From music to math teaching fractions through rhythm to fourth graders

From Music to Math: Teaching Fractions Through Rhythm

From Music To Math:
Teaching Fractions through
Rhythm to Fourth Graders
By: Beth Campbell, Music Educator, Illinois School District 73

asda
ta

ti ti

tikatika ta


Advocacy And Strategies for Cross-Curricular Learning:
In a study by Bahr and Christiansen, the researchers examined the transfer of
knowledge between math and music. They concluded that students performed better
in math if the tasks were of a similar structure to tasks in music class (2000, as cited in
Cox & Stephens, 2006). Another researcher suggested that students “must be able to
recognize how the tasks were of similar structure in order to apply knowledge from one
domain to another” Zohar, 1994, as cited in Cox & Stephens, 2006). From a music
teacher’s perspective, the best way to do this would be to enlist the help of math
teaching colleagues. Not only will students’ knowledge increase, but the conversations
may lead to potential cross-curricular communications in the future. Since music is
considered a more specialized field, many non-music educators feel nervous to
incorporate music in with their lessons. They may not know where to begin. According
to Argabright (2005, as cited in Jones & Pearson, 2013) “general music teachers are
being asked to facilitate the integration of state language-arts and math standards with
their general music curriculum.” From Music To Math is meant to be shared across
subject areas and meant to empower both the music teacher and the math teacher.
The first step suggested by this music educator is to talk to the math teacher
about the optimal time of the school year to teach the lesson. Discuss which activities
the math teacher can support in the academic classroom. The assignment is flexible
and can be done in a shorter amount of time, or longer, depending on what works for
the teachers’ schedules. Feel free to show students the example of the finished
portfolio included in this packet so students understand each step. Allow students to
follow their own creative ideas, as there is more than one way to complete the portfolio.
This will facilitate students as they take ownership over their creations. Modify the
activities to work for you and your teaching situation. To acquire a modifiable version of
this packet in Microsoft Word or Pages, please email me at
campbell.beth.ann@gmail.com. You can also contact me at http://
doremiandsoon.blogspot.com/.


Activity Overview:
Basic Information: Students express fractions based on their own four bar rhythmic
composition. The students use fraction bars, pie graphs, decimals, and percents to
complete a portfolio. The project ends in a performance of their rhythms on unpitched
percussion instruments and a visual display of their work.This activity is based in 4/4
time. The following materials are included in this packet:
• Directions and checklists for students.
• Rubrics for students and teachers.
• Rhythm creation worksheet.
• Fraction bar creation worksheet.
• Pie graph creation worksheet.
• Decimal creation worksheet.
• Percentage creation worksheet.
• Example of a ﬁnished portfolio.
• PLUS: Ideas for hooks, links to manipulatives, ideas for possible extensions, and a
list of helpful references used to create the unit.


Standards Covered
4th Grade Common Core Math Standards (ISBE, 2012)
• CCSS.Math.Content.4.NF.B.3a Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
• CCSS.Math.Content.4.NF.B.3d Solve word problems involving addition and
subtraction of fractions referring to the same whole and having like denominators,
e.g., by using visual fraction models and equations to represent the problem.
• CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10
or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate
0.62 on a number line diagram.
• CCSS.Math.Content.4.NF.C.7 Compare two decimals to hundredths by reasoning
about their size. Recognize that comparisons are valid only when the two decimals
refer to the same whole. Record the results of comparisons with the symbols >, =, or
<, and justify the conclusions, e.g., by using a visual model.
Music Education National Standards (NAfME, 2012)
2. Performing on instruments, alone and with others, a varied repertoire of music.
4. Composing and arranging music within speciﬁed guidelines.
5. Reading and notating music
7. Evaluating music and music performances.
8. Understanding relationships between music, the other arts, and disciplines outside
the arts.


Hooks, Warm Ups, and Manipulatives
Video Connection between Math and Music:
http://www.youtube.com/watch?v=IzZhSqc_uhU
This video shows a group of young students in an after school percussion group
talking about how they connect math to music. The students are playing world drums
and buckets with drumsticks. Because of the “cool” setting, and because of the multimedia aspect, students may have a better time connecting to the themes than if it were
just introduced by the teacher.

Rhythm Stick (or any unpitched percussion instrument) Activity:
Students are divided into ﬁve groups. Assign each group a type of note: whole note
( g), half note ( f), quarter note ( a), eighth notes ( s), or sixteenth notes ( d).
Practice starting with whole notes and slowly adding in smaller and smaller
subdivisions. Encourage students to listen to how their rhythm ﬁts with the whole. When
starting with whole notes, think about how fast the sixteenth note will be before giving
the students a tempo. Practice starting with sixteenth notes, and slowly adding in
groups of larger divisions. Extension possibilities include:
• mixing up which group begins, as well as the order to enter afterwards.
• having groups cut in and out to hear different note relationships.
• having student groups switch note values as many times as possible.
Afterward, have students discuss what they noticed the relationship to be between the
whole note and the half note. Encourage students to think about the notes as fractions.
Lead the discussion to show different ways to express fractions: fraction bars, pie
graphs, decimals, and percents.
100

75

50

25

0

Whole Note

Half Note

Quarter Note

Eighth Note

Sixteenth Note


Whole Note

Half Notes
Note Name

Quarters, Eighths, Sixteenths

Decimal

Whole Note

1

Half Note

0.5

Quarter Note

0.25

Eighth Note

0.125

Sixteenth Note

0.0625

Whole
Note =
100%

Half
Note =
50%

Quarter
Note =
25%

Eighth
Note =
12.5%

Sixteenth
Note =
6.25%


Rhythm Pizza Activity
The manipulatives in this activity were designed by music teacher and blogger, Susan
Paradis. The only rhythm missing in her free download is sixteenth note. Students will
still get a great grasp of the concept without the sixteenth note, especially if the
teacher uses the missing note as a discussion point to ask what the sixteenth slice
would look like. A teacher may also make their own manipulatives with the same idea
to include all of the notes in the overall activity. Students may take a measure of rhythm
on the board, and display the rhythm as a pizza. The teacher can designate one
quadrant of the pizza to be the ﬁrst note of the measure. Explaining and modeling the
measure progressing clockwise around the pizza will help students make the
connection between the measure format and the pie graph format. Here are some easy
examples of measures to use that get progressively harder:

1. f f
2. aaaa
3. aasa
4. sasa
5. assa
* Students may take ownership and make more connections if they are able to
volunteer their own measure creations for other students to display. This can be used
as an extension to the activity. Here are the links to the free print outs by Susan
Paradis:
http://www.susanparadis.com/catalog.php?ID=SP754
http://susanparadis.wordpress.com/2008/10/01/rhythmn-pizza-on-foam-board/


Name: _________________________________

Create a Rhythm!
Directions: Create rhythms to fill four measures of 4/4 time. Use any of the listed
rhythms to fill the measures. It may help you to write down how many beats each type
of note fills up, or how many of that note go into one (1) beat. Be sure to use a variety in
each measure. When you are done, double check that each of your measures adds up
to four (4) total beats.

f= ___

beat(s)

s= ___

notes in a beat

a= ___

beat(s)

d= ___

4

4

Teacher Initials: _______________

Great! You are ready for the next phase!

notes in a beat


Name: _________________________________

Rhythms = Math?
Directions: You will be converting your composition into a series of fractions. Choose
two ways to express fractions. One way must be from Category A, and the other from
Category B.

Category A
_______ Fraction Bars
_______ Pie Graphs
Category B
_______ Decimals
_______ Percents




Name: _________________________________

Rhythms Into Fraction Bars!
Directions: Think about each note in your composition. How much of the measure do
they take up? Color in this chart to help. Then write each measure as a series of
fraction bars.

f=

a=

Measure 1:

Measure 2:

Measure 3:

Measure 4:



s=
d=


Name: _________________________________

Rhythms Into Pie Graphs!
Directions: Think about each note in your composition. How much of the measure do
they take up? Color in this chart to help. Then, write each measure as a series of pie
graphs. Place the ﬁrst note beginning in the upper right hand quadrant.

f

a

=

s

=

Measure 1

d

=

=

Measure 2



Measure 3

Measure 4


Name: _________________________________

Rhythms Into Decimals!
Directions: If a full measure was equal to the number one (1), how much would a half
note ( f), quarter note ( a), eighth notes ( s), or sixteenth notes ( d) be? To find out,
you would divide one (1) by the denominator. Example: The denominator for a half
note ( f ) is two (2), because the bottom part of the fraction one half (1/2) is two
(2). Use long division to figure out the answer. Remember tricks your math teacher has
taught you! Fill in the first four (4) answers before moving on to the interpretation of
your measures.

f=

0.5

2

a=

s=

d=

1 .0

- 0↓
10

- 10
0

* Use commas to separate decimals within the measure, then use a period at the end
of the measure.

Measure 1:
Measure 2:
Measure 3:
Measure 4:


You are finished with your portfolio!


Name: _________________________________

Rhythms Into Percents!
Directions: If a full measure was equal to the number one, how much would a half note
( f), quarter note ( a), eighth notes ( s), or sixteenth notes ( d) be? To find out, you
would divide one (1) by the denominator, and then move the decimal over. Example
denominator: The denominator for a half note ( f ) is two (2), because the bottom
part of the fraction one half (1/2) is two (2). Use long division to figure out the
answer. Remember the tricks your math teacher has taught you! Then, move the
decimal over to the right two (2) spaces. Fill in the first four (4) answers before moving
on to the interpretation of your measures.

f=

0.5 = 50%

2

a=

s=

d=

1 .0

- 0↓
10

- 10
0

* Use commas to separate percents within the measure, then use a period at the end of
the measure.

Measure 1:
Measure 2:
Measure 3:
Measure 4:

You are finished with your portfolio!


Portfolio Rubric
1

2

3

All necessary
documents are
present.

Only some items
are present.

Only one item is
missing.

All items are
present.

Documents were
approved by a
teacher.

Only some
documents were
approved by a
teacher.

All but one
document was
approved by the
teacher.

Every document
was approved by
the teacher.

Documents are in
order.

Documents are not
in order.

Documents are
mostly in order

All documents are
in order.

* The rubric for the portfolio only goes to a three because the grading system is based on whether items
are present and completed, not the quality of the work. The quality of work can be a separate grade. I

would suggest calculating those grades as they complete each part, before the portfolio is put together.

Do You Have Everything?

✓Create a Rhythm!

✓Rhythms = Math?

✓Rhythms into Fraction Bars!
OR

✓Rhythms into Pie Graphs!

✓Rhythms into Decimals!
OR

✓Rhythms into Percents!
✓Rubric


Performance Rubric
1
Correct
Rhythms
Correct
Instrumental
Technique

2

3

4

0-7 beats are
played
correctly.

8-11 beats are
played
correctly.

12-15 beats
are played
correctly.

All beats are
played
correctly.

There were 3
or more times
student played
incorrect
technique.

There were 1
or 2 times
student played
incorrect
technique.

The student
used proper
technique the
entire time.

N/A or teacher
discretion.


Possible Extensions
• Change to a different time signature (5/4, 6/8, etc.).
• Students can create all four types of fraction expressions, instead of choosing two.
• Have struggling students write down the addition equation below each of the
measures they are working on, so they can be sure they used four beats.
• Encourage students to use more complex rhythms, such as o, p, jaj, h, etc.
• Have students assess their own work and performance.
• Assign a student to peer-review another student.
• Have students come up with the indicators on each of the rubric themselves.


References
Cox, H. A., & Stephens, L. J. (2006). The effect of music participation on mathematical achievement
and overall academic achievement of high school students. International Journal Of
Mathematical Education In Science & Technology, 37(7), 757-763. doi:
10.1080/002077390500137811
Illinois State Board of Education (2012). Illinois Learning Standards. retrieved from: http://
www.isbe.net/ils/default.htm
Jones, S. M., & Pearson, D. (2013). Music: Highly Engaged Students Connect Music To Math. General
Music Today, 27(1), 18-23. doi: 10.1177/1048371313486478
National Association for Music Education (2012). National Standards for Music Education. Retrieved
from http://musiced.nafme.org/resources/nationalstandards-for-music-education/
National Center for Quality Afterschool (2008). Afterschool Training Toolkit. Retrieved from
http://www.sedl.org/afterschool/toolkits/ and http://www.youtube.com/watch?
v=IzZhSqc_uhU
S. Paradis. (2013). Music and Teaching Materials by Susan Paradis. Retrieved from
http://www.susanparadis.com/catalog.php?ID=SP754


Example of a
Finished Portfolio

From music to math teaching fractions through rhythm to fourth graders

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