ARTFUL EQUATIONS – ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS | FRACTION SCULPTURES 5

FRACTION SCULPTURES

ARTFUL EQUATIONS–ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS:FRACTION SCULPTURES

Learning Description

In this lesson, students will explore fractions through a hands-on, art-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: 5
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 compare and contrast fractions from different sculptures created by other groups.
  • I can work collaboratively with my group to design and build a balanced sculpture inspired by "Seven Magic Mountains”.

Essential Questions

  • How do we add and subtract fractions with like and unlike denominators?
  • How can I use fractions to represent different parts of a whole in a piece of art?
  • How does comparing fractions help us understand similarities and differences in artworks?

 

Georgia Standards

Curriculum Standards

5.NR.3.3 Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Arts Standards

VA5.CR.2 Create works of art based on selected themes.

VA5.CR.4 Understand and apply media, techniques, processes, and concepts of three-dimensional works of art.

 

South Carolina Standards

Curriculum Standards

5.NSF.1 Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line.

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 signFractions

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" using See, Think, Wonder Artful Thinking Routine.
  • Show the following video to students: The Making of Seven Magic Mountains
  • Discuss the process of creating a sculpture. How does Rondinone use color and form?
  • Discuss how each sculpture can be seen as a “whole”, made up of smaller parts (colors), which represents fractions.

Work Session

  • Divide students into small groups. Each group will receive colored corn packing peanuts and a damp sponge.
  • Ask students to sketch out their ideas for a sculpture using at least four colors of packing peanuts inspired by “Seven Magic Mountains”.
  • Once students have designed their sculptures, they will build their design according to their sketch 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 30 peanuts and 10 are blue, then 10/30 or 1/3 of the sculpture is blue).
  • Have students complete the first two columns of the chart for their own sculpture.

Comparing and Adding Fractions:

  • Review how to compare fractions with like and unlike denominators.
  • Each group will compare the fractions of their sculpture’s colors with those of another group recording their findings on the chart
  • Then, have students add their fractions of like colors together and record them in the last column of the chart.

Closing Reflection

  • Reflect on how the sculptures are similar or different in their color compositions.
  • Highlight how fractions are a way to describe these differences mathematically.
  • Students will write a brief reflection on how they used fractions in their sculpture and what they learned about comparing and adding fractions with different denominators.

 

Assessments

Formative

  • Observe students during the creation of their sculptures and discussions within groups about fractions.
  • Use questioning to assess their understanding of fractions as parts of a whole and their ability to compare fractions.

Summative

  • Each group will record the total number of peanuts, the fraction of each color, and the comparison of fractions with another group.
  • Completed sculpture fraction chart with correct sums of fractions
  • Sculpture reflection: Students will write a brief reflection on how they used fractions in their sculpture and what they learned about comparing and adding fractions with different denominators.

 

Differentiation 

Acceleration: 

  • Set a minimum number of packing peanuts students must use in their sculptures.
  • Have students choose a denominator that is not a multiple of ten or five.

Remediation:

  • Limit the number of total packing peanuts students can use in their sculptures to a denominator students can manage.
  • Pair groups together of differing ability levels when adding and comparing fractions to support students with lower level skills.
  • Model the process of converting fractions.
  • Have students choose a denominator that is a multiple of ten or five.

 

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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ARTFUL EQUATIONS – ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS | IT’S ABOUT THE, LIKE, DENOMINATORS 5

IT’S ABOUT THE, LIKE, DENOMINATORS

ARTFUL EQUATIONS–ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS:IT’S ABOUT THE, LIKE, DENOMINATORS

Learning Description

Students will embody fractions, with awareness of their multiple equivalent expressions, to explore adding and subtracting with other fractions with like and unlike denominators.

 

Learning Targets

GRADE BAND: 5
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 and unlike denominators?
  • How do we work with partners to actively embody and express mathematical concepts?

 

Georgia Standards

Curriculum Standards

5.NR.3.3 Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Arts Standards

TA5.PR.1  Act by communicating and sustaining roles in formal and informal environments.

 

South Carolina Standards

Curriculum Standards

5.NSF.1 Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line.

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

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 equivalent fractions groupings (Fraction Role Cards Template)
  • Individual dry erase boards or note paper and utensils, if needed
  • Image of fraction chant

 

Instructional Design

Opening/Activating Strategy

Count-Up

  • Class tries to count up from the number one, one voice at a time, randomly. If two people say the same number, a new round starts. Emphasize that it is a listening game. Establish the rule that the same person can’t say the first number two rounds in a row. Stop the game and start a new round if a pattern of students participating emerges.
  • After Counting Up 1-2-3-etc., count by twos, threes, fours and sixes.
  • After Counting Up with whole numbers, use fractions:
    • Unit fractions: 1/2, 1/3, 1/4, 1/5, etc.
    • Equivalent fractions: 1/2, 2/4, 3/6, 4/8, etc.

Explain that these number and fraction sequences will be useful in the day’s lesson.

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 unlike denominators, we’ll wait to add later: After we find our common denominator.

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

With unlike denominators – we can’t subtract:  Till we find our common denominator, that’s a fact.

  • 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:

  • Assign each student a fraction role with a name tag. Depending on numbers, the same identity may be assigned to two or even three students.  Use the accompanying template or create tags for the following:

Hi I’m 1/2, 2/4, 3/6, 4/8

Hi I’m 1/3, 2/6, 3/9, 4/12

Hi I’m 2/3, 4/6, 6/9, 8/12

Hi I’m 1/4, 2/8, 3/12, 4/16

Hi I’m 3/4, 6/8, 9/12, 12/16

Hi I’m 1/6, 2/12, 3/18, 4/24

Hi I’m 5/6, 10/12, 15/18, 2/24

Hi I’m 1/8, 2/16, 3/24, 4/32

Hi I’m 3/8, 6/16, 9/24, 12/32

Hi I’m 5/8, 10/16, 15/24, 20/32

Hi I’m 7/8, 14/16, 21/24, 28/32

  • Have students practice introducing themselves using ‘aka’ or ‘also known as’ or, simply, ‘or.’ g., “Hi, I’m 3/4, aka 6/8, aka 9/12, aka 12/16.”  Let them introduce themselves to one another randomly.
  • Have students pair up. After introducing themselves to their partner, have them decide which of their identities to assume. Instruct them that their goal is to add themselves together. Redirect them to the chant and tell them to determine which couplet applies:

 

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

With unlike denominators, we’ll wait to add later:  After we find our common denominator.

  • If they have a common denominator, each using one of their several identities, they will use the first couplet. If they have chosen fractions without a common denominator, but can switch to equivalent fractions with a common denominator, they can do that, reciting the second couplet, and then the first. If they cannot find a common denominator, they will use the second couplet.  Each pair should recite the appropriate couplet in unison.
  • With individual dry erase boards or note paper and utensils, have students write out the calculations that reflect their simple scene. E.g., “3/4 + 3/24 = ?; 9/16 + 2/16 = 11/16”.
  • This process can be repeated with several partners.
  • Then have the students repeat the process but with the instruction that their goal is to subtract. Remind them that they will have to look for common denominators, and also determine which fraction has the greater value and which the lesser.  Have them select and recite from the third and fourth couplets:

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

With unlike denominators – we can’t subtract:  Till we find our common denominator, that’s a fact.

Optional: Have students trade roles, so they engage in the process with a new set of equivalent fractions.

Closing Reflection

  • Ask students: What was easy or hard about the activity? What was fun or interesting?
  • Ask students: How do we add and subtract fractions with like denominators? With unlike denominators?

 

Assessments

Formative

  • The teacher will observe how/whether:
    • Student pairs interact, choose fraction identities, and select and recite the appropriate couplet.
    • Students work together effectively and collaboratively.
    • Students use their voices to speak the couplets clearly.
    • Students readily assume the roles of fractions.

Summative

Students accurately write out the equations that reflect their process.

 

Differentiation 

Acceleration: 

  • Add mixed numbers to the collection of fraction roles.

Remediation:

  • Direct several pairs in front of the class to model the process clearly.
  • Reduce the number of possible roles to simplify the range of choices.

 

Credits

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

Ideas contributed by: Barry Stewart Mann, MFA

*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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ARTFUL EQUATIONS – ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS | FRACTIONS IN MOTION 5

FRACTIONS IN MOTION

ARTFUL EQUATIONS–ADDING AND SUBTRACTING WITH UNLIKE DENOMINATORS:FRACTIONS IN MOTION

Learning Description

In this lesson, students will create addition equations using fractions with unlike 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: 5
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 unlike denominators) in a written equation and a movement sequence that utilizes body shapes, levels, different types of movements, and varying relationships with other dancers.

Essential Questions

  • How do we add and subtract fractions with like and unlike denominators?
  • How can we represent the process of adding fractions with unlike denominators through written equations and movement?
  • How can we collaborate with others to show the relationship between fractions in a dance sequence?

 

Georgia Standards

Curriculum Standards

5. NR.3.3 Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Arts Standards

ESD5.CR.1 Demonstrate an understanding of the choreographic process.

ESD5.CN.3 Integrate dance into other areas of knowledge.

 

South Carolina Standards

Curriculum Standards

5.NSF.1 Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line.

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

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)
  • Relationship (self to others) - How dancers interact with other dancers in the space (close to, far away from, facing each other, facing different ways, etc.)

 

Materials

  • Upbeat instrumental music
  • Speaker or other device w/the ability to play music
  • Index cards with various fractions written on them

 

Instructional Design

Opening/Activating Strategy

Move It! Shape It!

  • Provide a vocabulary word or concept to express through movement.
  • When the music plays, students will move in their personal space, to express the vocabulary provided.
    • Teacher tip: Upbeat instrumental music is best.
  • When the music stops, students will freeze in a body shape.
  • Introduce levels (high–standing tall, middle, and low–low to the ground) and locomotor and non-locomotor movements.
  • Repeat as needed.

Vocabulary to utilize: Numerate, denominator, addition, equation, various locomotor movements, various non-locomotor movements, low level, middle level, high level, facing other students, not facing others, close proximity to others, far proximity to others

Work Session

  • Review adding fractions with like denominators. Next, review how to convert fractions that have different denominators into fractions that have like denominators.
  • Divide students into small groups of three to four.
    • 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. Movement sequences should include the following:
      • Movements:
        • Movement for numerator of Fraction A
        • Movement for denominator of Fraction A
        • Movement for numerator of Fraction B
        • Movement for denominator of Fraction B
        • Movement to represent for converting fractions to find the same denominator
        • Movement for the NEW numerator of Fraction A
        • Movement for the NEW denominator of Fraction A
        • Movement for NEW numerator of Fraction B
        • Movement for NEW denominator of Fraction B
        • Movement for the Sum
      • Students must also include the following when choreographing their movements:
        • Two types of relationships: Self to others (near/far, facing/not facing)
        • At least two non-locomotor movements
        • At least one locomotor movement
        • All three levels (high, middle, and low)
      • Before allowing groups to choreograph, ask them to think about how they would use levels, locomotor/non-locomotor movements, and relationships to express the mathematical concepts.
        • For example, students may say that locomotor movements may show converting fractions; students may say that a high level would represent a numerator and a low level would represent a denominator.
      • After work time, all groups will have a ‘dress rehearsal’. (All groups perform at the same time and may need two dress rehearsals so that the teacher can assess their work.)
        • After the rehearsals, have each group share their equation.
      • Invite groups that would like to perform their dance for the whole class to do so.
        • Review audience etiquette: Still, silent, supportive.
        • After each performance, have students analyze/give feedback on the group’s sequence. 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 questions:
    • Describe how your movements expressed the fraction addition equation.
    • What steps did you use to solve the equation?
    • What was the easiest and most challenging part of this project?
    • 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 addition equation correct?
    • Did the movement sequence include a movement for each part of the equation? (Fraction A, Fraction B, and Sum)
    • Did the sequence express two types of relationship: Self to others (near/far, facing/not facing)?
    • 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 

Acceleration: 

  • Include mixed fractions
  • Reduce group size

Remediation:

  • Simplify fractions given
  • Intentional grouping

 

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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CREATIVE CALCULATIONS – MULTIPLICATION AND DIVISION | MULTIPLICATION SCULPTURES 4

MULTIPLICATION SCULPTURES

CREATIVE CALCULATIONS–MULTIPLICATION AND DIVISION:MULTIPLICATION SCULPTURES

Learning Description

In this lesson, students will explore multiplication through a hands-on, art-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 design and build a sculpture inspired by “Seven Magic Mountains”.
  • I can use multiplication to find the cost of my sculpture based on the number of colored peanuts used.
  • I can add the costs of each color to find the total cost of my sculpture.

Essential Questions

  • How can I use multiplication to find the total cost of my art project?
  • How do choices in design impact the final outcome of an artwork?

 

Georgia Standards

Curriculum Standards

4.NR.2.3 Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NR.2.5 Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.

Arts Standards

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

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

VA4.CN.3 Develop life skills through the study and production of art (e.g. collaboration, creativity, critical thinking, communication).

 

South Carolina Standards

Curriculum Standards

4.NSBT.5 Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations.

4.NSBT.6 Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

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.

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

 

Key Vocabulary

Content Vocabulary

  • Multiplication - Repeated addition of numbers of the same size
  • Factors - The integers that divide that number without leaving a remainder
  • Product - The result of multiplying two or more numbers together
  • Equation - A mathematical sentence that has two equal sides separated by an equal sign
  • Cost - The amount of money required to purchase, produce, or maintain something

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". Lead students through the See, Think, Wonder Artful Thinking Routine.
    • Tell 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?

Work Session

  • Divide students into small groups. Each group will receive colored corn packing peanuts and a damp sponge.
  • Assign a three-digit number to each color of packing peanuts.
  • Ask students to sketch out their ideas for a sculpture using at least four colors of packing peanuts inspired by “ 7 Magic Mountains”.
  • ​​Students will build their design according to their sketch by pressing each peanut onto the damp sponge and then adhering it to another peanut.

Calculating cost:

  • After completing their sculptures, groups will use the assigned costs to determine the total price of their sculpture.
  • For each color used, students will multiply the number of peanuts by the cost of that color. For example, if 20 red peanuts are used and red costs $125, they will calculate 20 × 125.

They will record these calculations on their multiplication recording sheets. After finding the total for each color, groups will add up the amounts to determine the overall cost of their sculpture.

Closing Reflection

  • Have groups share their sculptures and their total costs with the class.
  • Reflect on how different choices in the design (such as the use of more expensive colors) affected the overall cost.
  • Discuss how multiplication and addition are used together to solve real-world problems.

 

Assessments

Formative

  • Observe students as they design their sculptures, keeping track of how they calculate costs and solve multiplication problems.
  • Use questioning to assess their understanding of multiplication and addition in the context of real-world scenarios.

Summative

  • Each group will record the number of each color used, the multiplication problem for each, and the sum of all costs.
  • Students will write a brief reflection on their design process, how they calculated the cost, and what strategies they used to solve the multiplication problems.

 

Differentiation 

Acceleration: 

  • Challenge students to calculate the cost of their sculpture if each peanut’s price increased by 10%.
  • Incorporate a comparison activity where students analyze which group’s sculpture was the most and least expensive and why.

Remediation:

  • Limit the number of peanuts and/or colors students can use to keep the multiplication numbers manageable.
  • Set the prices for the packing peanuts at a number that is manageable for students.

 

Additional Resources

Examples of ancient Roman mosaics

 

Credits

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

Ideas contributed by: Shannon Green

*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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CREATIVE CALCULATIONS – MULTIPLICATION AND DIVISION | MOSAICS AND MATH 4

MULTIPLICATION WITH MEDIEVAL TIMES

CREATIVE CALCULATIONS–MULTIPLICATION AND DIVISION:MOSAICS AND MATH

Learning Description

In this lesson, students will use multiplication and division to create a mosaic using a watercolor crayon resist.

 

Learning Targets

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

Download PDF of this Lesson

"I Can" Statements

“I Can…”

  • I can use multiplication and division to create a mosaic.
  • I can use crayon and watercolor to create a crayon watercolor resist painting.
  • I can determine factors of a given number.

Essential Questions

  • How can you utilize multiplication and division to create a mosaic?
  • How can you use an array to determine factors of a given number?

 

Georgia Standards

Curriculum Standards

4.NR.2.3 Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NR.2.5 Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.

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.3 Understand and apply media, techniques, processes, and concepts of two dimensional art.

VA4.CN.3 Develop life skills through the study and production of art (e.g. collaboration, creativity, critical thinking, communication).

 

South Carolina Standards

Curriculum Standards

4.NSBT.5 Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations.

4.NSBT.6 Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

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.

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

 

Key Vocabulary

Content Vocabulary

  • Equation - A mathematical sentence that has two equal sides separated by an equal sign
  • Array - A way of arranging objects or images in rows and columns
  • Multiplication - Repeated addition of numbers of the same size
  • Factors - The integers that divide that number without leaving a remainder
  • Product - The result of multiplying two or more numbers together
  • Division - Repeated subtraction of numbers of the same size

Arts Vocabulary

  • Line - A continuous mark made on some surface by a moving point. It may be two dimensional, like a pencil mark on a paper or it may be three dimensional (wire) or implied (the edge of a shape or form) often it is an outline, contour or silhouette.
  • Shape - A flat, enclosed line that is always two-dimensional and can be either geometric or organic
  • Space - The distance or area between, around, above or within things. Positive space refers to the subject or areas of interest in an artwork, while negative space is the area around the subject of an artwork. It can be a description for both two and three-dimensional portrayals.
  • Watercolor wash - A layer of watercolor that completely covers a surface and is translucent
  • Watercolor resist - A technique where specific areas of a paper being painted with watercolor are protected from absorbing paint using a resist material, such as wax (like a crayon or oil pastel) or tape
  • Mosaic - An artform that is a picture or pattern produced by arranging together small colored pieces of hard material, such as stone, tile, or glass (Oxford Languages)
  • Composition - How an artist arranges the Elements of Art (line, shape, form, value, color, space, texture) to create an artwork
  • Warm colors - Yellow, orange, red (and shades of each)
  • Cool colors - Purple/violet, blue, green (and shades of each)
  • Analogous colors - Colors next to each other on the color wheel (Example: red, orange, yellow)
  • Complementary colors - Colors that are across from each other on the color wheel (Example: Orange and blue)
  • Contrast - The arrangement of opposite elements in a composition (light vs. dark, rough vs. smooth, etc.) Similar to variety, which refers to the differences in a work, achieved by using different shapes, textures, colors and values.

 

Materials

  • 9 x 12-inch black construction paper
  • Printed 10x10 arrays on cardstock
  • Crayons or oil pastels in a variety of colors
  • Watercolor set
  • Paintbrushes
  • Water cups with water
  • Pencil
  • Scissors
  • Glue sticks
  • Paper towels
  • Color wheel

 

Instructional Design

Opening/Activating Strategy

Ancient math mosaic depicting an elephant adorned with decorative patterns, standing among round shields featuring geometric designs in shades of brown, yellow, and red—a striking tribute to division and multiplication in art.

  • Ask students to identify the colors, lines, and shapes that they see in the artwork.
  • Have students compare their findings with a partner.
  • Ask students how they think this artwork was made.
    • Define for students what a mosaic is. Explain that a mosaic is an artform in which an image is created by putting together separate pieces of material, such as small square stones.
      • Students should understand that in a mosaic, the image is created by combining individual pieces of a material.
    • Explain that Shape is one of the seven elements of art that they will be using to create their own mosaic.

Optional: For context, show students where the ancient Roman Empire was in relationship to where students live.

Work Session

Teacher notes:

  • Based on how much time you have available, this artwork can be created without adding a watercolor wash. Students can use crayons, colored pencils, markers, oil pastels, etc. to create designs on their array.
  • This lesson can be chunked over multiple days.

Introduce the Artwork:

  • Explain that students will be focusing on the Elements of Art: Line, Shape, and Space, in their mosaic.
  • Show students an example of an array (sample array).
  • Ask students to use mathematical concepts that they have learned to determine how many unit squares they have.
  • Next, ask students how many factor pairs there are and what the factors are in order of least to greatest.
  • Pass out a 10x10 array printed on cardstock.
  • Have students select one factor pair of 24. Students should use the 10x10 array to create an array of their factor pair (or allow them to create their own array if they want to do 1 x 24 or 2 x12).
  • Tell students that in the next step they will be creating a watercolor-resist painting. They will draw with crayon and paint over the crayon with watercolor. The wax in the crayon will “resist” the water in the watercolor.
    • Encourage students to draw various types of overlapping lines to their array. Give students three to five minutes to add lines to their array.
  • Optional: Show students a color wheel.
    • Discuss the different ways we can organize colors into color schemes: Warm, cool, complementary, and analogous (see color wheel).
  • Tell students that next they will be painting over the entire surface of the paper in watercolor. A watercolor wash is an even coat of paint that covers the entire surface of the paper. Students should paint over the crayon or oil pastel.
    • Project the image of the color wheel. Ask students to choose a color(s) for their watercolor wash that is different from the colors they already used. This will create contrast, so that their crayon or oil pastel will show up.
  • While the watercolor is drying, show students examples of finished artwork. Ask students what multiplication or division problems are represented in each of the artworks.

Three paper flowers with green stems on the left, each made from a circle and square petals. On the right, the same cut-out shapes are rearranged into math mosaics, creating abstract patterns on a black background.

  • Next, have students plan their mosaic artwork on a scratch piece of paper. Their plans should show the image they are creating out of equal groups.
    • Circulate and check that students understand how they will be creating an image out of equal groups.
  • Once the watercolor wash is mostly dry, students should cut out each square and divide them into their predetermined equal groups.
  • Explain that students are going to arrange their equal groups in a composition on their black paper. Once they have arranged them, they will glue them down.
    • Teacher tip: Have students place all of their pieces on their paper BEFORE beginning to glue them down. This will allow students to plan spatially as well as for the teacher to ensure that they have equal groups.

Students should write their multiplication or division problem on their artwork or on a notecard to be displayed with their artwork.

Closing Reflection

  • Have students explain to a partner how they created their mosaic using equal groups.
  • Ask students to identify which elements of art they used in their mosaic.

 

Assessments

Formative

  • Teachers will assess understanding through:
    • Discussion of the example mosaic in the activator
    • Students’ discussion of the factors of a given number
    • Students’ ability to group pieces of mosaic into factors of the total number provided by the teacher
    • Students’ plans for their final artwork

Summative

CHECKLIST

  • Students will demonstrate what they learned by creating a mosaic made by arranging pieces in equal groups to make an image.
  • Students can express their artwork in terms of a multiplication or division problem.

 

Differentiation 

Acceleration: 

  • Instead of using squares, have students determine other ways to divide their paper into equal sections (example) or allow them to create arrays of a different shape, such as circles.
  • Allow students to create their own arrays using rulers.
  • Give students different numbers to use to create their mosaic, such as 36 or 49.

Remediation:

  • Rather than creating a watercolor resist, have students use construction paper in contrasting colors to create their mosaic.
  • Provide students with a smaller number, such as 12.

 

Additional Resources

Examples of ancient Roman mosaics

 

Credits

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

Ideas contributed 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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