Chapter 3: The Queen's Judgement Symmetry Block Free Hand Only Symmetry Block Straight Line Only JavaScript HTML5 Applet Simulation Model

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Main Themes and Important Ideas:

1. Symmetry as a Concept: The first excerpt, through a narrative, introduces the idea of symmetry and its subjective interpretation. The "Queen's Judgement" story revolves around a vain queen who values symmetry above all else and becomes enraged when she discovers others are "at least as symmetrical as the queen." This establishes symmetry as a defining characteristic and a source of potential conflict or judgment.
2. Interactive Tools for Exploring Symmetry: Both excerpts point to the existence of interactive simulations (JavaScript HTML5 applets) focused on symmetry. The title of the first excerpt explicitly mentions "Symmetry Block Free Hand Only Symmetry Block Straight Line Only JavaScript HTML5 Applet Simulation Model." The second excerpt, "Symmetry Blocks Primary Math Interactives," further reinforces the availability of such interactive tools, specifically aimed at primary math education.
3. Practical Application through Drawing and Creation: The narrative in "The Queen's Judgement" culminates in the discovery of a "miraculous device to create symmetry." This device features a screen where drawing on one half is mirrored on the other, and upon completion, a symmetrical "being" is generated. The text explicitly invites the reader to "try your hand at drawing some symmetric beings on the device." This emphasizes the practical exploration of symmetry through creation and manipulation within the interactive environment.

• Quote: "In this simulation, you can try your hand at drawing some symmetric beings on the device. The screen is set up such that you can only draw on it by connecting the dots on the grid, but this should be sufficient for you to come up with some pretty creative shapes."

1. Educational Applications: The context of "Open Educational Resources / Open Source Physics @ Singapore" and the title "Symmetry Blocks Primary Math Interactives" clearly indicate an educational purpose for these resources. The inclusion of "Sample Learning Goals" (though the content is "[text]") and "For Teachers" (also "[text]") suggests that these simulations are designed to support teaching and learning about symmetry.
2. Different Modes of Interaction: The specific mention of "Free Hand Only" and "Straight Line Only" in the title of the first excerpt's simulation suggests that different constraints and tools might be available within the interactive environment to explore symmetry in various ways.
3. The Role of Technology in Learning: The reliance on JavaScript HTML5 applets highlights the use of modern web technologies to deliver interactive educational content, making it potentially accessible across various devices without the need for additional plugins (compared to older Flash-based resources also listed).
4. Broader Context of Educational Resources: The extensive list of other simulation applets and resources on the "Open Educational Resources / Open Source Physics @ Singapore" page indicates a larger initiative focused on developing and sharing interactive tools for various science and mathematics topics. The inclusion of links to blog posts and other resources ("Version:" and "Other Resources") further supports this.
5. Credits and Licensing: The inclusion of translator credits and the Creative Commons license information ("Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License") in the first excerpt, along with the copyright and licensing information in the second, emphasizes the open and collaborative nature of these educational resources.

Quotes Highlighting Key Ideas:

• Symmetry as a Judgment Criterion: "'So, my dear judge, how did the checks go? Not as symmetrical as they claim to be, I presume?'" (Queen speaking, demonstrating her preoccupation with symmetry).
• Interactive Creation of Symmetry: "The former king went up to the device, and with a rod, he started to draw some shapes on one half of the screen. Miraculously, the other half of the screen came to life, mirroring exactly what was drawn on the king's half. As soon as he finished his drawing, he pressed a button, and a symmetric being that was shaped exactly like what was drawn emerged from the sliding screen door." (Describing the core functionality of the symmetry creation device/simulation).
• Invitation to Explore: "'Why don't you give it a try?'" (The former king encouraging interactive engagement with the symmetry device).
• Creative Limitation: "As the concept of creative limitation goes, limiting your options can boost creativity, so go ahead and create! Have fun!" (Justification for the grid-based drawing and potential mode restrictions in the simulation).
• Target Audience: "Symmetry Blocks Primary Math Interactives" (Explicitly states the target age group and subject area).

Conclusion:

The provided excerpts introduce the concept of symmetry through an engaging narrative and highlight the availability of interactive JavaScript HTML5 applets, specifically the "Symmetry Block" simulation. These resources, part of a larger collection of open educational materials, offer a hands-on approach to learning about line symmetry through drawing and creation. The context of primary math interactives suggests these tools are designed to be accessible and engaging for younger learners. The emphasis on different drawing modes and the invitation to experiment underscore the potential for creative exploration and deeper understanding of symmetry.

The Queen's Judgement: A Study Guide

Key Concepts

• Symmetry: The quality of being made up of exactly similar parts facing each other or around an axis. In the context of the story, it refers to the physical appearance and arrangement of beings and objects.
• Line Symmetry: A type of symmetry where one half of an object is a mirror image of the other half across a dividing line (the line of symmetry).
• Rotational Symmetry: A type of symmetry where an object looks the same after being rotated by a certain angle around a central point. The text mentions rotational symmetry with orders that are perfect multiples of four.
• Asymmetry: The lack of symmetry or equality between parts or aspects of something. The majority of the "Symmetric Kingdom" inhabitants are described as asymmetric, which is ironic.
• Judgement: The act of forming an opinion or evaluation by discerning and comparing. In the story, the judge is tasked with evaluating the symmetry of visitors.
• Monarch/Queen: A sole and absolute ruler of a state, usually by hereditary right. The queen in the story is portrayed as vain and easily angered, particularly about her own level of symmetry.
• Exiled King: A former ruler who has been forced to leave their kingdom, often due to political upheaval. The exiled king in the story sought to create a perfectly symmetrical society using a special device.
• Technological Creation of Symmetry: The story introduces a device capable of generating symmetrical beings based on drawings. This highlights the distinction between naturally occurring symmetry and artificially created symmetry.
• Social Commentary: The narrative subtly critiques vanity, the abuse of power, and the arbitrary nature of judgment based on superficial qualities. It also explores themes of acceptance and harmony between different groups.

Quiz

1. Describe the initial task given to the judge by the queen. What was the queen's expectation regarding the symmetry of the visitors?
2. What was the judge's surprising report to the queen, and how did the queen react to this news?
3. Explain the judge's feelings about the symmetric beings and the reason for his imprisonment. What does this reveal about his character?
4. Describe the judge's discovery in the dungeon and where the secret passageway eventually led him.
5. What was the most striking characteristic of the refugee community the judge encountered? Provide two specific details from the text.
6. Who did the judge recognize in the refugee community, and what was this person's former role?
7. What was the exiled king's long-term goal, and how did he claim to have achieved a significant step towards it?
8. Describe the function of the "miraculous device" that the exiled king showed the judge. How did it create symmetric beings?
9. What was the exiled king's invitation to the judge after demonstrating the symmetry-creating device? What does this suggest about the nature of the simulation mentioned in the title?
10. What is the irony present in the name "Symmetric Kingdom" as observed by the imprisoned judge?

Quiz Answer Key

1. The queen tasked the judge with checking the symmetry of all the strange visitors. The queen fully expected the judge to report that the visitors were less symmetrical than she was.
2. The judge regretfully informed the queen that the vast majority of the visitors were extremely symmetrical. Upon hearing this, the queen's calm facade vanished, and she became enraged, ordering the judge's imprisonment.
3. The judge did not blame the symmetric beings for his imprisonment, recognizing that they were being punished for their existence, not any fault of their own. This shows the judge to be fair-minded and capable of empathy.
4. The judge discovered a small hole hidden by rubble in his dungeon cell. This hole led to a secret passageway that was once used as an escape route by previous rulers.
5. The refugee community was characterized by perfect symmetry in its layout and architecture, with perfectly symmetrical houses and roads divided by lines of symmetry. Additionally, structures with rotational symmetry had orders that were multiples of four, aligning with the cardinal directions.
6. The judge recognized the previous exiled king of the Symmetric Kingdom in the refugee community. He was described as jolly and encouraging of openness among his subjects.
7. The exiled king's goal was to build something magnificent and symmetric. He claimed to have come across a "miraculous device" that allowed him to create symmetric beings.
8. The device had a large screen with a grid that doubled as a sliding door. Drawing a shape on one half of the screen would cause the other half to mirror the drawing, and pressing a button would result in a symmetric being emerging from the screen door.
9. The exiled king invited the judge to try drawing on the device himself. This suggests that the "simulation model" mentioned in the title is an interactive component allowing users to create symmetric shapes using the principles demonstrated by the king's device.
10. The irony is that the kingdom is named the "Symmetric Kingdom" even though the judge observes that nearly all of its original inhabitants (the ones ruled by the queen) were actually asymmetric.

Essay Format Questions

1. Analyze the character of the queen. What motivates her actions and how does her obsession with symmetry shape the events of the story?
2. Discuss the significance of the refugee community and the exiled king's actions. What commentary might the author be making about societal values and leadership?
3. Explore the role of technology in the story, specifically the symmetry-creating device. What are the implications of being able to artificially generate symmetry?
4. Examine the theme of justice and judgment in the narrative. Were the judge's actions just? Was the queen's judgment fair?
5. Consider the symbolism of symmetry and asymmetry in the story. What might these concepts represent in the context of the kingdom and its inhabitants?

Glossary of Key Terms

• Symmetry: Correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or center.
• Line Symmetry: A type of symmetry in which an object can be divided into two identical halves by a straight line.
• Rotational Symmetry: A type of symmetry in which an object can be rotated around a central point by a certain angle and still look the same.
• Asymmetric: Lacking symmetry.
• Monarch: A sole and absolute ruler, such as a king or queen.
• Exiled: Having been expelled and barred from one's native country or home, typically for political reasons.
• Coup: A sudden, violent, and illegal seizure of power from a government.
• Delirium: An acutely disturbed state of mind characterized by restlessness, illusions, and incoherence of thought and speech.
• Cardinal Directions: The four main compass points: north, south, east, and west.
• Simulation: A model or enactment of a real-world process or system, often used for study or experimentation.

App

https://play.google.com/store/apps/details?id=com.ionicframework.symmetryblock

Sample Learning Goals

[text]

For Teachers

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Research

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Video

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 Version:

1. http://weelookang.blogspot.sg/2017/10/symmetry-block-javascript-html5-applet.html 
2. https://vle.learning.moe.edu.sg/personallibrary/lesson/view/8cf547b4-8fc3-42b5-bd53-98c838e2b1cc
3. http://weelookang.blogspot.com/2018/07/created-primary-4-math-lesson-on.html 

Other Resources

1. http://iwant2study.org/lookangejss/math/flash/Primary%20Level/Symmetry%20with%20block%20painting/Symmetry_Block.swf
2. http://iwant2study.org/lookangejss/math/flash/Primary%20Level/symmetry%20by%20drawing/Symmetry_Drawing.swf