Jane Smith
Algebra, Ratios and Proportions
Material Type:
Lesson Plan
Middle School
6, 7
  • Beats Per Minute
  • Music
  • Rate
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    Media Formats:
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    Rate and Music - Using Beats Per Minute

    Rate and Music - Using Beats Per Minute


    In this lesson, students are introduced to rate in the context of music. They will explore beats per minute and compare rates using mathematical representations including graphs and double number lines.

    Key Concepts

    Beats per minute is a rate. Musicians often count the number of beats per measure to determine the tempo of a song. A fast tempo produces music that seems to be racing, whereas a slow tempo results in music that is more relaxing. When graphed, sets with more beats per minute have smaller intervals on the double number line and steeper lines on the graph.

    Goals and Learning Objectives

    • Investigate rate in music.
    • Find beats per minute by counting beats in music.
    • Represent beats per minute on a double number line and a graph.

    Mixing Music

    Lesson Guide

    Have students listen to the sample track and tap the beat as a class.

    Watch for any students who have difficulty keeping the beat. Pair these students with those who tap the beat with confidence.

    Before moving on to Work Time, make sure students understand that they will need to count the number of beats per minute in each of the sample tracks they listen to during Work Time.


    Make sure these points come out in the class discussion:

    • What makes music sound as if it belongs together? ( Mostly it is tempo; students might also mention the key or other features of music .)
    • What is tempo? ( Speed, or beats per minute )
    • How can you measure tempo? ( The usual measure is number of beats per minute. Help students understand that they need to measure not just one but two aspects of the situation: number of beats and amount of time .)
    • Can you change tempo? ( Yes, by playing faster or slower or by changing the tempo electronically )


    Technically, beats per minute is not exactly the same as tempo. However, beats per minute and tempo are synonymous in the context of this lesson. If students are interested, they can read more about beats per minute and tempo on the Internet. Students should also know that legally mixing samples of other people’s work and presenting the mix as a new song requires getting permission from the copyright holders of the original songs.

    SWD: Though this discussion of mathematics is informal, consider it as an introduction or preview for students with special needs. Be sure to emphasize key information and critical concepts that will be introduced. This will support students as they work to determine salient information throughout the lesson.


    Mixing Music

    • Listen to the music as a class and tap out the beat with your classmates.

    AUDIO: Beats

    Math and Music

    Lesson Guide

    As a class, discuss the question “How is math connected to music?”

    If students are struggling with this discussion, see if there are any musicians in class who might have ideas to share or might be willing to demonstrate something they have learned in music class. Some possible topics for discussion are as follows:

    • Note lengths are measured in fractions, such as a quarter note, a half note, an eighth note, and a sixteenth note.
    • In string instruments ratios are used to determine the tones created by varying string lengths. Changing the length of the string that is allowed to vibrate changes the tone it creates.
    • The volume of an instrument affects the sound the instrument makes. Portions of instruments that can have varied volumes include the length of a flute, the body of a guitar, the trumpet of a horn, the body of a drum, and more.
    • The rhythm in music is actually a pattern of sounds. The scales on a piano are an example of a repeating pattern.
    • Musicians often count the number of beats per measure. This count determines the tempo of a song. A fast tempo produces music that seems to be racing, whereas a slow tempo results in music that is more relaxing.


    Math and Music

    Give some examples of how math is connected to music.


    • When might a musician use counting?
    • Can the volume of an instrument change its sound?
    • If you know how to read music, how are notes measured?

    Creating Your Own Beat

    Students will use an app to sound out their own beat.

    Work Time

    Click the link to the app and create your own beat.

    Reflect On Your Work

    Lesson Guide

    Have each student do a quick reflection before the end of class. Review the reflections.

    If any reflections look interesting enough to pursue later, save them to share with the class when appropriate.

    Work Time


    Write a reflection about the ideas discussed in class today. Use one of the the sentence starters below if you find it to be helpful.

    • Something I have learned about rates is …
    • Something I still wonder about rates is...