LEARN NC

K–12 teaching and learning · from the UNC School of Education

Seeing music

http://illuminations.nctm.org/LessonDetail.aspx?ID=L686

A lesson plan for Grades 9–12 Algebra 1

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra, applied mathematics)
Provider
National Council of Teachers of Mathematics

Legal

Creative Commons License

This catalog record is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License. This license applies to the content of this page only and does not apply to the referenced website.

In this lesson students will calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They will then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations. Illuminations provides questions and an activity sheet necessary for completing this lesson. After completing pre-activity questions, students consider the mathematics involved with musical scales. Using an online chromatic scale, a mathematical formula and a calculator, students determine the intersection of sine waves.

Students will:

  • Connect musical scales to frequencies generated by a geometric sequence.
  • Relate sine waves to musical harmony and dissonance.

NCTM Standards and Expectations:

  • Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.
  • Use symbolic algebra to represent and explain mathematical relationships.
  • Draw reasonable conclusions about a situation being modeled.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 9–12 — Algebra 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.01: Write equivalent forms of algebraic expressions to solve problems.
      • Apply the laws of exponents.
      • Operate with polynomials.
      • Factor polynomials.
    • Objective 1.02: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.
  • Goal 3: Data Analysis and Probability - The learner will collect, organize, and interpret data with matrices and linear models to solve problems.
    • Objective 3.03: Create linear models for sets of data to solve problems.
      • Interpret constants and coefficients in the context of the data.
      • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use linear functions or inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret constants and coefficients in the context of the problem.
    • Objective 4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.
    • Objective 4.04: Graph and evaluate exponential functions to solve problems.