The Music of Math The Pythagorean discovery that “all things known have number – for without this, nothing could be thought of or known” – was made in music. Kitty Ferguson, 2008

In pythagorean Times… In the 1600’s mathematicians considered music to be a mathematical science (Field, 2003) Pythagoras – The Father of Math and Music Donald Duck in Math Magic Land - Music https://www.youtube.com/watch?v=iEVGQKwKeCc

Reading Music https://www.facebook.com/TEDEducation/videos/1125483490798189/ To integrate music and math you don’t have to know a lot about music, but it is useful to know a little bit about reading music. Essentially reading music comes down to recognizing symbols and interpreting their meaning. It is just like reading letters or numbers and applying them to the system that which they belong. Teach the group how to read basic rhythms using the chart board. Practice reading/clapping through a Rowloff chart.

Kindergarten Outcome: PK.1 Demonstrate an understanding of repeating patterns (two or three elements) by: identifying reproducing extending creating patterns using manipulatives, sounds, and actions. Do you see music in this outcome? How can repeated patterns be represented and recreated through sound?

Lessons & Ideas http://lessonplanspage.com/music/ Lesson plans for every grade level and subject area with integration FREE The Patterns of Music by Geist, Geist, and kuznik (2012)

Grade 1 Music Math N1.9 Demonstrate an understanding of addition of numbers with answers to 20 and the corresponding subtraction facts, concretely, pictorially, physically, and symbolically by: using familiar and mathematical language to describe additive and subtractive actions from their experience creating and solving problems in context that involve addition and subtraction modelling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically.

Music Tech Teacher http://www.musictechteacher.com/ Lessons Worksheets Printable Quizzes Games FREE

Grade 2 Patterns Outcome: P2.1 Demonstrate understanding of repeating patterns (three to five elements) by: describing representing patterns in alternate modes extending comparing creating patterns using manipulatives, pictures, sounds, and actions.

Grade 3 Graphing & Measuring SP3.1 Demonstrate understanding of first-hand data using tally marks, charts, lists, bar graphs, and line plots (abstract pictographs), through: collecting, organizing, and representing solving situational questions.

Graphing Graphing Pitch Objectives This group activity explains the musical relationship between the length of instruments and their pitch. Objectives •Students will collect, organize, and graph data, demonstrating their grasp of the relationship between the length of an instrument and its pitch.

Grade 4 Exploring the Science of Sound Outcome: CP4.5 Demonstrate increased skills and abilities in the use of voice and instruments (traditional and/or homemade) and develop compositions using Saskatchewan as inspiration. Outcome: SO4.1 Explore natural and artificial sources of sound in the environment and how those sounds are detected by humans and animals. Outcome: SO4.2 Draw conclusions about the characteristics and physical properties of sound, including pitch and loudness, based on observation

Building Musical Instruments http://www.bashthetrash.com/Instruments_Intro/How_Instruments_Work_- _Easy.html

Grade 5 Transformation compositions Outcome: SS5.7 Identify, create, and analyze single transformations of 2-D shapes (with and without the use of technology). Carry out different transformations (translations, rotations, and reflections) concretely, pictorially (with or without the use of technology), or physically and generalize statements regarding the position and orientation of the transformed image based upon the type of transformation.

Grade 6 Exploring the Frequency Of Sound Arts Education: CP6.7 Demonstrate increased skills and abilities in the use of voice and instruments. Grade 6 Math: N6.2 Demonstrate understanding of factors and multiples (concretely, pictorially, and symbolically) including: determining factors and multiples of numbers less than 100 relating factors and multiples to multiplication and division determining and relating prime and composite numbers. Grade 6 Math: N6.3 Demonstrate understanding of the order of operations on whole numbers (excluding exponents) with and without technology.

How does a piano work? Terminology Vibration – sound is produced when something vibrates such as a drum head, a hard surface, a string, or air. Frequency – is the number of vibrations per second Pitch – The faster the vibrations, the higher the pitch we hear. The slower the vibrations, the lower the pitch we hear. Hammer – Pianos have small hammers inside connected to the piano keyboard. When a key is depressed, a corresponding hammer strikes the appropriate strings to create the tone.

Calculating frequencies Using two knowns: A4 = 440 vibrations per second Each octave vibrates twice as fast as the previous See the piano keyboard image & the frequency chart for reference Use problem solving and math skills to calculate various frequencies and then hear the pitch it makes on the piano. Full lesson plan and assignment provided. Photos?

Middle Years https://www.teachervision.com/math/resource/10340.html

High School pdxscholar.library.pdx.edu

references Ferguson, Kitty (2008). The music of Pythagoras. New York: Walker Publishing Compqny, Ltd. Field, J.V. (2003). Musical cosmology: Kepler and his readers. In J. Fauvel, R. Flood, & R. Wilson (Eds.), Music and Mathematics (pp. 29-44). New York: Oxford University Press.