Artistic Inequalities: Graphing Solutions Through Visual Art

Created bySheila Corrigan

1 views0 downloads

Artistic Inequalities: Graphing Solutions Through Visual Art

Grade 9Math4 days

In this project, 9th-grade students explore the intersection of mathematics and art by using systems of linear inequalities to design and create visual artwork. Students begin by analyzing existing inequality-based art to understand the mathematical principles behind the designs. They then translate real-world constraints into mathematical inequalities and use these inequalities to create their own artistic compositions, demonstrating their understanding of both mathematical concepts and artistic design. The project culminates in a final art piece accompanied by an artist statement explaining the mathematical concepts and artistic choices.

Linear InequalitiesSystems of EquationsGraphingArtistic DesignReal-World ConstraintsMathematical Modeling

Want to create your own PBL Recipe?Use our AI-powered tools to design engaging project-based learning experiences for your students.

📝

Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use systems of linear inequalities to design and create a visual work of art that reflects real-world constraints or themes?

Essential Questions

Supporting questions that break down major concepts.

How can we represent real-world constraints using mathematical inequalities?
How do you graph a linear inequality on a coordinate plane?
How can systems of inequalities create artistic designs?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Understand and apply linear inequalities to create artistic designs.
Graph linear inequalities on a coordinate plane.
Represent real-world constraints using mathematical inequalities.

Common Core Standards

AI-A.REI.12

Primary

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.Reason: Directly addresses the core math skill of graphing linear inequalities, which is fundamental to the project.

Entry Events

Events that will be used to introduce the project to students

"Inequality Art Challenge: The Gallery"

Students enter a "gallery" showcasing seemingly abstract art pieces. Each piece is accompanied by a cryptic artist statement hinting at mathematical rules. The challenge: decode the math (inequalities) behind the art and create their own piece in response.

📚

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

Inequality Investigator: Decoding the Gallery

Students analyze existing inequality art pieces to reverse-engineer the mathematical inequalities that define them. This activity builds foundational understanding and analytical skills.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Examine several provided art pieces, each created using systems of linear inequalities. These should vary in complexity.

2. For each artwork, identify key visual elements such as lines, shapes, and shaded regions.

3. Translate these visual elements into mathematical inequalities. Start by determining the equations of the lines and then consider the shaded regions to deduce the inequality signs.

4. Document the process for each artwork, including sketches, identified lines, derived inequalities, and explanations of the reasoning.

Final Product

What students will submit as the final product of the activityA portfolio page for each analyzed artwork, including the artwork image, a list of the inequalities used to create it, and a written explanation of the mathematical reasoning.

Alignment

How this activity aligns with the learning objectives & standardsAI-A.REI.12 (Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.)

Activity 2

Constraint Crafter: Real-World Rules

Students brainstorm real-world scenarios with constraints and represent these constraints using mathematical inequalities. This activity bridges mathematical concepts with practical applications.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Brainstorm real-world scenarios that involve constraints. Examples: budget limitations for a project, time restrictions, resource availability, or physical limitations.

2. Choose a scenario and define the variables involved. For instance, if the scenario involves spending money, define variables for the quantities of different items being purchased.

3. Translate the constraints of the scenario into mathematical inequalities. For example, "The total cost must be less than $100" can be written as an inequality.

4. Graph the inequalities on a coordinate plane, labeling axes and shading the feasible region (the region that satisfies all inequalities).

Final Product

What students will submit as the final product of the activityA report detailing the chosen scenario, defined variables, derived inequalities, and the graph of the feasible region. Include a written explanation of how the graph represents the real-world constraints.

Alignment

How this activity aligns with the learning objectives & standardsAI-A.REI.12 (Graph the solutions to a linear inequality in two variables as a half-plane...)

Activity 3

Artistic Architect: Inequality Blueprint

Students design an art piece using systems of linear inequalities, planning the shapes, colors, and overall composition mathematically. This activity emphasizes creative application of learned skills.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Sketch a design for the art piece, considering the desired shapes, colors, and overall composition. Plan how inequalities can define these elements.

2. Translate the sketched design into mathematical inequalities. Determine the equations of the lines that form the boundaries of the shapes.

3. Graph the inequalities on a coordinate plane to visualize the design mathematically. Adjust inequalities as needed to refine the design.

4. Choose colors or patterns for each region defined by the inequalities, adding artistic flair to the mathematical structure.

Final Product

What students will submit as the final product of the activityA detailed blueprint of the art piece, including the sketch, the list of inequalities used, the graph of the inequalities, and a color key.

Alignment

Activity 4

Inequality Artist: The Final Piece

Students create the final art piece based on their mathematical blueprint, bringing their inequality art to life. This activity provides a tangible outcome and reinforces understanding through application.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Transfer the design from the blueprint onto a chosen medium (e.g., paper, canvas, digital art software).

2. Carefully create the shapes and regions defined by the inequalities, using the corresponding colors or patterns.

3. Refine the artwork, ensuring that it accurately reflects the mathematical inequalities and the planned design.

4. Write an artist statement explaining the mathematical concepts behind the artwork, the challenges faced, and the artistic choices made.

Final Product

What students will submit as the final product of the activityThe completed art piece and the accompanying artist statement.

Alignment

How this activity aligns with the learning objectives & standardsAI-A.REI.12 (Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality))

🏆

Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Inequality Art Portfolio Rubric

Category 1

Mathematical Accuracy

Focuses on the correct application of linear inequalities and their graphical representation.

Criterion 1

Inequality Formulation

Assesses the ability to accurately translate visual elements and real-world constraints into mathematical inequalities.

Exemplary

4 Points

Consistently and accurately formulates complex inequalities that precisely represent the visual elements or constraints.

Proficient

3 Points

Accurately formulates most inequalities, with only minor errors that do not significantly impact the overall representation.

Developing

2 Points

Formulates some inequalities correctly, but with significant errors or omissions that affect the accuracy of the representation.

Beginning

1 Points

Struggles to formulate inequalities, with numerous errors and a lack of understanding of the relationship between visual elements/constraints and mathematical expressions.

Criterion 2

Graphical Representation

Assesses the ability to accurately graph linear inequalities on a coordinate plane.

Exemplary

4 Points

Graphs all inequalities accurately, including correct shading, boundary lines (solid vs. dashed), and clear labeling of axes and lines.

Proficient

3 Points

Graphs most inequalities accurately, with only minor errors in shading or labeling that do not significantly impact the overall representation.

Developing

2 Points

Graphs some inequalities correctly, but with significant errors in shading, boundary lines, or labeling that affect the accuracy of the representation.

Beginning

1 Points

Struggles to graph inequalities, with numerous errors and a lack of understanding of the relationship between inequalities and their graphical representation.

Criterion 3

Solution Set Identification

Focuses on the correct identification of feasible region.

Exemplary

4 Points

Correctly identifies and clearly indicates the solution set (feasible region) for all systems of inequalities.

Proficient

3 Points

Identifies the solution set for most systems of inequalities, with only minor errors.

Developing

2 Points

Identifies the solution set for some systems of inequalities, but with significant errors.

Beginning

1 Points

Struggles to identify the solution set for systems of inequalities.

Category 2

Creative Design & Application

Focuses on the artistic design and the creative application of inequalities in the artwork.

Criterion 1

Design Concept

Assesses the originality and clarity of the design concept.

Exemplary

4 Points

Demonstrates a highly original and well-defined design concept that is clearly communicated through the artwork and artist statement.

Proficient

3 Points

Demonstrates a clear design concept that is effectively communicated through the artwork and artist statement.

Developing

2 Points

Demonstrates a basic design concept, but the communication through the artwork and artist statement is not always clear.

Beginning

1 Points

Lacks a clear design concept, and the artwork and artist statement do not effectively communicate any intentional design.

Criterion 2

Integration of Inequalities

Assesses how effectively inequalities are used to create the design.

Exemplary

4 Points

Masterfully integrates inequalities to create complex and visually appealing designs.

Proficient

3 Points

Effectively integrates inequalities to create a visually appealing design.

Developing

2 Points

Integrates inequalities into the design, but the connection between the math and the art is not always clear.

Beginning

1 Points

Struggles to integrate inequalities into the design, and the artwork appears disconnected from the mathematical concepts.

Criterion 3

Artistic Execution

Focuses on the quality of the final artwork, including use of color, composition, and overall presentation.

Exemplary

4 Points

The artwork is exceptionally well-executed, demonstrating a strong understanding of artistic principles and attention to detail.

Proficient

3 Points

The artwork is well-executed, demonstrating a good understanding of artistic principles.

Developing

2 Points

The artwork shows some attention to artistic principles, but there are areas for improvement in execution.

Beginning

1 Points

The artwork lacks attention to artistic principles and the execution is weak.

Category 3

Reflection & Explanation

Focuses on the student's ability to explain their mathematical reasoning and artistic choices.

Criterion 1

Mathematical Reasoning

Assesses the clarity and accuracy of the student's explanation of the mathematical concepts behind the artwork.

Exemplary

4 Points

Provides a clear, concise, and accurate explanation of the mathematical concepts, demonstrating a deep understanding of the relationship between inequalities and the artwork.

Proficient

3 Points

Provides a clear and accurate explanation of the mathematical concepts.

Developing

2 Points

Provides an explanation of the mathematical concepts, but it may be unclear or contain some inaccuracies.

Beginning

1 Points

Struggles to explain the mathematical concepts behind the artwork, demonstrating a limited understanding of the relationship between inequalities and the art.

Criterion 2

Artistic Choices

Assesses the student's ability to articulate their artistic choices and the reasons behind them.

Exemplary

4 Points

Articulates artistic choices with clarity and purpose, demonstrating a thoughtful consideration of the design elements and their impact on the overall message of the artwork.

Proficient

3 Points

Articulates artistic choices and provides reasons for those choices.

Developing

2 Points

Attempts to explain artistic choices, but the reasoning may be unclear or superficial.

Beginning

1 Points

Struggles to articulate artistic choices or provide reasons for those choices.

Criterion 3

Reflection on Learning

Assesses the student's ability to reflect on their learning process and identify areas for growth.

Exemplary

4 Points

Provides a thoughtful and insightful reflection on their learning process, identifying specific challenges, successes, and areas for future growth.

Proficient

3 Points

Reflects on their learning process and identifies areas for growth.

Developing

2 Points

Provides a basic reflection on their learning process, but the insights are limited.

Beginning

1 Points

Struggles to reflect on their learning process or identify areas for growth.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

How did your understanding of linear inequalities evolve as you worked through the project, from analyzing existing art to creating your own?

Text

Required

Question 2

What real-world constraints did you explore, and how did you translate them into mathematical inequalities?

Text

Required

Question 3

To what extent do you agree with the following statement: "Mathematics can be a form of artistic expression."

Scale

Required

Question 4

What was the most challenging aspect of creating art with inequalities, and how did you overcome it?

Text

Required

Question 5

If you were to continue this project, what additional mathematical concepts or artistic techniques would you explore?

Text

Optional