacher, United Junior High School
• Katie Van Horne, Assessment Specialist

BSCS Science Learning

• Stacey Luce, Editorial Production Lead and Copyeditor
• Valerie Maltese, Marketing Specialist & Project Coordinator
• Alyssa Markle, Project Coordinator
• Chris Moraine, Multimedia Graphic Designer

This unit was adapted from How Can We Sense So Many Different Sounds From a Distance?, originally developed by the Next Generation Science Storylines project at Northwestern University. Used with permission. How Can We Sense So Many Different Sounds From a Distance? was developed with support from the Gordon and Betty Moore Foundation to Northwestern University and support from the NGSX Project at Clark University, Tidemark Institute, and Northwestern University.

An integral component of OpenSciEd’s development process is external validation of alignment to the Next Generation Science Standards by NextGenScience’s Science Peer Review Panel using the EQuIP Rubric for Science. We are proud that this unit has earned the highest score available and has been awarded the NGSS Design Badge. You can find additional information about the EQuIP rubric and the peer review process at the nextgenscience.org website.