CONTENT StandardCCSS.MATH.CONTENT.4.NF.B.3.B

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Additional Standards Addressed: NGSS 4-PS4-1

ARTS StandardMU:Cr2.1.4b

Use standard and/or iconic notation and/or recording technology to document personal rhythmic, melodic, and simple harmonic musical ideas.

Additional Standards Addressed: VA:Cr1.1.4a

Essential Question How can we represent numbers?

Lesson Objective Students will create and document a melodic piece using the letters in their name.

Lesson Overview Decomposing fractions and seeing parts of a whole directly correlates to an understanding of music. Both pieces also have unique representations (the form of a fraction and the notes of music). Students will see the alignment of these two pieces, breaking down the parts of their name into pieces that compose the notes of a musical idea.

Colors / Shapes / Lines routine Have students look at the artwork Composition with Grid IX by Piet Mondrian

• What colors do you see?

• What shapes do you see?

• What lines do you see?

Artful Thinking Routine

Artful Thinking by Project Zero is licensed under a Creative Commons AttributionNonCommercial 4.0 International License. Routine found here: http://pzartfulthinking.org/

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G R A D E

Melodic Names4 MATH • MUSIC

Pacing

Assessment

2-3 sessions

SUMMATIVE

Students will document a melodic composition based on fractional parts.

Materials List• Drinking glasses, mason jars

or other glass containers (beakers, tubes). Each student will need multiple glasses.

• Playing cards

21st Century Skills • Creative Thinking • Productivity • Communication • Critical Thinking

decompose notation melody pitch

VOCABULARY

Elements of MUSIC

• PITCH • FORM

Review with students how to decompose a whole into fractional parts. Use Mondrian’s art from the Artful Thinking Activity to break the whole into fractional pieces (see the student resource).

After finding the fractions, challenge students to break down the fractions even farther. For example, how could they take the fraction of yellow pieces and decompose it into smaller pieces?

Tell students to write out their name (first and last) and then decompose it into fractions. For example: Name: PIPPI LONGSTOCKING

• There are 17 letters, so the denominator will be 17

• There are 3 “P” so P = 3/17, and so on for each letter

• There are ten different letters represented in the name, so students would discover ten fractions. Many letters will have the same fraction (t, c, k, l = 1/17, ), so there are really only 3 different fractions.

Note: For the main activity of this lesson, students will need at least three different fractions. If they do not have enough, have them use their middle name as well.

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Introduction

Decomposing Fractions

Play a game of fraction war. This could be done in pairs, which would create a longer activity, or you can play one game against the class. Each player flips over two playing cards. They need to make the biggest fraction possible, deciding which card will be the numerator, and which is the denominator, using their pencil as the line in between.

After each player makes their fraction, compare fractions. The owner of the higher fraction gets a point. If the fractions are equivalent, both players get a point. The player that reaches 10 points first wins.

Your notes:

Teacher to Teacher

For students that may have trouble with this, have them put each letter on its own piece of paper (or use letter tiles) and group common letters together. The number of letters in each group is the numerator of the fraction.

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Your notes:

Main ActivityReview musical pitches with students. Many may be familiar with the alignment of pitch and music notes using “do re mi”, but ask students to consider pitch and sound. How would they communicate pitch with various tones?

Use 3-4 glass jars, with varying amounts of water. Ask students to listen to the different pitches that are made by tapping on the glass. Why are the different pitches happening based on water levels?

Musical Pitches

Musical notes are based on fractions. Remind students, as they have learned in music, there are whole notes, quarter notes, half notes, eighth notes. sixteenth notes and rests, which are represented on a staff. Consider what we know about this notation system:

• Universal • Easy to understand • Simple to write • Consistent • Associated with types of sound

Ask students to create a new notation system to align with the fractions of their name. They will need one symbol for each different fraction.

Eventually, they will be be associating it with sound, but this section should be about the notation. As students are working, circulate to ensure they are not being overly complicated in their creations. It may help to have students think of each new notation as a unique symbol.

For students needing a challenge, or students with musical knowledge, challenge them to have their notes relate to each other in the look and feel, as traditional music notes do.

Musical Notation

Estimated Time: 1 session

Your notes:

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Main Activity

Students will create a musical idea based on the fractions of their name.

For each fraction in their name, students will need a glass container, filled with a different level of water. (In the Pippi Longstocking name example, the student would need 3 glass containers.)

• For each jar, students will assign a different pitch. • They will label each jar with their notation. • Create a musical idea that consists of at least 15

notes.

After students have created a musical idea, they need to record the melody by writing the notation.

Pair students up and have them exchange notes/musical ideas. Can they replicate the composers piece by playing the notation? If not, allow the composer/musician to convert and decide what to do to make it more consistent.

CLOSURE

Teacher to Teacher

For increased difficulty and differentiation, require that the amount of water be fractionally equivalent in each glass container.

Example: The “t” in Pippi Longstocking is 1/17, but the “p” is 3/17. The amount of water in the “p” jar should be three times as much as the “t” jar.

For students that may have difficulty with recording the notation and keeping notation and pitches straight, color the water, making each container a different color. When students write out their musical idea, they could also write the notations in the corresponding colors, which would help students be successful in the closure piece.

G R A D E

4 MATH • MUSIC

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Literature Connections

Your other favorites:

By using the links on this page to purchase the books listed, we will receive a small commission as an affiliate. We only recommend books that are high quality, have been used in our own classrooms, and which have direct connections to this lesson.

Becoming Bach Tom Leonard

The story of Johann Sebastian Bach and the way he created song from patterns, which he saw everywhere. A gorgeously illustrated book which proves the connections between math and music.

Because Mo Willems

The amazing Mo Willems takes us on a simple but powerful journey to show us how we are all connected by music, and how one persistence and discovery can change the course of a life.

Do Re Mi: If You Can Read Music, Thank Guido D’Arezzo Susan Roth

The story of the man who found a way to create notation - the way way we write the sounds of a song. Large fonts combined with torn paper illustrations provide a unique look at the innovation of one man that is now used around the world.

Making Music John Langstaff

Musical creativity abounds through ideas that encourage kids to create music from everyday household objects such as zippers, pencils, forks and hoses. Allow your students to think creatively about how to bring their compositions to life.

Melodic Names

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Student RESOURCE

MATH • MUSIC

Name:

Decompose Piet Mondrian’s Composition with Grid IX into smaller fractions.

If the entire piece of art is one whole, what fraction of a whole are:

yellow pieces:

blue pieces:

red pieces:

gray (dark and light) pieces:

Now write an equation using the fractions you identified:

Melodic Names

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Student RESOURCE

MATH • MUSIC

Look at 5 of your peers’ collages. Write down one or two sentences for each about the main idea you take away from viewing it.

Step 1: Decompose your name into fractions:

1 Print your first and last name

2 How many letters are there?

3What fraction of your name does each letter represent? Write them all here

4 How many DIFFERENT fractions are there?

5 Write your fractional name in two different equations

Step 2: Iconic Notation

Create notation for EACH of the fractions of letters in your name. Remember to make it:

• Easy to understand • Simple to write • Consistent • Associated with types of

sound

** Whatever the number is in step 4 above is how many different pieces of notation you need

Name:

Melodic Names

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Student RESOURCE

MATH • MUSIC

Look at 5 of your peers’ collages. Write down one or two sentences for each about the main idea you take away from viewing it.

Step 3: Create a musical idea!

After you create your musical idea, record the notation here so that someone else could play it!

Name:

Melodic Names

CRITERIA Distinguished (4 Points)

Excelled (3 Points)

Adequate (2 Points)

Basic (1 Point)

The student is able to: • Decompose a

fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

• Justify decompositions, by using a visual fraction model.

The student is able to efficiently and logically decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. The student is able to create and justify logical decompositions, by using a visual fraction model.

The student is able to decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. The student is able to justify decompositions, by using a visual fraction model.

With support, the student is able to decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. The student is able to justify decompositions with guided questions, by using a visual fraction model.

The student is unable to decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. The student is unable to justify decompositions, by using a visual fraction model.

The student is able to use iconic notation to document personal rhythmic, melodic, and simple harmonic musical ideas.

The student is able to effectively use and develop iconic notation to document personal musical ideas which may have complex rhythms and melodies.

The student is able to use iconic notation to document personal rhythmic, melodic, and simple harmonic musical ideas.

The student has difficulty using iconic notation to document personal rhythmic, melodic, and simple harmonic musical ideas.

The student is unable to use iconic notation to document personal rhythmic, melodic, and simple harmonic musical ideas.

NOTES: Consider the overall process of the student.

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Student: ______________________________________________Total Score:

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TEACHER ASSESSMENT

MATH • MUSIC