Analyzing Graphs of

5.A Use mathematical representations of position versus time graphs generated from a tool used to scale up the vibrations of an object to describe wave patterns and support scientific conclusions about how objects move when they make higher-pitch and lower-pitch sounds.

Collect this exit ticket at the end of class or at the start of the next class. This will give you a day or two before the individual assessment at the end of the next lesson to provide feedback to students to help guide their understanding and revisions before that assessment. This is a key practice opportunity for students to work with the kind of graphs they will see in the assessment. If students struggle to connect the high note on the xylophone to Graph B (highest frequency of vibrations), suggest that students draw a mini xylophone on their paper and then write in which bar would have made each note. Then for each note ask students why they chose that bar. Have students return to Graphs A, B, and C and see if they can now tell which graph represents each pitch (high, middle, and low). If you are short on time to give feedback on the exit ticket, consider having students check their work with a partner and/or against a provided answer key (so they can self-correct).

Additional Lesson 5 Teacher Guidance

SUPPORTING STUDENTS IN MAKING CONNECTIONS IN MATH

CCSS.MATH.8.FA.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

In this lesson, students analyze patterns in graphical representations of the stick’s motion in order to figure out that a sound maker moves back and forth more often in a given time (has a greater frequency) for higher-pitched sounds. During this analysis, students identify and describe wave-like properties in the graph of the stick’s motion, including a repeating pattern of peaks and valleys in the function of the stick’s distance from the detector over time.

Students also compare graphs of the stick’s motion for higher-pitched and lower-pitched sounds with an eye for comparing the properties of the two functions in order to understand what changes about how a sound maker vibrates for sounds of different pitch. During this analysis, they identify that the function for higher-pitched sounds has a shorter horizontal distance between peaks and valleys. They then use this observation to conclude that for higher-pitched sounds, the sound maker moves back and forth more often over the same amount of time.

If students have trouble making comparisons between the graphical representations for loud vs. soft sounds, they may benefit from seeing the two graphs displayed side by side. Students can then come up to the projection and point out differences between the two functions that the class can then use to draw conclusions about how the motion of the stick changes when simulating sounds of different pitch.

SUPPORTING STUDENTS IN MAKING CONNECTIONS IN MATH

• CCSS.MATH.6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b where b does not equal zero, and use rate language in the context of a ratio relationship.
• CCSS.MATH.6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
• CCSS.MATH.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities.

In this lesson, students define and calculate frequency as the number of complete vibrations in one second. Students use graphs of the stick’s motion to count the number of times that the stick vibrates and then divide that by the amount of time over which the stick was vibrating. We label this unit rate of how many times the stick vibrates in one second as the frequency of the stick’s vibration.

If students struggle to calculate the frequency, refer them to the class’s definition for frequency on their word wall or in their notebooks. Students may benefit from seeing an example of this calculation starting from a graph of the stick’s motion over time as a refresher on how to derive a unit rate from the ratio between the number of vibratio…