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Module Title: The Music Wall

Standards:

Congruence – Experiment with Transformations in the Plane (G.CO.A.4, G.CO.A.5):
Students will apply translations, rotations, reflections, and dilations to design the blueprint for their music wall. They will experiment with these transformations to create symmetry and congruence in the design.
Congruence – Understand Congruence in Terms of Rigid Motions (HSG.CO.B.6):
Students will explore how different transformations preserve congruence, ensuring the shapes and patterns on their music wall maintain the same size and form through rigid motions.
Congruence – Prove Geometric Theorems (HSG.CO.C.11):
Students will use theorems and proofs, such as the Pythagorean Theorem and triangle congruence theorems, to justify the relationships between different elements in their design.
Modeling with Geometry – Apply Geometric Concepts in Modeling Situations (HSG.MG.A.1, HSG.MG.A.3):
Students will apply geometric modeling to create the xylophone and music wall, scaling and positioning objects to fit within the blueprint while maintaining proportionality.
Similarity, Right Triangles, and Trigonometry – Understand Similarity in Terms of Similarity Transformations (HSG.SRT.A.1):
Students will use dilations to scale the xylophone bars and other elements of the wall while maintaining similarity in their shapes.
Similarity, Right Triangles, and Trigonometry – Prove Theorems Involving Similarity (HSG.SRT.B.5):
Students will prove relationships between similar triangles or other geometric elements in their design, demonstrating how proportionality holds across dilations.
Trigonometric Functions – Model Periodic Phenomena with Trigonometric Functions (HSF.TF.B.5):
The construction of the xylophone will connect to sound waves, where students will model the frequencies and sinusoidal patterns of sound using the sine function to represent periodic motion.

PBL Goal:

Students will have two parts to this project. The first is creating a blueprint of their music wall which should include various types of transformations with proofs. The second component is building a xylophone and modeling the sound waves mathematically.

Structure:

Each lesson in the "The Music Wall" module follows the 5E lesson framework to guide students through a comprehensive learning experience. The structure includes:

Engage: Capture students' interest with real-world scenarios, like providing either videos, simulations or short information bytes about either the cultural significance of the lesson or unique math perspectives.
Explore: Allow students to investigate mathematical principles or cultural context without constraints.
Explain: Guide students through a direct lesson complete with additional practice to ensure comprehension. This bridges the Explore and the Engage together with new content.
Elaborate: Encourage deeper thinking by applying their knowledge to complex problems or exploration of the final module project.
Evaluate: Assess students' comprehension with formative assessments, project submissions, or testing.

Overview:

In the "The Music Wall" module, students will explore the interaction of art, culture, and mathematics by designing a music wall blueprint as well as a working xylophone prototype. This module integrates several key math standards from both geometry and trigonometry. Throughout the lessons, students will deepen their understanding of geometry, by reviewing key concepts explored previously in the course such as transformations, and increasing the rigor by adding in the distance formula as well as geometric proofs. The culmination of the module is with a fourth lesson exploring how sound waves can be modeled with sine, applying geometry, trigonometry and music in one final exposition.

Lesson 1:
In Lesson 1, students will review what they have learned about transformations, rotations, reflections, translations, and dilations. This will be the introduction to their blueprint. They will use this information to decide how they want to display their musical instruments.

Lesson 2:
In Lesson 2, students will learn about similarity, the distance formula and dilations. They will learn how to use the distance formula to prove congruence.

Lesson 3:
Lesson 3 introduces students to writing two-column proofs in geometry. They will review various theorems and practice doing proofs.

Lesson 4:
They will be introduced to sound waves and how waves can be modeled with sine. In this lesson, they learn about various components of waves, such as frequency and amplitude, as well as visualizing how the waves can be graphed on a graphing calculator.

Place-Based Significance:

Music is part of every cultural landscape. In this module, students will be provided a playlist of inspired songs. Music is always evolving and changing. This module is rooted more in centering different sites and sounds and encouraging students to consider their own unique musical tastes. Each lesson has a themed playlist to help provide inspiration for the lesson. The first highlights artists from New Mexico and artists inspired by New Mexico. The second playlist features songs related to "transformations" such as Michael Jackson's "Man in the Mirror." The third playlist is titled "Something to Prove" including songs where artists feel they must prove how they feel or other plays on words. The final playlist features music from xylophones since the students will be creating a xylophone in their final project.