Composing With Fractions
Content: Music & Math (Fractions) Teacher: Bobbi Jo Will
Topic: Pie Graphs, Fractions, and Composing Date: November 12th, 2009
Level: Grade4 Time: 45 minutes
Standards:
National Standards for Music:
1. Given instruction, group collaboration, and accompanying materials, students will compose a four measure song utilizing the fraction/pie graph form.
2. Given instruction and group collaboration, students will perform the four measure 'song' that the group created using various instruments.
3. Given instruction and measures visible on overhead, students will perform the class song (each group’s four measures put together into one song) using various instruments.
Materials:
Since students learn in a wide variety of ways, it is vital for teachers to differentiate instruction. Visual and multidisciplinary instruction is becoming increasingly important due to the multitude of learners we have in our classrooms. When students can see that what they are learning is connected to other subject matter, they may see it as more applicable to their lives. This composition activity will allow students to practice manipulating fractions. The learning objective is sort of hidden in this activity since the students may be focused more on composing measures with a total of four beats (focusing more on the musical composition format).
Background for teachers
Math is all around us. We use it in our everyday lives without even realizing it. This lesson is to show students one way math is connected to music.
Fraction: a number that can represent a 'part' over a 'whole'. Example: ½, ¾, 9/10
Pie/Circle Graphs (called both) are used to represent a part to whole relationship. I decided to use a pie graph for this lesson because an entire measure can be seen as the 'whole' while the individual notes in the measure is the 'parts.'
Steps in Lesson:
Introduction/Building Background Knowledge:
· Review notes and beat values in 4/4 time signature.
o Whole note=four beats
o Half note= 2 beats
o Quarter note= 1 beat
o Eighth note= ½ beat
o 1 measure= 4 beats
· Review of pie/circle graph
o Visual representation of data
Body
· Today we are using a pie graph to visually represent one measure (4 beats), which is the whole.
· Draw full pie graph (full circle) on overhead to represent the entire measure.
o How many beats are in this measure if the time signature is 4/4?
· Draw another full pie graph under the 'measure'.
o If the fractional pieces of the pie graph represent notes, how many beats is this note?
§ 4 beats---whole note
· Repeat this exercise with half note, quarter note, and eighth note.
o How many eighth notes can there be in one measure?
§ Model putting eight eighth notes into the ‘measure’ pie graph
· Let's try to create a measure as a class. Ask for students to volunteer suggestions for notes.
o Model doing it correctly and incorrectly
o Add note values underneath the measures
§ ¼ + ½ + ¼ = 4/4 = 1 (the whole)
§ Show how if you put the fractional pieces together, it will make a 'whole' pie graph.
§ Remember last week we learned equivalent fractions? (8/8=4/4=1)
§ What would this measure we created song like?
· Count 4 beats before students start clapping.
· Clapping together
· Now we are going to work with our classmates to compose four measures using this pie graph fraction method.
o Directions:
§ Work together to compose four measures
§ Use a variety of notes to make the piece interesting for audience
§ So what should each measure add up to? (1 whole=4/4 or 8/8, etc.)
· Check for understanding…any questions?
o Thumbs up if you understand, thumbs sideways if you somewhat understand, thumbs down if you are confused
· Break class into four groups. Hand them an envelope of 'notes'- fractional pieces, accompanying worksheet, and transparency.
Closure
1. Each group performs their composition with available instruments.
2. Put each group's four measure song into one sixteen measure 'class song.' Perform together with instruments.
3. Discussion about what would happen if the time signature was different…would the activity change? How?
4. Class discussion on their thoughts of the activity.
a. Did this help their understanding?
b. Did they like doing this?
Assessment
· Teacher will informally assess individual participation during whole class discussion and small group work.
· Teacher will formally assess each group’s four measure composition and check for understanding of the content (are their four beats in each measure?, Did they use a variety of notes?)
· Teacher will assess student performance to see if all group members are participating in the performance.
Adaptations/Extensions:
Since this lesson pertains to different representations of musical notes, it would be interesting to extent this lesson to have the students evaluate how people in different countries write and/or represent music notes. Does everyone use time signatures and scales?
Next Steps/Connections to Other Subjects:
I could proceed by implementing a lesson where students also incorporate dotted half notes, sixteenth notes, etc. Students could also investigate and create a visual representation for composing music with a time signature of 3/4, 6/8, etc. Students could also create melodies by assigning the fractional parts to a specific note on the scale.
Content: Music & Math (Fractions) Teacher: Bobbi Jo Will
Topic: Pie Graphs, Fractions, and Composing Date: November 12th, 2009
Level: Grade4 Time: 45 minutes
Standards:
National Standards for Music:
- 4.b. Create and arrange short songs and instrumental pieces within specific guidelines.
- 5.a. Read whole, half, quarter, and eighth notes and rests in 2/4, ¾, and 4/4 meter signatures.
- A.4.3 Connect mathematical learning with other subjects, personal experiences, current events, and personal interests
- see relationships between various kinds of problems and actual events
- use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies)
- B.4.1 Represent and explain whole numbers*, decimals, and fractions with
- physical materials
- number lines and other pictorial models*
- verbal descriptions
1. Given instruction, group collaboration, and accompanying materials, students will compose a four measure song utilizing the fraction/pie graph form.
2. Given instruction and group collaboration, students will perform the four measure 'song' that the group created using various instruments.
3. Given instruction and measures visible on overhead, students will perform the class song (each group’s four measures put together into one song) using various instruments.
Materials:
- Collection of pie graph fractional pieces (many for each group)- whole notes (whole circle), half notes (half circle), quarter notes (quarter circle), and eighth notes (eighth of circle).
- 1 Worksheet for each group that summarizes note/pie graph piece value and four measures for pie pieces to be placed onto
- 1 Transparency for each group to place their final composition onto (tape or just setting onto transparency)
- Overhead
- 1 transparency with 16 measures
- Various Musical Instruments (instruments available in room including using personal belongings and body)
Since students learn in a wide variety of ways, it is vital for teachers to differentiate instruction. Visual and multidisciplinary instruction is becoming increasingly important due to the multitude of learners we have in our classrooms. When students can see that what they are learning is connected to other subject matter, they may see it as more applicable to their lives. This composition activity will allow students to practice manipulating fractions. The learning objective is sort of hidden in this activity since the students may be focused more on composing measures with a total of four beats (focusing more on the musical composition format).
Background for teachers
Math is all around us. We use it in our everyday lives without even realizing it. This lesson is to show students one way math is connected to music.
Fraction: a number that can represent a 'part' over a 'whole'. Example: ½, ¾, 9/10
Pie/Circle Graphs (called both) are used to represent a part to whole relationship. I decided to use a pie graph for this lesson because an entire measure can be seen as the 'whole' while the individual notes in the measure is the 'parts.'
Steps in Lesson:
Introduction/Building Background Knowledge:
· Review notes and beat values in 4/4 time signature.
o Whole note=four beats
o Half note= 2 beats
o Quarter note= 1 beat
o Eighth note= ½ beat
o 1 measure= 4 beats
· Review of pie/circle graph
o Visual representation of data
Body
· Today we are using a pie graph to visually represent one measure (4 beats), which is the whole.
· Draw full pie graph (full circle) on overhead to represent the entire measure.
o How many beats are in this measure if the time signature is 4/4?
· Draw another full pie graph under the 'measure'.
o If the fractional pieces of the pie graph represent notes, how many beats is this note?
§ 4 beats---whole note
· Repeat this exercise with half note, quarter note, and eighth note.
o How many eighth notes can there be in one measure?
§ Model putting eight eighth notes into the ‘measure’ pie graph
· Let's try to create a measure as a class. Ask for students to volunteer suggestions for notes.
o Model doing it correctly and incorrectly
o Add note values underneath the measures
§ ¼ + ½ + ¼ = 4/4 = 1 (the whole)
§ Show how if you put the fractional pieces together, it will make a 'whole' pie graph.
§ Remember last week we learned equivalent fractions? (8/8=4/4=1)
§ What would this measure we created song like?
· Count 4 beats before students start clapping.
· Clapping together
· Now we are going to work with our classmates to compose four measures using this pie graph fraction method.
o Directions:
§ Work together to compose four measures
§ Use a variety of notes to make the piece interesting for audience
§ So what should each measure add up to? (1 whole=4/4 or 8/8, etc.)
· Check for understanding…any questions?
o Thumbs up if you understand, thumbs sideways if you somewhat understand, thumbs down if you are confused
· Break class into four groups. Hand them an envelope of 'notes'- fractional pieces, accompanying worksheet, and transparency.
Closure
1. Each group performs their composition with available instruments.
2. Put each group's four measure song into one sixteen measure 'class song.' Perform together with instruments.
3. Discussion about what would happen if the time signature was different…would the activity change? How?
4. Class discussion on their thoughts of the activity.
a. Did this help their understanding?
b. Did they like doing this?
Assessment
· Teacher will informally assess individual participation during whole class discussion and small group work.
· Teacher will formally assess each group’s four measure composition and check for understanding of the content (are their four beats in each measure?, Did they use a variety of notes?)
· Teacher will assess student performance to see if all group members are participating in the performance.
Adaptations/Extensions:
Since this lesson pertains to different representations of musical notes, it would be interesting to extent this lesson to have the students evaluate how people in different countries write and/or represent music notes. Does everyone use time signatures and scales?
Next Steps/Connections to Other Subjects:
I could proceed by implementing a lesson where students also incorporate dotted half notes, sixteenth notes, etc. Students could also investigate and create a visual representation for composing music with a time signature of 3/4, 6/8, etc. Students could also create melodies by assigning the fractional parts to a specific note on the scale.
