Lesson 3: Golden Ratio and Proportions
Big Idea: The golden ratio creates balance and harmony in art and design.
Essential Question:
* How does the golden ratio influence art and design?
Objectives:
* Apply the golden ratio in art compositions.
* Understand and use proportions to create balanced designs.
Defined Vocabulary:
* Golden Ratio
* Proportions
* Balance
* Harmony
* Fibonacci Sequence
Materials & Resources:
* Graph paper
* Rulers
* Compasses
* Colored pencils or markers
* Examples of artworks utilizing the golden ratio (e.g., Da Vinci's "Vitruvian Man," the Parthenon)
* Precut shapes demonstrating the golden ratio
* Storage bins for portfolios and reading books
Teacher Preparation:
1. Set Up Workstations:
* Arrange graph paper, rulers, colored pencils/markers, compasses, and precut shapes at each workstation.
* Ensure each table has a clear space for working with easy access to materials.
2. Prepare Examples:
* Print and display examples of the golden ratio in art and architecture around the room.
* Prepare a few sample art pieces using the golden ratio to show during the demonstration.
3. Organize Storage:
* Set up storage bins for portfolios and reading books near the entrance.
* Label bins for each table group to streamline the clean-up process.
4. Set Up Visual Aids:
* Ensure visual aids, such as examples of the golden ratio and steps for applying it, are displayed clearly.
* Prepare a chart or board with key vocabulary and their definitions.
Sequencing:
1. Entrance Routine (5 minutes):
* Scripted Interaction at the Door:
* Scripted Interaction at the Door:
* Teacher: "Greetings, everyone! Let's make this a fantastic day! Remember, silent and speedy entry. Store everything in the bin under your seat, then find me with your eyes. Let's dive right in!"
* Ensure students follow the entrance routine, transitioning them into a productive mindset for the lesson.
2. Introduction (5 minutes):
* Scripted Interaction:
* Teacher: "Good morning, everyone! Today, we are going to explore the golden ratio and how it creates balance and harmony in art and design. Can anyone tell me what the golden ratio is?"
* Possible Student Responses: "It's a special number that appears in nature and art", "It helps make things look balanced."
* Teacher: "Exactly! The golden ratio is a special number, approximately 1.618, that helps create balance and harmony. Let's look at some examples in art and architecture."
* Show examples of the golden ratio and discuss their characteristics.
* Scripted Interaction:
* Teacher: "Look at these examples. What do you notice about the balance and harmony in these designs?"
* Possible Student Responses: "They look very balanced", "The proportions seem perfect", "They look very pleasing to the eye."
* CHARGE Badge Opportunity:
* Teacher: "I see some great engagement here! Who can earn a CHARGE badge for engagement by explaining why the golden ratio is important in these designs?"
3. Demonstration (10 minutes):
* Demonstrate how to apply the golden ratio using a think-aloud process.
* Scripted Interaction:
* Teacher: "Now I am going to show you how to apply the golden ratio in your art compositions. (CFU) What am I going to do?"
* Possible Student Responses: "Show us how to use the golden ratio in art."
* Teacher: "Notice how I measure and draw shapes using the golden ratio. (CFU) What are you paying attention to?"
* Possible Student Responses: "How you measure and draw the shapes", "How you use the golden ratio."
* Think-Aloud Process:
* Teacher: "Watch as I start with a rectangle. First, I’ll measure the longer side and divide it by 1.618 to find the shorter side. This creates a golden rectangle. Now, I’ll use the compass to draw a spiral inside the rectangle, following the golden ratio."
* Teacher: "When using the compass, make sure to measure carefully and draw lightly. After using the ruler, remember to check your measurements for accuracy."
* Scripted Interaction:
* Teacher: "Does anyone have any questions so far?"
* Possible Student Questions: "Can I use different shapes?", "How do I make sure the proportions are correct?", "Do I have to use a compass?"
* Teacher: "Great questions! You can use different shapes, but the proportions should follow the golden ratio. Using a compass helps to draw accurate curves, but you can also use a ruler for straight lines."
* CFU after Demonstration:
* Teacher: "How did I use the golden ratio to create the design?"
* Possible Student Responses: "You measured the sides of the rectangle", "You divided the longer side by 1.618", "You drew a spiral inside the rectangle."
* CHARGE Badge Opportunity:
* Teacher: "I noticed some excellent observations. Who can earn a CHARGE badge for engagement by explaining why the golden ratio is important in creating balanced designs?"
4. Activity (20 minutes):
* Scripted Interaction:
* Teacher: "Now it's your turn! You have 20 minutes to create your designs using the golden ratio. Remember, each shape should follow the golden ratio to create balance and harmony. If you need help, just raise your hand. Let's set our timer for 20 minutes. Also, remember to handle the compasses and rulers carefully, and to cap your markers when not in use."
* Set the timer for 20 minutes.
* Monitor noise levels:
* Scripted Interaction:
* Teacher: "We are moving into a yellow zone, which means you can talk quietly with your neighbors. If the noise level gets too high, we will move to a red zone of silence."
* Circulate the room to provide guidance and support.
* Scripted Interaction:
* Teacher (to individual students): "Great start! Can you show me how you’re applying the golden ratio in your design?"
* Possible Student Responses: "I’m measuring the sides to follow the ratio", "I’m drawing a spiral using the compass", "I’m making sure the proportions are correct."
* Teacher: "Excellent! Keep going and make sure all the proportions follow the golden ratio."
* CHARGE Badge Opportunity:
* Teacher: "I see some excellent use of the golden ratio. Who will earn a CHARGE badge for engagement by demonstrating how they used the golden ratio in their designs?"
5. Reflection and Clean-Up (5 minutes):
* Scripted Interaction:
* Teacher: "Macaroni Cheese, Everybody Freeze! Time's up! (Scan for no movement, sounds off) Take one minute to clean up our work areas. Remember to cap your markers, put your compasses and rulers back in the bin, and store your designs in your portfolios. Let's do this quickly and quietly! I am looking for the first table with the materials put away, artwork stored in the portfolio, and eyes in their independent reading book, which table will earn a CHARGE badge for engagement?"
* Set the timer for one minute.
* CHARGE Badge Opportunity:
* Teacher: "I see Table 3 is almost ready. Who will be the first to earn a CHARGE badge for engagement?"
* Have students share their designs and discuss the use of the golden ratio in their artwork.
* Scripted Interaction:
* Teacher: "Let's take a few minutes to share our designs. Who would like to show their artwork and explain how they used the golden ratio to create balance and harmony?"
* Possible Student Responses: "I used the ratio to measure the sides", "I drew a spiral to follow the ratio", "I made sure my proportions were correct."
* Ask students how the golden ratio enhances the visual appeal of their designs.
* Scripted Interaction:
* Teacher: "How does the golden ratio make your design more balanced? What did you find challenging or interesting about using the golden ratio?"
* Possible Student Responses: "It makes the design look perfect", "It was hard to get the measurements right", "I liked seeing how the spiral turned out."
Test Content Included here
Big Idea:
Tessellations showcase the beauty of repeating patterns and geometric transformations.
Essential Question:
What makes tessellations visually interesting and complex?
Objectives:
Create tessellations using geometric transformations (rotations, reflections, translations).
Explore pattern repetition.
Understand the principles of tessellation in art and nature.
Vocabulary:
Tessellation: Imagine fitting puzzle pieces together perfectly, with no gaps and no overlaps. That's a tessellation! It's like a repeating pattern that covers a whole flat surface. Think of honeycomb shapes or cool floor patterns!
Geometric Transformation: This is a fancy way of saying "shape change." In art and math, we can move, flip, turn, or resize shapes in different ways.
Rotation: When you turn a shape around a point, like a center dot. A pinwheel spinning is a great example!
Reflection: This is when an image is flipped exactly like looking in a mirror. You can see reflections in shiny surfaces or create them by flipping a piece of paper with a drawing!
Translation: Think of sliding a book across your desk. Translation is when you move a shape in a straight line, keeping the size and direction the same. Imagine ants marching in a straight line – that's translation!
Pattern Repetition: This is when a design or shape keeps repeating over and over again, creating a cool pattern. Stripes on a shirt or a row of flowers are both examples of pattern repetition.
Tile: A flat piece of material used to cover a surface, forming a pattern.
Materials & Resources:
Graph paper
Rulers
Colored pencils or markers
Examples of tessellations (e.g., works by M.C. Escher)
Scissors
Glue sticks
Precut geometric shapes (for students needing additional support)
Templates or stencils
Small containers for collecting scraps
Art Historical References:
M.C. Escher’s tessellations
Islamic geometric patterns
Patterns in nature (e.g., honeycombs, turtle shells)
Teacher Preparation:
Set Up Workstations:
Arrange graph paper, rulers, colored pencils/markers, scissors, glue sticks, precut geometric shapes, and templates at each workstation.
Ensure each table has a clear space for working with easy access to materials.
Place a small container at each table for collecting scraps and used materials (e.g., paper scraps, used glue sticks).
Prepare Examples:
Print and display examples of tessellations around the room.
Prepare a few sample tessellations using different geometric transformations to show during the demonstration.
Organize Storage:
Set up storage bins for portfolios and reading books near the entrance.
Label bins for each table group to streamline the clean-up process.
Set Up Visual Aids:
Ensure visual aids, such as examples of tessellations and steps for creating them, are displayed clearly.
Prepare a chart or board with key vocabulary and their definitions.
Activities:
Entrance Routine (2 minutes):
TWS: "Good morning! Enter the room silently and urgently. Place your portfolio and reading book in the bin under your chair and get your eyes on me. Let's get started quickly today."
Introduction (5 minutes):
Brief discussion on tessellations.
TWS: "Good morning, everyone! Today, we are going to explore tessellations and how they create beautiful repeating patterns. Can anyone tell me what a tessellation is?"
"It's a pattern that repeats without any gaps"
"Shapes that fit together perfectly".
Show examples of Tessellations art and discuss their characteristics.
TWS: "Now, let's talk about Tessellations. Tessellations are patterns made of shapes that fit together perfectly without any gaps or overlaps. Let's look at some examples."
TWS: "Look at these tessellations. What do you notice about the shapes and patterns? How do they repeat?" PUSH: why are they interesting?
"The shapes are the same", "They repeat over and over", "They fit together perfectly". = CHARGE Badge for Engagement
Demonstration (10 minutes):
Demonstrate how to create tessellations using geometric transformations with a think-aloud process.
TWS: "Now I am going to show you how to create a tessellation using a simple shape. (CFU) What am I going to do?
Show us how to create a tessellation using a shape.
TWS: "Notice how I use rotations, reflections, and translations to make the pattern repeat. (CFU) What are you paying attention to?"
How you rotate, reflect, and translate the shape", "How the pattern repeats."
TWS: "I will start with a square.
First, I’ll cut a shape out of one side and tape it to the opposite side.
Now, I’ll trace this new shape on my graph paper, rotating it as I go to create a repeating pattern.
How did I use the transformations to create the tessellation?
"You cut and taped the shape to the other side", "You traced and rotated the shape to make it repeat", "You made sure there were no gaps or overlaps." = CHARGE badge for Engagement
Why transformations are important in creating tessellations?"
Activity (20 minutes):
Students create their own symmetrical designs using geometric shapes.
TWS: Now it's your turn! You have 20 minutes to create your tessellations using geometric transformations. Remember, each shape should fit together perfectly without any gaps or overlaps. If you need help, just raise your hand. Let's set our timer for 20 minutes. Also, remember to handle the scissors and glue sticks carefully and to cap your markers when not in use."
Set timer for 20 minutes
TWS: "We are moving into a yellow zone, which means you can talk quietly with your neighbors. If the noise level gets too high, we will move to a red zone of silence."
Circulate the room to provide guidance and support.
Can you show me how you’re using rotations, reflections, or translations in your tessellation?
"I’m rotating my shape to make it fit", "I’m reflecting the shape to repeat the pattern", "I’m translating the shape across the paper.
Timer goes off
TWS: I see some excellent use of transformations. Let's take a few minutes to share our designs. Who would like to show their artwork and explain how they used transformations to create the pattern?
Cleanup, Reflection, & Transition (10 minutes):
TWS: "Macaroni Cheese, Everybody Freeze! Time's up! (Scan for no movement, sounds off) Take one minute to clean up our work areas. Remember to cap your markers, put your scissors and glue sticks back in the bin, and store your tessellations in your portfolios. Let's do this quickly and quietly! I am looking for the first table with the materials put away, artwork stored in the portfolio, and eyes in their independent reading book, which table will earn a CHARGE badge for engagement?"
Set timer for one minute
TWS: "Today, we learned how to create tessellations using geometric transformations. Who can remind us why transformations are important in creating tessellations? Great job, everyone!"
Ensure students follow the entrance routine, be ready for a Positive Do It Again.
CHARGE Badge: First table with their items put away, sounds off, and eyes on me.
Pacing:
Entrance Routine: 2 minutes
Introduction: 5 minutes
Demonstration: 10 minutes
Activity: 20 minutes
Reflection and Clean-Up: 8 minutes
Notes:
Include images of different tessellations and designs for visual reference.
Provide templates or stencils for students who need additional guidance to create tessellations.
Offer one-on-one assistance for students struggling with using the transformations.
Encourage peer collaboration by pairing students to help each other and discuss their designs.
Geometric shapes and symmetry are fundamental elements in both art and nature.
Essential Question:
How can we use geometric shapes and symmetry in art?
What makes symmetry aesthetically pleasing?
Objectives:
Identify and use geometric shapes in art.
Create symmetrical designs.
Understand the role of symmetry in aesthetic appeal.
Vocabulary:
Geometric Shapes: These are flat figures with straight or curved sides that come in all sorts of sizes. Think of squares, circles, triangles, and more!
Symmetry: Imagine a perfect mirror image. In shapes, symmetry means one half is the exact mirror image of the other. You can check for it by folding the shape in half!
Balance:Distribution of visual weight in a piece of art to create a sense of stability.
Reflection: This is when an image is flipped exactly like looking in a mirror. You can see reflections in shiny surfaces or create them by flipping a piece of paper with a drawing!
Materials & Resources:
Drawing paper/Graph paper(preferred)
Rulers
Compasses
Colored pencils or markers
Examples of symmetrical art (e.g., mandalas, kaleidoscopic images)
Mirrors (for demonstrating reflection symmetry)
Setup of Materials:
Prepare a slideshow with examples of geometric shapes and symmetrical art.
Arrange materials on each table: drawing paper, rulers, compasses, colored pencils/markers.
Have mirrors available for students to use during the activity.
Art Historical References:
Mandalas in various cultures
Islamic geometric art
Works by M.C. Escher
Activities:
Entrance Routine (5 minutes):
Scripted Interaction at the Door:
TWS: "Good morning! Enter the room silently and urgently. Place your portfolio and reading book in the bin under your chair and get your eyes on me. Let's get started quickly today."
Ensure students follow the entrance routine, be ready for a Positive Do It Again.
CHARGE Badge: First table with their items put away, sounds off, and eyes on me.
Introduction (5 minutes):
Brief discussion on geometric shapes and symmetry.
TWS: "Today, we are going to explore how geometric shapes and symmetry can be used to create beautiful artworks. Can anyone give me an example of a geometric shape?"
Shapes like circles, squares, and triangles are all geometric shapes.
Show examples of symmetrical art and discuss their characteristics.
TWS: "Now, let's talk about symmetry. Symmetry is when one side of something is a mirror image of the other side. Let's look at some examples."
TWS: "Look at this mandala. What do you notice about its symmetry? What effect does it have on the design?
"Both sides are the same", "It looks balanced", "It’s very pretty because it's even".
Demonstration (10 minutes):
Demonstrate how to create symmetrical designs using rulers and compasses.
TWS: "Now I am going to use a ruler and compass to create a symmetrical design. (CFU) What am I going to do?
"Use a ruler and compass to create a symmetrical design."
TWS: "Notice how I use the materials to make sure each side is identical. (CFU) What are you paying attention to?
"How you use the ruler and compass", "Making sure each side is identical".
TWS: "SCENE. I have graph paper with a grid so that can help with accuracy.
First, I’ll draw a line down the center to serve as my line of symmetry.
Then, I’ll measure equal distances on both sides. Let’s say I want to draw a triangle. I’ll measure two units to the left and two units to the right, making sure they are equal."
Now, I’m placing the compass point on the line of symmetry and drawing a circle. See how the circle is symmetrical around this line?
I’ll use the ruler to measure and draw another shape, ensuring it’s the same distance from the center on both sides."
How did I use the materials to create a symmetrical design?
"You used the ruler to draw straight lines and the compass to make circles", "You measured equal distances on both sides", "You drew a line of symmetry down the middle." = CHARGE badge for Engagement
Show how to use mirrors to find lines of symmetry in different shapes.
Activity (20 minutes):
Students create their own symmetrical designs using geometric shapes.
TWS: "Now it's your turn! You have 20 minutes to create your symmetrical designs using your rulers and compasses. Remember, each side should be a mirror image of the other. If you need help, just raise your hand. Let's set our timer for 20 minutes. Also, remember the markers need to be capped when not in use and the rulers are not for bending or hitting."
Set timer for 20 minutes
TWS: "We are moving into a yellow zone, which means you can talk quietly with your neighbors. If the noise level gets too high, we will move to a red zone of silence."
Circulate the room to provide guidance and support.
Can you show me where the line of symmetry is in your design?
Let's take a few minutes to share our designs. Who would like to show their symmetrical artwork and explain how they used symmetry?
How can you make sure both sides are the same?
CHARGE Badge for respecting materials
Cleanup, Reflection, & Transition (10 minutes):
TWS: "Macaroni Cheese, Everybody Freeze! Time's up! (Scan for no movement, sounds off) Take one minute to clean up our work areas. Remember to cap your markers and put your rulers and compasses back in the bin. Let's do this quickly and quietly! I am looking for the first table with the materials but away, art work stored in portfolio and eyes in their independent reading book, which table will earn a CHARGE badge for engagement?"
Have students share their designs and discuss the use of symmetry in their artwork.
TWS: "Let's take a few minutes to share our designs. Who would like to show their symmetrical artwork and explain how they used symmetry?"
Ask students how symmetry can enhance the visual appeal of their designs.
TWS: How does symmetry make your design more appealing? What did you find challenging or interesting about creating symmetrical art?
TWS: "Today, we learned how to use geometric shapes and symmetry to create beautiful artworks. Who can remind us why symmetry is important in art?"
Pacing:
Introduction: 5 minutes
Demonstration: 10 minutes
Activity: 20 minutes
Reflection: 5 minutes
Assessment of Challenges & Learning Gaps
Procedural: Ensuring students can use rulers and compasses accurately.
Conceptual: Understanding and applying the concept of symmetry.
Reintroduce basic geometric shapes and provide extra support with ruler and compass use.
Use peer assistance and teacher guidance during the activity.
Changes/Visual Consequences:
Emphasize how altering the position of shapes affects symmetry and balance in design.
Universal Design Learning Based Differentiation:
Provide visual aids and step-by-step instructions.
Allow for verbal explanations for students needing additional support.
Interdisciplinary Connections:
Mathematics: Geometry and symmetry.
Cultural studies: Mandalas and Islamic geometric art.
Notes:
Include images of different geometric shapes and designs for visual reference.
Allow students to explore different materials or methods for creating symmetrical designs if they express interest.
Folding Method: Take a piece of paper and fold it in half (horizontally for mirror symmetry, vertically for bilateral symmetry). You can make additional folds for more complex designs (e.g., fold in fourths for mandala-style). Draw your design on one half, and the fold will create the mirrored image on the other half.
Grid Method: Draw a grid on your paper. The grid lines will act as your guides for creating a mirrored design on one side that continues across the grid.
Be prepared to adjust the pace of the lesson based on student engagement and understanding.
Title Slide: "Introduction to Geometric Shapes and Symmetry" Slide 1: Definition and examples of geometric shapes. Slide 2: Explanation of symmetry with visual examples. Slide 3: Symmetrical art in different cultures (mandalas, Islamic art). Slide 4: Steps to create symmetrical designs. Slide 5: Student activity instructions.
Resources:
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