Classroom Resource

Scale City | Proportions and Music in the Real World

Subject Area

Mathematics

Grade(s)

6, 7

Overview

In this video—through footage of the calliope aboard the Belle of Louisville, a church pipe organ, and various instruments at a recording studio—students are introduced to the mathematical concept that the length of a musical pipe or a string has a proportional relationship with the sound it produces.  In the accompanying activity, stringed instruments are used to demonstrate the concept presented in the video. This resource is part of the Math at the Core: Middle School Collection.

 

Although Proportions and Music in the Real World ("Belle of Louisville") and the Proportions and Music in Practice interactive ("Musical Scales") can be used independently, they are deliberately designed to complement each other.

 

The video introduces students to the relationship between music and mathematics, specifically how the length of a pipe or string is related to its frequency, as they learn about the calliope aboard the Belle of Louisville steamboat, a massive pipe organ, and a variety of instruments at a recording studio. 

 

The matching interactive allows students to play a virtual pan pipe, measure the length of its pipes, record their frequency, and understand the inverse proportional relationship between these frequencies and the instrument’s corresponding pipe lengths.

 

Be sure to use the Proportions and Music in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).

Mathematics (2019) Grade(s): 6

MA19.6.3

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Unpacked Content

UP:MA19.6.3

Vocabulary

  • Rate
  • Ratio
  • Rate reasoning
  • Ratio reasoning
  • Transform units
  • Quantities
  • Ratio Tables
  • Double Number Line Diagram
  • Percents
  • Coordinate Plane
  • Ordered Pairs
  • Quadrant I
  • Tape Diagrams
  • Unit Rate
  • Constant Speed

Knowledge

Students know:
  • Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
  • Strategies for finding equivalent ratios,
  • Strategies for using ratio reasoning to convert measurement units.
  • Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
  • Strategies for converting between fractions, decimals and percents.
  • Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
  • Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
  • Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

Skills

Students are able to:
  • Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
  • Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
  • Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
  • Plot ratios as ordered pairs.
  • Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
  • Solve problems and justify solutions when finding the whole given a part and the percent.
  • Model using an equivalent fraction and decimal to percents.
  • Use ratio reasoning, multiplication, and division to transform and interpret measurements.

Understanding

Students understand that:
  • A unit rate is a ratio (a:b) of two measurements in which b is one.
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
  • When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.
Mathematics (2019) Grade(s): 7

MA19.7.2

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

Unpacked Content

UP:MA19.7.2

Vocabulary

  • Equivalent ratios
  • proportional
  • Coordinate plane
  • Ratio table
  • Unit rate
  • Constant of proportionality
  • Equation
  • ordered pair

Knowledge

Students know:
  • (2a) how to explain whether a relationship is proportional.
  • (2b) that the constant of proportionality is the same as a unit rate. Students know:
    • where the constant of proportionality can be found in a table, graph, equation or diagram.
    • (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.

Skills

Students are able to:
  • (2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane.
  • (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
  • (2c) model a proportional relationship using coordinate graphing.
  • Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.

Understanding

Students understand that:
  • (2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
  • (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context. (2c) The context of a problem can help them interpret a point on a graph of a proportional relationship.
Link to Resource
https://aptv.pbslearningmedia.org/resource/mket-math-rp-belleoflou/belleoflou/

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility
License

License Type

PD

Comments or Notes

This resource contains the following activities:

Proportions and Music in the Real World Viewing Guide: PDFProportions and Music in the Real World Viewing Guide Answer Key: PDF

Proportions and Music in the Real World - Activity

Proportions and Music in the Real World - Connections

Approved Date

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