from music to math teaching fractions through rhythm to fourth graders

$: From music to math teaching fractions through rhythm to fourth graders$
From Music To Math:Teaching Fractions through Rhythm to Fourth Graders

By: Beth Campbell, Music Educator, Illinois School District 73

From Music to Math: Teaching Fractions Through Rhythm

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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 [email protected]. You can also contact me at http://doremiandsoon.blogspot.com/.


mailto:[email protected]

mailto:[email protected]

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 music7. Evaluating music and music performances.8. Understanding relationships between music, the other arts, and disciplines outside

the arts.


http://www.corestandards.org/Math/Content/4/NF/B/3/a

http://www.corestandards.org/Math/Content/4/NF/B/3/a

http://www.corestandards.org/Math/Content/4/NF/B/3/d

http://www.corestandards.org/Math/Content/4/NF/B/3/d

http://www.corestandards.org/Math/Content/4/NF/C/6




Hooks, Warm Ups, and ManipulativesVideo Connection between Math and Music:http://www.youtube.com/watch?v=IzZhSqc_uhUThis 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 multi-media 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.


0

25

50

75

100

Whole Note Half Note Quarter Note Eighth Note Sixteenth Note

http://www.youtube.com/watch?v=IzZhSqc_uhU


Whole Note Half Notes Quarters, Eighths, Sixteenths

Note Name 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 ActivityThe 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=SP754http://susanparadis.wordpress.com/2008/10/01/rhythmn-pizza-on-foam-board/


http://www.susanparadis.com/catalog.php?ID=SP754


http://susanparadis.wordpress.com/2008/10/01/rhythmn-pizza-on-foam-board/

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) a= ___ beat(s)

s= ___ notes in a beat d= ___ notes in a beat

4

4

Teacher Initials: _______________Great! You are ready for the next phase!


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= s= d=

Measure 1:

Measure 2:

Measure 3:

Measure 4:



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= d=

Measure 1 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 a= s= d=2 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:

Teacher Initials: _______________ 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% a= s= d=2 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:

Teacher Initials: _______________ You are finished with your portfolio!


Portfolio Rubric1 2 3

All necessary documents are

present.

Documents were approved by a

teacher.

Documents are in order.

Only some items are present.

Only one item is missing.

All items are present.

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 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 Rubric1 2 3 4

Correct Rhythms

Correct Instrumental Technique

0-7 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.isbe.net/ils/default.htm




http://musiced.nafme.org/resources/national

http://musiced.nafme.org/resources/national

http://www.sedl.org/afterschool/toolkits/

http://www.sedl.org/afterschool/toolkits/









Example of a Finished Portfolio
