Using GeoGebra to Design Origami Simulations by Mark Kaercher

GeoGebra
15 May 202449:28

TLDRMark Kaercher presents a session on using GeoGebra to create origami simulations, suitable for educators and learners of any age. He emphasizes the importance of hands-on activities combined with digital tools, particularly for teaching geometric concepts. Kaercher demonstrates how to fold paper into various shapes, explaining the difference between valley and mountain folds. He guides the audience through creating a basic square with folds, then advancing to more complex origami models using GeoGebra's tools. The session highlights the educational potential of integrating traditional origami with digital simulation, showcasing the versatility of GeoGebra for teaching mathematics creatively.

Takeaways

  • 😀 The presenter, Mark Kaercher, is an experienced mathematics teacher who uses GeoGebra to teach origami simulations to middle school students.
  • 📐 Mark demonstrates the basics of origami with simple folds like the 'hot dog' and 'hamburger' folds, explaining the difference between valley and mountain folds.
  • 🖊️ Students are instructed to use colored pencils to color the creases on their paper to represent the folds, with blue for valley and red for mountain folds.
  • 🔵 The importance of the color blue in origami is highlighted, as it represents water features like rivers, which are often found in valleys.
  • 💻 The session transitions from physical origami to digital simulations using GeoGebra, allowing students to explore the principles of folding on-screen.
  • 📐 Mark guides the audience through constructing a square in GeoGebra, emphasizing the simplicity of the tool's segment tool for creating shapes.
  • 🎨 In GeoGebra, the color and opacity of the segments are adjusted to represent different types of folds, with 100% opacity indicating a full fold.
  • 📄 The process of exporting the GeoGebra construction as an SVG file and importing it into an origami simulator for digital folding is explained.
  • 🤔 The origami simulator provides a visual representation of the stress and tension in the paper model through different color shades.
  • 📚 Mark shares resources and encourages further exploration of origami simulations, suggesting activities like creating GIFs or using the models for adult-focused events.

Q & A

  • What is the main topic of the presentation?

    -The main topic of the presentation is using GeoGebra to design origami simulations.

  • Why did the presenter choose to present on origami simulations instead of drones?

    -The presenter chose to present on origami simulations because it aligns better with the audience's background and interests, as indicated by their introductions and experiences.

  • What is the presenter's background in education?

    -The presenter has been teaching mathematics for 30 years, mostly at the high school level, but currently teaches middle school sixth graders.

  • What is the significance of origami in various fields?

    -Origami has significant applications in engineering and medicine, such as the deployment mechanism of the James Webb Space Telescope which utilized origami principles.

  • What is the purpose of folding paper in the presentation?

    -The purpose of folding paper is to demonstrate the basic principles of origami and to transition into digital origami simulations using GeoGebra.

  • What are the two primary folds in origami mentioned in the script?

    -The two primary folds in origami are the valley fold and the mountain fold.

  • How does the presenter optimize the use of paper for the origami activity?

    -The presenter optimizes paper use by using small squares of paper, often sourced from copy rooms or old school guillotine paper cutters.

  • What is the purpose of coloring the paper folds blue and red in the origami activity?

    -The blue color represents valley folds and the red represents mountain folds, which helps in visualizing the crease pattern for the origami simulation.

  • Why does the presenter prefer using the segment tool in GeoGebra?

    -The presenter prefers the segment tool because it is simple to use and sufficient for the origami simulations being taught to sixth graders.

  • What is the importance of the 'Origami Simulator' in the digital part of the presentation?

    -The 'Origami Simulator' is important as it allows the presenter and participants to visualize and interact with the digital origami models created in GeoGebra.

  • How does the presenter suggest using the origami simulations beyond the classroom?

    -The presenter suggests using origami simulations for educational purposes at various age levels, and even for recreational activities like 'Geo sip', similar to paint and sip events.

Outlines

00:00

🎓 Introduction to Presentation Choices and Teaching Philosophy

The speaker begins by expressing gratitude for the opportunity to present and mentions the difficulty of choosing between two topics, comparing it to choosing a favorite child. They highlight their experience teaching mathematics for 30 years, mostly at the high school level, but currently teaching middle school sixth graders. The speaker emphasizes the sophistication of the curriculum and the advanced technological skills of today's youth. They introduce a unit on origami simulations using Geogebra as part of their teaching, aiming to inspire further exploration and application in the classroom.

05:02

📐 Basic Origami Folds and Their Digital Representation

The speaker instructs the audience to perform basic origami folds on a square piece of paper, explaining the concepts of valley and mountain folds. They relate these folds to geographical features like rivers and demonstrate how to represent them digitally using Geogebra. The audience is guided through coloring the folds with pencils to represent different types of terrain. The speaker also discusses the transition from analog teaching methods to embracing digital tools like Geogebra, which combines hands-on activities with digital technology.

10:04

🛠️ Geogebra Interface and Creating a Square

The speaker provides a tutorial on using Geogebra, focusing on creating a square using the segment tool. They guide the audience through the interface, explaining how to navigate and use the tools effectively. Emphasis is placed on customizing settings to simplify the construction process, such as turning off automatic labeling. The speaker also discusses the importance of putting tools away after use to maintain a clean workspace in Geogebra.

15:05

🖌️ Coloring and Opacity Control in Geogebra

The audience is instructed on how to color the segments created in Geogebra to represent different types of origami folds. The speaker explains the importance of selecting the correct shades of blue and red to mimic the colors used in the origami simulator. They also demonstrate how to adjust the opacity of the segments to control the visibility and intensity of the colors, which can affect the perception of the folds in the digital simulation.

20:08

🔄 Downloading and Transferring Geogebra Models to Origami Simulator

The speaker shows how to download Geogebra constructions as SVG files and import them into the Origami Simulator. They discuss the importance of turning off the axes in Geogebra before downloading to ensure a clean import. The audience is encouraged to explore the simulator, understand its tools, and observe how different folds affect the model. The speaker also touches on the concept of strain in origami and how it can be visualized in the simulator.

25:09

📚 Advanced Origami Models and Multiple Object Creation

The speaker challenges the audience to create more complex origami models using Geogebra, explaining how to handle multiple objects and folds. They discuss the possibility of creating multiple models simultaneously and importing them into the Origami Simulator. The speaker also addresses the use of different tools in Geogebra and the importance of keeping the process simple for younger students.

30:10

🎨 Coloring and Segmentation in Advanced Models

The audience is guided through the process of coloring and segmenting more complex origami models in Geogebra. The speaker emphasizes the importance of selecting the correct colors and opacities for valley and mountain folds. They also demonstrate how to handle cuts in the models, which are represented by a different color. The speaker encourages collaboration and learning from one another during the process.

35:14

📝 Saving and Sharing Geogebra Models

The speaker discusses how to save Geogebra constructions for future use and how to share them with others. They mention the use of Google Drive for sharing files and provide guidance on exporting models as SVG files. The speaker also highlights the importance of exploring the examples available in Geogebra and encourages the creation of animated GIFs to showcase the folding process.

40:18

📝 Conclusion and Invitation for Further Exploration

In conclusion, the speaker reiterates the value of using Geogebra and origami simulations for teaching geometric concepts across various age groups. They extend an invitation for further exploration and learning, offering their contact information for anyone interested in discussing the topic further. The speaker also encourages the audience to check out the examples and resources provided for additional inspiration.

Mindmap

Keywords

💡GeoGebra

GeoGebra is a dynamic mathematics software that combines geometry, algebra, spreadsheets, graphing, statistics, and calculus. In the context of the video, GeoGebra is used to create origami simulations, demonstrating how mathematical concepts can be applied to the art of paper folding. The script mentions using GeoGebra to design squares and segments, which are then folded in the origami simulation.

💡Origami

Origami is the traditional Japanese art of paper folding. In the video, origami is used as a means to explore geometric concepts through hands-on activities. The script describes simple origami folds like the 'Valley fold' and 'Mountain fold', and how these can be translated into digital simulations using GeoGebra.

💡Valley fold

A valley fold in origami is a crease made by folding the paper such that the fold line appears like a valley, with both sides of the paper sloping downwards towards the fold. The script uses this concept to instruct how to fold paper and then replicate that fold digitally in GeoGebra.

💡Mountain fold

A mountain fold is the opposite of a valley fold, where the paper is folded so that the fold line appears like a mountain ridge, with both sides of the paper sloping upwards towards the fold. The script mentions creating mountain folds and coloring them to understand the concept better.

💡Crease pattern

A crease pattern in origami is a diagram that shows all the necessary creases to fold a particular model. In the video, the presenter guides the audience to create a crease pattern using GeoGebra, which is then used to simulate the folding process in the origami simulator.

💡SVG

SVG stands for Scalable Vector Graphics, an XML-based vector image format for two-dimensional graphics with support for interactivity and animation. The script mentions downloading GeoGebra constructions as SVG files to import into the origami simulator.

💡Origami simulator

An origami simulator is a digital tool that allows users to simulate the folding of paper based on crease patterns. The script describes using an origami simulator to import GeoGebra's SVG files and visualize the folding process digitally.

💡Hands-on

Hands-on activities are those that involve practical participation or experimentation, as opposed to theoretical or observational learning. The script emphasizes the combination of hands-on paper folding with digital simulations in GeoGebra to enhance learning.

💡Digital tools

Digital tools refer to software or applications that are used on computers or other devices to perform tasks. In the video, digital tools like GeoGebra and origami simulators are used to complement traditional teaching methods and provide a modern approach to learning origami and geometry.

💡Geogebra tools

GeoGebra tools are the various features and functionalities available within the GeoGebra software that allow users to construct geometric figures, plot graphs, and perform simulations. The script discusses using specific tools like the segment tool to create squares and folds.

💡Fold percentage

In the context of the video, fold percentage refers to the degree to which a paper fold is made. The script explains how to adjust the fold percentage in GeoGebra to simulate different stages of folding, from no fold (0%) to a complete fold (100%).

Highlights

Presenter chooses Origami Simulations over Drones for the session.

Excitement about being with like-minded educators and the joy of learning.

30 years of teaching mathematics, now teaching Middle School sixth graders.

Sophisticated technology use by today's sixth graders.

Introduction to a unit on origami simulations using GeoGebra.

Simple origami experiences like paper airplanes are relatable to everyone.

Origami's influence in engineering and medicine, like the web telescope.

Starting with simple origami simulations using squares of paper.

Explanation of valley and mountain folds in origami.

Hands-on folding practice with paper to understand basic principles.

Transition to digital origami using GeoGebra tools.

Creating a square in GeoGebra to represent the paper.

Constructing folds in GeoGebra using the segment tool.

Coloring segments in GeoGebra to represent valley and mountain folds.

Adjusting fold percentages in GeoGebra for accuracy.

Exporting GeoGebra constructions as SVG for origami simulation.

Using the origami simulator to visualize the folding process.

Importing GeoGebra designs into the origami simulator.

Creating a more complex origami model step by step.

Adding cuts to the origami model and selecting the right color for them.

Importing and folding multiple GeoGebra models in the origami simulator.

Invitation to explore geometric concepts through origami at any age.

GeoGebra's potential for adult education and team-building activities.

Availability of resources and examples for further learning.