FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: FRACTION SCULPTURES 4

FRACTION SCULPTURES

FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: FRACTION SCULPTURES

Learning Description

In this lesson, students will explore fractions through a hands-on, arts-integrated math activity inspired by the sculpture "Seven Magic Mountains". This hands-on activity encourages collaboration, creativity, and the application of mathematical concepts.

 

Learning Targets

GRADE BAND: 4
CONTENT FOCUS: VISUAL ARTS & MATH
LESSON DOWNLOADS:

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can build a sculpture using colored materials and identify the fraction of each color used in my design.
  • I can add fractions with like-denominators.
  • I can work collaboratively with my group to design and build a balanced sculpture inspired by "Seven Magic Mountains”.

Essential Questions

  • How can I describe the parts of a sculpture using fractions?
  • How can I use fractions to design a sculpture?
  • How do we add and subtract fractions with like denominators?

 

Georgia Standards

Curriculum Standards

4.NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Arts Standards

VA4.CR.1 Engage in the creative process to generate and visualize ideas by using subject matter and symbols to communicate meaning.

VA4.CR.2 Create works of art based on selected themes.

VA4.CR.4 Understand and apply media, techniques, processes, and concepts of three-dimensional art.

 

South Carolina Standards

Curriculum Standards

4.NSF.3 Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.

a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Arts Standards

Anchor Standard 1: I can use the elements and principles of art to create artwork.

Anchor Standard 2: I can use different materials, techniques, and processes to make art.

 

Key Vocabulary

Content Vocabulary

  • Fraction - A number that represents a part of a whole
  • Numerator - The number above the line that indicates how many parts of a whole are being counted
  • Denominator - The number below the line that indicates the total number of equal parts in the whole
  • Addition - Combining two or more numbers to find a total or sum
  • Equation - A mathematical sentence that has two equal sides separated by an equal sign
  • Equivalent – Have equal value
  • Like denominator – A denominator that is found in two or more fractions
  • Unlike denominators – Denominators in two or more fractions that are different from each other

Arts Vocabulary

  • Sculpture - A three-dimensional work of art that can be made from a variety of materials, such as wood, clay, metal, or stone.
  • Form - An object that is three-dimensional and encloses volume (cubes, spheres, and cylinders are examples of various forms)
  • Color - An element of art with three properties: 1) Hue: the name of the color, e.g. red, yellow, etc., 2) Intensity: the purity and strength of the color (brightness or dullness), 3) Value: the lightness or darkness of the color (shades and tints)
  • Pattern - Repetition of specific visual elements such as a unit of shape or form

 

Materials

 

Instructional Design

Opening/Activating Strategy

  • Introduction to "Seven Magic Mountains": Show images of Ugo Rondinone's sculpture "Seven Magic Mountains" to students. Have students go through the See, Think, Wonder Artful Thinking Routine.
    • Instruct students to look at the artwork for a moment. Then ask students:
      • What do you see?
      • What do you think about what you see?
      • What do you wonder about?
    • Show the following video to students: The Making of Seven Magic Mountains.
    • Discuss the process of creating a sculpture. Ask students: How does Rondinone use color and form?
      • Discuss how each sculpture can be seen as a “whole,” made up of smaller parts (colors). Ask students how this is like fractions.
    • Review adding fractions with like-denominators.
    • Tell students that they will be using fractions to design and create their own sculptures inspired by “Seven Magic Mountains”.

Work Session

  • Divide students into small groups. Each group will receive colored corn packing peanuts and a damp sponge.
  • Students will first design their sculpture. Tell students that they will sketch out a design for their sculpture inspired by “7 magic Mountains” and label the colors that they will use.
    • Students must use at least four colors of packing peanuts.
    • Students then need to check how many peanuts of each color they need by writing an addition equation, such as: 5/20 yellow peanuts + 7/20 green peanuts + 4/20 blue peanuts + 4/20 orange peanuts = 20/20 peanuts.
  • Students will then build their sculpture based on their design by pressing each peanut onto the damp sponge and then adhering it to another peanut.

Identifying Fractions:

  • After completing their sculptures, groups will count the total number of peanuts used in their design.
  • They will then count how many peanuts of each color were used and express this as a fraction of the total sculpture (e.g., if there are twenty peanuts and four are blue, then 4/20 or 1/5 of the sculpture is blue).

Adding Fractions:

  • Students will then write a word problem to explain how to recreate their sculpture.
  • The word problem should express an addition problem to show how they created their sculpture. For example, if the students used 20 packing peanuts, they would include the following equation in their word problem: 5/20 yellow peanuts + 7/20 green peanuts + 4/20 blue peanuts + 4/20 orange peanuts = 20/20 peanuts.

Closing Reflection

  • Discuss and reflect on the following with students:
    • Reflect on how the sculptures are similar or different in their color compositions.
    • Highlight how fractions are a way to describe these differences mathematically.
    • Discuss how each sculpture can be expressed in terms of a mathematical equation.
    • Have students write a brief reflection on how they used fractions in their sculpture and what they learned about adding fractions.

 

Assessments

Formative

  • Observe student responses during See, Think, Wonder.
  • Observe students during the creation of their sculptures and their discussions within groups about fractions.
  • Use questioning to assess their understanding of fractions as parts of a whole and their ability to add fractions with like-denominators.

Summative

  • Each group will record the total number of peanuts, the fraction of each color, and an addition word problem that expresses the composition of the sculpture.
  • Sculpture reflection: Students’ brief reflection on how they used fractions in their sculpture and what they learned about adding fractions

 

Differentiation 

Accelerated: 

Have students swap their word problems with another group. Each group should then try to follow the word problem to recreate the sculpture. Then, the groups should compare the finished products.

Remedial:

Allow students to express their sculpture in terms of an addition equation without requiring them to write it in the context of a word problem.

 

Additional Resources

https://sevenmagicmountains.com

 

Credits

U.S. Department of Education- STEM + the Art of Integrated Learning

Ideas contributed by: Shannon Green. Edited by: Katy Betts

*This integrated lesson provides differentiated ideas and activities for educators that are aligned to a sampling of standards. Standards referenced at the time of publishing may differ based on each state’s adoption of new standards.

Revised and copyright:  June 2025 @ ArtsNOW

 

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FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: BE THE FRACTION 4

BE THE FRACTION

FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: BE THE FRACTION

Learning Description

Students will bring fractions to life by becoming characters, such as ¼, setting off to find others who will complete their "fraction family" and help them add up to one whole. Through this role-play, students will work together to form complete “wholes” by joining with the right fractional parts.

 

Learning Targets

GRADE BAND: 4
CONTENT FOCUS: THEATRE & MATH
LESSON DOWNLOADS:

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can determine the best way to add and subtract fractions based on their denominators.
  • I can imagine being a fraction and interacting with other fractions to convey math concepts.

Essential Questions

  • How do we add and subtract fractions with like denominators?
  • How do we work with partners to actively embody and express math concepts?

 

Georgia Standards

Curriculum Standards

4.NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Arts Standards

TA4.PR.1  Act by communicating and sustaining roles in formal and informal environments.

 

South Carolina Standards

Curriculum Standards

4.NSF.3 Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.
a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Arts Standards

Anchor Standard 3: I can act in improvised scenes and written scripts.

 

Key Vocabulary

Content Vocabulary

  • Fraction - A number that represents a part of a whole
  • Numerator - The number above the line that indicates how many parts of a whole are being counted
  • Denominator - The number below the line that indicates the total number of equal parts in the whole
  • Addition - Combining two or more numbers to find a total or sum
  • Equation - A mathematical sentence that has two equal sides separated by an equal sign
  • Equivalent – Have equal value
  • Like denominator – A denominator that is found in two or more fractions
  • Unlike denominators – Denominators in two or more fractions that are different from each other

Arts Vocabulary

  • Recite – To speak or read a text out loud in a formal or performative manner
  • Role – A part played by an actor in a play, scene or drama activity
  • Unison – All together at once


Materials

  • Name tags with fractions written on them
  • Individual dry erase boards or note paper and utensils, if needed


Instructional Design

Opening/Activating Strategy

  • Explain that fractions are parts of a whole. Today, they’ll “become” fractions and work together to add up to one whole.
  • Tell the students that each of them will take on the role of a fraction and work with classmates to add up to a whole. Explain that fractions with the same denominator can be added by adding the numerators together.
  • Fraction warm-up game: Play a game where students must “freeze” in shapes that represent different fractions. For instance, a “1/2” could be a shape taking up half the space, while a “1/4” might be a quarter circle. This encourages them to visualize fraction sizes.

Work Session

Like Denominators Chant

  • Discuss/review how to add and subtract fractions. Introduce the following chant (as a projection, handout, or both):

With like denominators, we just add our numerators

And keep the original shared denominator.

With like denominators, we subtract the lesser numerator

From the greater, and keep the same denominator.

  • Work with students to find the best rhythm for the language of the chant. Establish a beat and recite the chant in unison.
  • Possibly, assign lines to individuals or pairs to recite rhythmically.

Role-Play

  • Hand out a fraction card to each student and ask them to wear it on their shirt or hold it visibly.
  • Explain that each student is part of a fraction family but each family has been separated. They must work to find the rest of their fraction family so that when added together, they total one whole.
    • For example, a student with ¼ will need to find others in the “fourths family” with fractions like ¾ or two students with ¼ and 2/4.
  • Have students practice introducing themselves using dialogue. “Hi, I’m ¼”. Students should articulate clearly and project their voices.
  • Allow students time to experiment by joining up with different classmates, testing if their fractions add up to a whole. Encourage them to double-check their math each time they form a new group.
    • Instruct students to stay in character and introduce themselves as the fraction every time they encounter a new student. Students can use dialogue, such as, "I am ¼. Are you the piece I need to make a whole?"
    • Once a group thinks they’ve completed their fraction family, they should write down their fractions in an addition sentence (e.g., ¼ + ¼ + 2/4 = 4/4 or 1).

Closing Reflection

  • Ask each group to share how they reached their solution and explain their thought process. If they made mistakes, ask them to talk about those too and how they adjusted.
    • Ask students: “What was the most challenging part of finding your whole?”.
  • Talk about different ways to make one whole with fractions (e.g., two students with ½, four students with ¼). Write these examples on the board and let students observe the patterns.

Conclude the lesson with the chant:
            With like denominators, we just add our numerators
            And keep the original shared denominator.

            With like denominators, we subtract the lesser numerator
            From the greater, and keep the same denominator.

Assessments

Formative

  • Assess students based on their ability to collaborate, add fractions correctly, and explain their thought process.
  • Observe whether students use their voices to speak the couplets clearly and readily assume the roles of fractions.

Summative

  • Students can accurately write out the equations that reflect their process.
  • Students can create complete fraction families that when added together, equal one whole.


Differentiation

Accelerated: 

  • Challenge students to try making fractions that add up to numbers other than 1, like ½ or ¾.
  • Challenge students to create an illustration of their fraction group adding up to one whole, like a pie chart or bar graph representation.
  • Have students add fractions with unlike denominators.

Remedial:

  • Direct several pairs in front of the class to model the process clearly.
  • Limit the number of denominators so that the focus is on addition.
  • Have students draw a fraction image on their name tag to help with visualization.


Credits

U.S. Department of Education- STEM + the Art of Integrated Learning

Ideas contributed by: Barry Stewart Mann and Katy Betts

*This integrated lesson provides differentiated ideas and activities for educators that are aligned to a sampling of standards. Standards referenced at the time of publishing may differ based on each state’s adoption of new standards.

Revised and copyright:  June 2025 @ ArtsNOW

 

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FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: FRACTIONS IN MOTION 4

FRACTIONS IN MOTION

FRACTION FUSION–WHERE ART AND NUMBERS COLLIDE: FRACTIONS IN MOTION

Learning Description

In this lesson, students will create addition equations using fractions with like denominators. They will work in groups to express this equation in written form and through a movement sequence. The lesson will close with a self-reflection on the project.

 

Learning Targets

GRADE BAND: 4
CONTENT FOCUS: DANCE & MATH
LESSON DOWNLOADS:

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can create and express a fraction addition problem (with like denominators) in a written equation and a movement sequence that utilizes body shapes, levels, and different types of movements.

Essential Questions

  • What different types of body shapes, levels, and movements can I use to express a mathematical concept like adding fractions?
  • How can I represent the addition of fractions with like denominators?

 

Georgia Standards

Curriculum Standards

4. NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Arts Standards

ESD4.CR.1 Demonstrate an understanding of the choreographic process.

ESD4.CN.3 Integrate dance into other areas of knowledge.

 

South Carolina Standards

Curriculum Standards

4.NSF.3 Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.

a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Arts Standards

Anchor Standard 1: I can use movement exploration to discover and create artistic ideas and works.

Anchor Standard 2: I can choreograph a dance.

Anchor Standard 7: I can relate dance to other arts disciplines, content areas, and careers.

 

Key Vocabulary

Content Vocabulary

  • Fraction - A number that represents a part of a whole
  • Numerator - The number above the line that indicates how many parts of a whole are being counted
  • Denominator - The number below the line that indicates the total number of equal parts in the whole
  • Addition - Combining two or more numbers to find a total or sum
  • Equation - A mathematical sentence that has two equal sides separated by an equal sign
  • Equivalent – Have equal value
  • Like denominator – A denominator that is found in two or more fractions
  • Unlike denominators – Denominators in two or more fractions that are different from each other

Arts Vocabulary

  • Movement sequence - A series of movements; a short dance
  • Levels - One of the aspects of movement (there are three basic levels in dance: high, middle, and low)
  • Body shape - Refers to an interesting and interrelated arrangement of body parts of one dancer; the visual makeup or molding of the body parts of a singular dancer; the overall visible appearance of a group of dancers (they may be curved/angular, symmetrical/asymmetrical, positive/negative)
  • Locomotor movement - A movement that travels through space
  • Non-locomotor movement - A movement that does not travel through space (e.g. shaking, bending, stretching, twisting, turning & more)

 

Materials

  • Upbeat instrumental music
  • Speaker or other device with the ability to play music
  • Index cards with various fractions written on them (grouped in pairs by fractions with like denominators)

 

Instructional Design

Opening/Activating Strategy

Move It! Shape It!

  • Provide a vocabulary word or concept to express through movement (see below).
  • When the music plays, students move in their personal space, to express vocabulary given.
    • Upbeat instrumental music is best.
  • When the music stops, students will freeze in a body shape.
  • Repeat as needed.

Vocabulary to utilize: Numerate, denominator, addition, towards, away, equation, various locomotor movements, various non-locomotor movements, low level, middle level, high level

Work Session

  • Review adding fractions with like denominators.
  • Divide the class into groups of three to four students.
    • Give each group a pair of fraction cards.
    • Each group will write an addition equation with their fraction cards including the sum.
    • Each group will choreograph a movement sequence that expresses their equation including the following:
      • Movement for Fraction A
      • Movement for Fraction B
      • Movement for the sum
      • At least two non-locomotor movements
      • at least one locomotor movement
      • All three levels (high, middle, and low)
    • After designated work time, all groups will have a ‘dress rehearsal’. (All groups will perform at the same time and may need two dress rehearsals so that the teacher can assess their work.)
      • After the performances, have each group share their equation.
    • Review audience etiquette with students: Still, silent, supportive.
    • Invite groups that would like to perform their dance for the whole class to do so.
      • Students can comment on:
        • Interesting movements
        • Where they saw certain sequence requirements, etc.
        • How the group used the dance concepts to communicate the mathematical concepts

Closing Reflection

  • Have students complete the following Exit Ticket by answering one or more of the following reflection prompts/questions:
    • Describe how your movements expressed the fraction addition equation.
    • What was the easiest and most challenging part of this task?
    • What did your group do to be successful in this project?
    • What would you change or improve to be more successful?
    • Describe what you learned in this project.

 

Assessments

Formative

  • Teacher observation of students during “Move It! Shape It!” to check for understanding of vocabulary
  • Individual group check-ins during group work time
  • Exit Ticket

Summative

Checklist for ‘Fraction Addition Equation and Movement Sequence”:

  • Was the fraction addition equation written accurately?
  • Was the sum of the fraction equation correct?
  • Did the movement sequence include a movement for each part of the equation? (Fraction A, Fraction B, and Sum)
  • Did the sequence include at least two non-locomotor movements?
  • Did the movement sequence include at least one locomotor movement?
  • Did the movement sequence include all three levels (low, middle, and high)?

 

Differentiation 

Accelerated: 

  • Include mixed fractions
  • Reduce group size

Remedial:

  • Simplify fractions given
  • Intentional grouping
  • Model an example as a class

 

Credits 

U.S. Department of Education- STEM + the Art of Integrated Learning

Ideas contributed by: Christopher Crabb

*This integrated lesson provides differentiated ideas and activities for educators that are aligned to a sampling of standards. Standards referenced at the time of publishing may differ based on each state’s adoption of new standards.

Revised and copyright:  June 2025 @ ArtsNOW

 

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VOLUME OF RIGHT RECTANGULAR PRISMS : DISCOVERING VOLUME THROUGH CHOREOGRAPHY 5

DISCOVERING VOLUME THROUGH CHOREOGRAPHY

VOLUME OF RIGHT RECTANGULAR PRISMS: DISCOVERING VOLUME THROUGH CHOREOGRAPHY

Learning Description

In this lesson, students will discover how the volume of a right rectangular prism can be found by creating choreography to represent the formula for volume.

 

Learning Targets

GRADE BAND: 5
CONTENT FOCUS: DANCE & MATH
LESSON DOWNLOADS:

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can find the volume of a right rectangular prism.
  • I can create a piece of choreography to demonstrate how to find the volume of a right rectangular prism.

Essential Questions

  • How can I create a piece of choreography that demonstrates how to find the volume of a right rectangular prism?
  • How can I find the volume of a rectangular prism?

 

Georgia Standards

Curriculum Standards

5.GSR.8.3 Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.

Arts Standards

ESD5.CR.1 Demonstrate an understanding of the choreographic process.
ESD5.CR.2 Demonstrate an understanding of dance as a form of communication.

 

South Carolina Standards

Curriculum Standards

5.MDA.3 Understand the concept of volume measurement.
a. Recognize volume as an attribute of right rectangular prisms;
b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes;
c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes.

Arts Standards

Anchor Standard 1: I can use movement exploration to discover and create artistic ideas and works.
Anchor Standard 2: I can choreograph a dance.

 

Key Vocabulary

Content Vocabulary

  • Volume - The amount of space occupied by a three-dimensional object or shape
  • Height - The perpendicular distance from the base of a shape or object to its topmost point
  • Length - The distance from one end of an object to the other along its longest side
  • Width - The measurement of the shorter side of an object or shape when compared to its length; it is usually the horizontal dimension
  • Three-dimensional figure - A figure that has length, width, and height

Arts Vocabulary

  • Choreography - The art of designing and arranging sequences of movements, steps, and gestures to create a dance piece
  • Levels - One of the aspects of movement (there are three basic levels in dance: high, middle, and low)
  • Locomotor - a movement that travels through space
  • Non-locomotor - A movement that does not travel through space
  • Rhythm - The pattern of timed beats and movements that align with the music

 

Materials

  • Volume equations
  • Music (optional) for students performances (upbeat instrumental music is recommended)
  • Rubric (see “summative assessment”)

 

Instructional Design

Opening/Activating Strategy

  • Explain to students that different levels can be used in choreography to communicate different ideas.
    • Have students get into a circle facing each other. Explain to them that they will follow your movements.
    • Start showing them one movement and have them copy you to the rhythm of a steady beat.
    • Change the movement to one of a different level. Explain to students that there are levels in dance–high, medium, low. Now, put the two movements together.
    • Next add locomotor movement moving either to the side, front, or back. Put the three movements together and have students follow along. Explain that when we put movements together, we create choreography.
    • Allow students to take turns being the “leader” showing a new movement that the class will follow. Encourage them to utilize levels and locomotor movement to add variety.

Work Session

  • Next, explain to the students that they will be using choreography to help them understand and remember how to find the volume of right rectangular prisms.
    • Address the misconception that volume is the same as area.
  • Divide the students into small groups.
    • Instruct students to create a movement sequence that demonstrates the formula for finding volume.
    • Students must create a movement for length, width, height, and volume as well as a movement to show “multiply” and “equal”. Students will have seven movements total in their choreography.
    • Students must use levels and locomotor and non-locomotor movements in their choreography.
    • Monitor student work by circulating and providing guidance as needed.
    • After groups have choreographed their movement sequences, assign each group three volume equations to solve. Students should use the formula to solve each equation.

 

Closing Reflection

  • As a class, ask students to share one thing they learned about finding volume through choreography. This can be done as a whole class or with a neighboring student.
  • Ask students how they used choreography as a tool of communication in this lesson.

 

Assessments

Formative

  • Ask questions throughout the process to assess whether the students understand volume.
  • Make observations of the choreographic process to ensure the students are using the dance vocabulary and applying it to the task in a meaningful way.

 

 

Summative

  • Student work on the three volume equations
  • Rubric for choreography:
A rubric table with five criteria—Accuracy, Creativity, Execution, Presentation, and Overall Impact—rated from 0 to 3 points, describing performance levels for choreography about discovering volume of right rectangular prisms.

 


Differentiation

Accelerated: 

Challenge students to create their own choreography sequence that represents a different geometric shape. Instruct them to write down the corresponding volume formula and steps to find the volume of the shape they created.

Remedial:

  • Create choreography for the formula to find volume as a class.
  • Have students solve the volume with smaller numbers and whole numbers only.


Credits 

U.S. Department of Education- STEM + the Art of Integrated Learning

Ideas contributed by: SAIL Grant Teacher Leaders

*This integrated lesson provides differentiated ideas and activities for educators that are aligned to a sampling of standards. Standards referenced at the time of publishing may differ based on each state’s adoption of new standards.

Revised and copyright:  June 2025 @ ArtsNOW

 

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VOLUME OF RIGHT RECTANGULAR PRISMS : EXPLORING VOLUME THROUGH MUSICAL DYNAMICS 5

EXPLORING VOLUME THROUGH MUSICAL DYNAMICS

VOLUME OF RIGHT RECTANGULAR PRISMS: EXPLORING VOLUME THROUGH MUSICAL DYNAMICS

Learning Description

Students will learn and apply the formula for finding the volume of a rectangular prism (V = l × w × h) by integrating mathematical concepts with dynamics through an original musical composition.

 

Learning Targets

GRADE BAND: 5
CONTENT FOCUS: MUSIC & MATH
LESSON DOWNLOADS:

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can represent the dimensions and volume of a rectangular prism through musical composition.
  • I can explain how the dynamics in each musical composition reflect the dimensions and volume of the corresponding rectangular prism.

Essential Questions

  • How can we represent the dimensions and volume of a rectangular prism through musical composition?
  • How does the dynamics in each musical composition reflect the dimensions and volume of the corresponding rectangular prism?

 

Georgia Standards

Curriculum Standards

5.GSR.8: Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.

Arts Standards

ESGM5.RE.1 Listen to, analyze, and describe music.

b. Describe music using appropriate vocabulary.

ESGM5.CR.2 Compose and arrange music within specified guidelines.

 

South Carolina Standards

Curriculum Standards

5.MDA.3 Understand the concept of volume measurement.

a. Recognize volume as an attribute of right rectangular prisms;

b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes;

c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes.

Arts Standards

Anchor Standard 1: I can arrange and compose music.

Anchor Standard 6: I can analyze music.

 

Key Vocabulary

Content Vocabulary

  • Two-dimensional shape - An object with height and width
  • Volume - The amount of space occupied by a three-dimensional object or shape
  • Height - The perpendicular distance from the base of a shape or object to its topmost point
  • Length - The distance from one end of an object to the other along its longest side
  • Width - The measurement of the shorter side of an object or shape when compared to its length; it is usually the horizontal dimension
  • Right rectangular prism - A three-dimensional geometric shape with the following characteristics:
    • Faces: It has six faces, all of which are rectangles.
    • Right Angles: Each of its edges meets at a right angle (90°), making it a "right" prism.
    • Parallel and Perpendicular: Opposite faces are parallel, and adjacent faces are perpendicular.
    • Vertices and Edges: It has 8 vertices (corners) and 12 edges.

Arts Vocabulary

  • Dynamics - Loud and soft sounds; volume
    • Piano - Soft
    • Pianissimo - Very soft
    • Mezzo-forte - Moderately loud
    • Forte - Loud
    • Fortissimo - Very loud
    • Crescendo - Get louder
    • Decrescendo - Get softer (synonymous with diminuendo)
  • Form/Composition - The organization of a piece (how the music is put together)

 

Materials

 

Instructional Design

Opening/Activating Strategy

  • Begin by reviewing the formula for finding the volume of a rectangular prism (V = l × w × h).
  • Discuss the three dimensions of the rectangular prism: Length (l), width (w), and height (h).
  • Explain that students will integrate this mathematical concept into the creation of a musical composition.

Work Session

  • Choose a specific rectangular prism model or display a visual representation on the whiteboard.
  • Guide students through the process of calculating the volume using the formula.
  • Emphasize the importance of accurately identifying and labeling the dimensions in cubic units.
  • Play an example of music with varying dynamics (soft to loud). A good example is In the Hall of the Mountain King.
    • Ask students what emotions they felt at various points in the piece and why.
    • Ask students how the tempo (speed of the music) changed. What did this make them feel?
    • Ask students how the dynamics (volume of the music) changed. What did this make them feel?
    • Introduce musical terms related to dynamics:
      • Crescendo (gradually getting louder) and decrescendo (gradually getting softer)
      • Piano - Soft
      • Pianissimo - Very soft
      • Mezzo-forte - Moderately loud
      • Forte - Loud
      • Fortissimo - Very loud
      • Crescendo - Get louder
      • Decrescendo - Get softer (synonymous with diminuendo)
    • Connect the concept of volume in mathematics to the dynamic levels in music. The smaller the volume, the softer the sound.
    • Introduce students to various body percussion techniques–clapping, snapping, stomping, patting, tapping, etc.
    • Divide the class into small groups.
    • Provide each group with four rectangular prism models or visual representations.
    • Instruct students to create a short musical composition using body percussion that mirrors the dimensions and volume of the given rectangular prisms.
      • Compositions should include one body percussion sound for each dimension and one for the volume. This will mean that students must calculate the volume for each prism. There will be 16 sounds total in the composition.
      • Encourage creativity in using dynamics to represent the mathematical dimensions. Students should connect that the smaller the volume or dimensions the softer the sound.

 

Closing Reflection

  • Each group will perform their musical composition for the class. After each performance, discuss how changes in dynamics reflected the dimensions and volume of the corresponding rectangular prism.
  • Reflect as a class on how dynamics connect to mathematical concepts like volume.

 

Assessments

Formative

  • The teacher will observe students’ ability to recognize changes in dynamics during listening to a musical sample.
  • The teacher will make observations during the musical composition activity, focusing on the incorporation of volume-related dynamics.
  • The teacher will solicit informal reflections through question and answer from students on the relationship between volume in mathematics and dynamics in music.

 

 

Summative

  • Students can compose a musical piece using body percussion that demonstrates their understanding of volume through their use of dynamics.
  • Students will submit their calculations for all four assigned prisms.

 

Differentiation 

Accelerated: 

  • Allow students to incorporate “found sound” (making sounds with objects that are readily available like tapping pencils together or tearing paper) into their compositions.
  • Allow students to use Incredibox to compose their pieces.
  • Have students record and explain their pieces using a platform such as Flipgrid.

Remedial:

  • Reduce the number of prisms students must calculate and use in their composition from four to two.
  • Scaffold the lesson by creating a composition for one prism together as a class talking through the process of choosing body percussion and dynamics.

 

Credits 

U.S. Department of Education- STEM + the Art of Integrated Learning

Ideas contributed by: SAIL Grant Teacher Leaders

*This integrated lesson provides differentiated ideas and activities for educators that are aligned to a sampling of standards. Standards referenced at the time of publishing may differ based on each state’s adoption of new standards.

Revised and copyright:  June 2025 @ ArtsNOW

 

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