Graph Art: Crafting Pictures with Equations
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Graph Art: Crafting Pictures with Equations

Grade 10Math1 days
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5.0 (1 rating)
In the 'Graph Art: Crafting Pictures with Equations' project, 10th-grade math students create visually appealing artwork by exploring and applying various mathematical equations and graph properties. The project encourages students to use linear, quadratic, and exponential equations to design intricate graph-based images, demonstrating the connection between mathematical concepts and artistic expression. Through activities such as exploring equation properties, applying geometric transformations, and synthesizing multiple equations, students enhance their skills in graph interpretation, artistic creativity, and the practical application of math in art. This experiential learning project aims to deepen students' understanding of graphing skills while fostering creativity and innovation in merging art with mathematics.
GraphingMathematical EquationsArtistic ExpressionGeometric TransformationsCreativitySymmetryLinear and Quadratic Functions
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use various mathematical equations and graph properties to design a visually appealing picture, and what does this reveal about the connection between technical mathematical concepts and creative artistic expression?

Essential Questions

Supporting questions that break down major concepts.
  • How can different types of mathematical equations, such as linear, quadratic, and exponential, be used to create visual representations?
  • What are the properties of different types of graphs and how do these properties affect the overall picture design?
  • How can we use our understanding of geometric transformations to manipulate equations for artistic purposes?
  • In what ways do the principles of symmetry and asymmetry apply to graph-based design?
  • What are the connections between mathematical analysis and creative expression through graphing?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will understand how to graph various types of equations, such as linear, quadratic, and exponential, to create a cohesive picture.
  • Students will develop skills in manipulating equations to achieve specific visual effects, incorporating geometric transformations.
  • Students will analyze the impact of different graph properties, such as symmetry and asymmetry, on artistic design.
  • Students will connect mathematical concepts with artistic expression, enhancing their creativity through technical applications.

Common Core Standards for Mathematics

CCSS.MATH.CONTENT.HSF.IF.C.7
Primary
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.Reason: This standard aligns well as it requires students to graph various types of functions, which relates to the project's task of using mathematical equations to create a picture.
CCSS.MATH.CONTENT.HSF.BF.A.1
Secondary
Write a function that describes a relationship between two quantities.Reason: This standard supports the project by emphasizing the ability to write functions that define relationships, crucial for designing graph-based pictures.
CCSS.MATH.CONTENT.HSF.LE.A.2
Supporting
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.Reason: This standard assists in constructing functions from graph descriptions, which is essential in creating images using graphs.

Entry Events

Events that will be used to introduce the project to students

Math in Motion Art Gala

Invite students to an art exhibition where all the artworks are created using mathematical equations and graphs. Each piece challenges the students to determine the equations that represent the artistic curves, inviting curiosity about how math can transform into visual art.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Equation Exploration Adventure

In this introductory activity, students will explore different mathematical equations such as linear, quadratic, and exponential. They will learn how each type of equation is graphically represented and understand their basic properties.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Choose a simple equation type, such as linear equations, and its standard form.
2. Graph the selected equation by hand and identify its features (e.g., slope, intercepts).
3. Repeat the process for quadratic equations, exploring features such as the vertex and axis of symmetry.
4. Explore exponential equations, focusing on growth and decay aspects.

Final Product

What students will submit as the final product of the activityA portfolio of simple graph sketches for each equation type, annotated with their properties.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.MATH.CONTENT.HSF.IF.C.7 - Graph functions expressed symbolically.
Activity 2

Geometric Transformation Wizards

Students will use geometric transformations to manipulate equations, allowing them to see how shifts, reflections, and stretches affect the graph visually.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review the concept of transformations: translations, reflections, and dilations.
2. Select an equation and apply a translation, noting the changes in graph positioning.
3. Apply reflections over the x-axis or y-axis and observe the changes.
4. Use dilations to stretch or compress the graph and describe the visual effect.

Final Product

What students will submit as the final product of the activityA series of graphs showcasing transformed equations, with notes on the transformations applied.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.MATH.CONTENT.HSF.BF.A.1 - Write a function that defines relationships through transformation.
Activity 3

Graph Design Masterpieces

In the culminating activity, students synthesize their understanding of graph equations and transformations to create a unique piece of visual art using a variety of equations.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Plan the artwork by selecting which types of equations will represent different parts of the design.
2. Combine linear, quadratic, and other equations to create complex patterns.
3. Incorporate transformations and symmetry to enhance the artistic aspects.
4. Use graphing software to perfect the artwork and ensure precision.

Final Product

What students will submit as the final product of the activityA completed graph-based artistic piece demonstrating mastery of equations and transformations.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.MATH.CONTENT.HSF.IF.C.7, CCSS.MATH.CONTENT.HSF.BF.A.1, CCSS.MATH.CONTENT.HSF.LE.A.2 - Combining expression, symmetry, and transformation to create art.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Graphing and Art Design Rubric

Category 1

Graph Interpretation and Application

Evaluation of students' understanding and application of various graph types such as linear, quadratic, and exponential equations.
Criterion 1

Equation Graphing

Ability to graph different mathematical equations precisely and identify their key features such as slope and intercepts for linear equations, and vertex and axis of symmetry for quadratic equations.

Exemplary
4 Points

Graphs all equation types with precision, clearly annotating all key features and demonstrating a deep understanding of graph properties.

Proficient
3 Points

Accurately graphs most equation types and annotates key features, with a solid understanding of graph properties.

Developing
2 Points

Graphs some equations correctly, but annotations and understanding of key features are incomplete or partially inaccurate.

Beginning
1 Points

Struggles to graph equations correctly and lacks clear annotations or understanding of graph properties.

Criterion 2

Transformation Application

Effectively applies geometric transformations such as translations, reflections, and dilations to mathematical equations for altering graph shapes.

Exemplary
4 Points

Applies transformations with creativity and precision, demonstrating a comprehensive understanding of their effects on graph shapes.

Proficient
3 Points

Properly applies basic transformations, showing clear understanding of their effects on graph shapes.

Developing
2 Points

Demonstrates inconsistent application of transformations, with partial understanding of their visual effects.

Beginning
1 Points

Struggles to apply transformations, with minimal understanding of their impact on graph shapes.

Category 2

Artistic Design Integration

Assessment of students' ability to integrate mathematical concepts creatively to produce a cohesive and visually appealing artwork.
Criterion 1

Creative Synthesis

Synthesizes multiple equation types and transformations to create a unified and aesthetically pleasing design.

Exemplary
4 Points

Seamlessly integrates multiple equations and transformations, creating a visually striking and coherent artwork.

Proficient
3 Points

Successfully combines equations and transformations into a cohesive design, with strong visual appeal.

Developing
2 Points

Combines some equations and transformations, but design lacks coherence or visual impact.

Beginning
1 Points

Struggles to integrate equations or transformations effectively, resulting in a disjointed or unclear design.

Criterion 2

Artistic Creativity

The extent to which the artwork demonstrates original thought and creativity in the use of mathematical equations and transformations.

Exemplary
4 Points

Demonstrates exceptional creativity and originality, using mathematical concepts to deliver a unique and inspiring artwork.

Proficient
3 Points

Shows solid creativity, effectively using mathematical concepts to create interesting visual elements.

Developing
2 Points

Displays basic creativity, with some original use of mathematical concepts in the design.

Beginning
1 Points

Shows limited creativity or originality in using mathematical concepts within the artwork.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How did your understanding of using mathematical equations to design a visually appealing picture evolve throughout this project?

Text
Required
Question 2

To what extent do you feel confident in using different types of mathematical equations to create visual art?

Scale
Required
Question 3

Which mathematical concept did you find most challenging when creating your artwork, and why?

Text
Required
Question 4

Which graphing technique or transformation do you believe had the most impact on your final artistic expression, and why?

Multiple choice
Required
Options
Linear equations
Quadratic equations
Exponential equations
Graph transformations (translations, reflections, dilations)
Symmetry applications
Question 5

How effectively did the project help you connect mathematical analysis with creative artistic expression through graphing?

Scale
Required