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Translations

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Credits

Shaun Quek; Loo Kang Wee; based on idea by Theresa Heng; Francisco Esquembre; Félix Jesús Garcia Clemente

 

Main Themes:

  • Open Educational Resource (OER): The game is presented as part of the "Open Educational Resources / Open Source Physics @ Singapore" initiative, emphasizing its accessibility and potential for free use and adaptation in educational settings.
  • Interactive Learning Tool: The core theme is the use of an interactive HTML5 Javascript applet to engage students in a mathematical and strategic game based on the knight's movement in chess.
  • Development Credits and Collaboration: The source explicitly credits the individuals involved in the creation and conceptualization of the game, highlighting a collaborative effort.
  • Educational Goals: The primary aim of the game is to "facilitate the critical thinking of students as they plan out the best route for the knight to achieve the highest score."
  • Technical Information and Access: The document provides technical details such as the embed code for integrating the game into webpages and links to run the applet.
  • Variations and Challenges: The game offers different board sizes (3x3, 4x4, 5x5), with a specific hint about the possibility of covering every square on the 5x5 board.
  • Context within a Broader Platform: The game is listed within a larger collection of interactive simulations and resources covering various subjects, primarily science and mathematics.

Most Important Ideas and Facts:

  • Game Description: The "Knight's Tour Game HTML5 Javascript Applet" is a single-player interactive game where the objective is to move a knight chess piece to cover as many squares as possible on a chosen board size (3x3, 4x4, or 5x5), touching each square only once, until no legal moves remain.
  • Quote: "The player can start from any square on the board, and the objective is to cover as many squares as possible with the knight chess piece (only touching each square once) until the knight runs out of moves."
  • Educational Purpose: The game is designed to enhance students' critical thinking skills through strategic planning of the knight's moves.
  • Quote: "The aim of this game is to facilitate the critical thinking of students as they plan out the best route for the knight to achieve the highest score."
  • Board Size and Solvability: The game offers three board sizes, and it is explicitly stated that covering every square is not possible on the 3x3 or 4x4 boards but is achievable on the 5x5 board.
  • Quote: "(Hint: It is not possible to cover every square for a 3 by 3 or 4 by 4 board, but it is possible for a 5 by 5 board.)"
  • Accessibility and Embedding: The applet can be easily embedded into webpages using the provided iframe code.
  • Quote: "Embed this model in a webpage: <iframe width="100%" height="100%" src="https://iwant2study.org/lookangejss/math/ejss_model_knight_intro/knight_intro_Simulation.xhtml " frameborder="0"></iframe>"
  • Credits: The game is credited to Shaun Quek and Loo Kang Wee, based on an idea by Theresa Heng, with contributions from Francisco Esquembre and Félix Jesús Garcia Clemente.
  • Sample Learning Goals: While the specific learning goals are presented as "[text]", the context implies that they relate to strategic thinking, problem-solving, and potentially spatial reasoning within the constraints of the knight's movement.
  • Broader Resource Context: The game is part of a larger collection of OERs hosted on the "Open Educational Resources / Open Source Physics @ Singapore" platform, which includes a wide variety of interactive simulations and tools for mathematics and science education. The extensive list of other resources demonstrates the scope of this initiative, encompassing topics from physics and chemistry to mathematics and even language learning, often utilizing Javascript HTML5 applets.

Source 2: Excerpts from "Knight's Move Game for 1 PLayer Strategy Game to maximise number of moves"

Main Themes:

  • Alternative Title and Emphasis: This source provides an alternative title for what appears to be the same game, further emphasizing its nature as a "1 Player Strategy Game" with the goal of maximizing the number of moves.
  • Consistent Author and Credits: The author and contributors listed are identical to those in the first source, confirming it is likely the same game or a closely related version.
  • Licensing Information: This source explicitly mentions the game being released under a license, although the specific details of the license are not provided in the excerpt.
  • Development Tool: It states that the game was "Compiled with EJS 6.1 BETA (201115)," indicating the software used for its development.

Most Important Ideas and Facts:

  • Alternative Title Reinforcement: The title "Knight's Move Game for 1 PLayer Strategy Game to maximise number of moves" reinforces the game's core mechanics and objective.
  • Consistent Credits: The repetition of the credits confirms the collaborative nature of the project.
  • Licensing: The game is released under a license, suggesting specific terms of use and distribution.
  • Quote: "Released under a license."
  • Development Technology: The game was compiled using "EJS 6.1 BETA (201115)," providing insight into the development process and potentially relevant software for those interested in modifying or creating similar applets.
  • Quote: "Compiled with EJS 6.1 BETA (201115)"

Overall Summary:

Both sources describe the same or a very similar educational game applet, "Knight's Tour Game" or "Knight's Move Game," designed to promote critical thinking and strategic planning in students. The game, available as an interactive HTML5 Javascript applet, allows players to attempt a knight's tour on different sized chessboards with the objective of covering as many squares as possible. It is presented as an Open Educational Resource from Singapore, emphasizing its free accessibility and potential for integration into educational materials. The sources credit the developers and highlight the game's intended use in facilitating mathematical and strategic reasoning. The technical details provided, such as the embed code and development software, offer practical information for educators and developers interested in utilizing or adapting the resource.

 

 

Knight's Tour Game Study Guide

Overview:

This study guide is designed to help you review your understanding of the Knight's Tour Game applet, its purpose, and related concepts as presented in the provided source materials. The game is an interactive tool that allows players to explore the classic mathematical problem of the Knight's Tour on different sized chessboards. The objective is to move the knight piece, according to its standard "L" shaped movement, to as many unique squares as possible. The applet aims to foster critical thinking and strategic planning skills.

Key Concepts:

  • Knight's Tour: A mathematical problem involving a knight on a chessboard. The goal is to find a sequence of moves such that the knight visits every square exactly once. A closed tour is one where the knight ends on a square that is one knight's move from the starting square.
  • Heuristic: A problem-solving approach that uses practical methods or shortcuts to produce solutions, which may not be optimal or perfect but are sufficient for the immediate goals. Playing the Knight's Tour game often involves applying heuristics to find a good, if not perfect, solution.
  • Critical Thinking: The objective analysis and evaluation of an issue in order to form a judgment. In the context of the game, this involves planning moves, considering future possibilities, and adapting strategies based on the board state.
  • Strategic Planning: The process of defining a strategy, or direction, and making decisions on allocating resources to pursue this strategy. In the game, this involves thinking several moves ahead to maximize the number of visited squares.
  • Interactive Learning: A method of learning that involves active engagement from the learner through activities, simulations, and feedback. The Knight's Tour applet provides an interactive environment for exploring the mathematical concept.
  • Open Educational Resources (OER): Educational materials and resources offered freely and openly for anyone to use, adapt, and share. The Knight's Tour applet is presented as an OER.
  • HTML5 Javascript Applet: A small application or program that is written using HTML5 and Javascript and can be embedded and run within a web browser. This is the technology used to create the Knight's Tour game.

Quiz:

Answer the following questions in 2-3 sentences each.

  1. What is the primary objective of the Knight's Tour Game applet?
  2. What are the different chessboard sizes available to play on in the applet?
  3. According to the text, is it possible to cover every square on all available board sizes? If not, specify which board(s) make this possible.
  4. What type of movement is the knight chess piece restricted to in the game?
  5. What are some of the credited individuals involved in the creation or inspiration of the Knight's Tour Game applet?
  6. Where can a user typically find and run the Knight's Tour Game applet?
  7. What skill is the game specifically designed to facilitate in students?
  8. What does it mean for the player to run out of moves in the context of the game?
  9. Besides mathematics, what other category or subject is the applet listed under on the webpage?
  10. What is the license under which the EasyJavaScriptSimulations Library is available for commercial use, as mentioned in the broader website context?

Quiz Answer Key:

  1. The primary objective of the Knight's Tour Game applet is to allow players to simulate a Knight's Tour and cover as many squares as possible on a chessboard without visiting any square more than once. The goal is to achieve the highest possible score by strategically planning the knight's moves.
  2. The Knight's Tour Game applet offers three different chessboard sizes for the player to choose from: a 3 by 3 board, a 4 by 4 board, and a 5 by 5 board. This allows for varying levels of challenge and exploration of the game's mechanics.
  3. According to the provided text, it is not possible to cover every square on either the 3 by 3 or the 4 by 4 board. However, the text explicitly states that it is possible to cover every square on the 5 by 5 board, presenting a greater strategic challenge.
  4. In the game, the knight chess piece is restricted to its standard "L" shaped movement, which consists of moving two squares in one of the four cardinal directions (horizontally or vertically) and then one square at a right angle. This unique movement pattern forms the basis of the game's challenge.
  5. The credited individuals involved in the creation or inspiration of the Knight's Tour Game applet include Shaun Quek, Loo Kang Wee, Theresa Heng (based on whose idea it is), Francisco Esquembre, and Félix Jesús Garcia Clemente. These individuals contributed to the conception, development, and sharing of the applet.
  6. A user can typically find and run the Knight's Tour Game applet by accessing the provided link, which leads to an embedded HTML5 Javascript application. This allows the game to be played directly within a web browser without the need for additional software installation.
  7. The game is specifically designed to facilitate the critical thinking of students as they plan out the optimal route for the knight to achieve the highest score. By strategically considering each move and its consequences, players develop their analytical and problem-solving abilities.
  8. In the context of the game, the knight runs out of moves when it reaches a square from which no further legal "L" shaped moves can be made to an unvisited square. At this point, the game ends, and the player's score is determined by the number of squares visited.
  9. Besides mathematics, the applet is also listed under the category of Games on the webpage. This highlights its dual purpose as both an educational tool for exploring mathematical concepts and an engaging interactive game.
  10. The EasyJavaScriptSimulations Library is available under a separate license for commercial use, as mentioned by the link to the EJSLicense and the instruction to contact fem@um.es directly for permissions. The broader website content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License.

Essay Format Questions:

  1. Discuss how the Knight's Tour Game applet can be used as an effective tool for teaching and learning critical thinking and strategic planning skills in a mathematical context. Provide specific examples of how a student might engage with the game to develop these skills.
  2. Analyze the design and functionality of the Knight's Tour Game applet as an example of an Open Educational Resource. What are the benefits of offering such a tool as an OER for educators and learners?
  3. Compare and contrast the challenges and strategies involved in playing the Knight's Tour Game on the different board sizes (3x3, 4x4, and 5x5). How does the change in board size affect the player's approach to maximizing visited squares?
  4. Explore the mathematical problem of the Knight's Tour beyond the scope of the applet. Discuss the historical significance of the problem, different approaches to solving it (including Warnsdorff's Rule), and its relevance to graph theory and computer science.
  5. Consider the role of interactive simulations and games, like the Knight's Tour applet, in enhancing student engagement and understanding of abstract concepts in mathematics and other subjects. What are the pedagogical advantages of using such tools in the classroom?

Glossary of Key Terms:

  • Applet: A small application, often written in Java or JavaScript, designed to be run within another application (typically a web browser).
  • Critical Thinking: The ability to analyze information objectively and make reasoned judgments. It involves evaluating evidence, identifying assumptions, and considering different perspectives.
  • HTML5: The latest evolution of the standard that defines the structure and content of the Web. It enables multimedia and interactive elements without the need for plugins.
  • Interactive: Involving two-way communication or action between the user and a system or interface. Allows for active participation and response.
  • Javascript: A high-level, often just-in-time compiled language that conforms to the ECMAScript specification. It is commonly used to make web pages interactive.
  • Knight's Move: The unique movement of the knight in chess, consisting of moving two squares in one direction (horizontal or vertical) and then one square perpendicularly.
  • Knight's Tour: A sequence of moves of a knight on a chessboard such that the knight visits every square exactly once.
  • Open Educational Resources (OER): Teaching, learning, and research materials that are in the public domain or have been released under an open license, permitting no-cost access, use, adaptation, and redistribution by others with no or limited restrictions.
  • Simulation: A model of a real or imagined system that allows users to interact with it and observe the outcomes of different actions or inputs.
  • Strategic Planning: The process of setting long-term goals and determining the best way to achieve them, often involving careful consideration of resources and potential obstacles.

Sample Learning Goals

[text]

For Teachers

Knight's Tour Game HTML5 Javascript Applet 

Initial state of the game

The link to the game can be found here.

Description

This is a simple interactive that attempts to simulate a "Knight's Tour" game. The player can start from any square on the board, and the objective is to cover as many squares as possible with the knight chess piece (only touching each square once) until the knight runs out of moves. This game allows the player to choose from 3 different boards: a 3 by 3, 4 by 4, or 5 by 5 board. The aim of this game is to facilitate the critical thinking of students as they plan out the best route for the knight to achieve the highest score. 
(Hint: It is not possible to cover every square for a 3 by 3 or 4 by 4 board, but it is possible for a 5 by 5 board.)
The game in progress
The link to the game can be found here.
 

Research

[text]

Video

[text]

 Version:

  1. https://iwant2study.org/lookangejss/math/ejss_model_knight_intro/

Other Resources

[text]

 

Frequently Asked Questions: Knight's Tour Game

Q1: What is the Knight's Tour Game applet? The Knight's Tour Game applet is an interactive single-player strategy game, implemented using HTML5 and JavaScript, that simulates the movement of a knight chess piece on a board. The objective is for the player to move the knight to as many unique squares as possible without landing on the same square twice, until no valid moves remain.

Q2: What are the learning goals of this game? The primary learning goal of the Knight's Tour Game is to facilitate and enhance the critical thinking skills of students. By planning out the sequence of moves, players can develop their strategic thinking and problem-solving abilities as they aim to achieve the highest possible score by covering the maximum number of squares.

Q3: What board sizes are available in the game? The game offers a choice of three different board sizes: a 3x3, a 4x4, and a 5x5 grid. This allows players to experience the game with varying levels of complexity and explore how the board size impacts the possible moves and strategies.

Q4: Is it possible to visit every square on each of the available board sizes? The game provides a hint regarding the possibility of completing a full tour (visiting every square exactly once). It explicitly states that it is not possible to cover every square on either the 3x3 or the 4x4 boards. However, it is indeed possible to visit every square on the 5x5 board. This adds an element of discovery and encourages players to experiment with different strategies.

Q5: How do you play the Knight's Tour Game? To play, the user starts by selecting a board size (3x3, 4x4, or 5x5) and then clicks on any square to begin the knight's tour. From the current square, the player must choose a valid "L-shaped" move (two squares in one of the four cardinal directions, then one square at a right angle). Each square can only be visited once. The game ends when the knight has no remaining valid moves to an unvisited square. The player's score is the number of unique squares visited.

Q6: Who developed this Knight's Tour Game applet? This HTML5 JavaScript applet was developed by Theresa Heng, with contributions and adaptations by Shaun Quek and Loo Kang Wee. The project also acknowledges the work of Francisco Esquembre and Félix Jesús Garcia Clemente, likely for the underlying Easy JavaScript Simulations (EJS) framework used in its creation.

Q7: Where can I access and play this Knight's Tour Game? The Knight's Tour Game can be accessed and played through the embed provided in the source, which links to the following address: https://iwant2study.org/lookangejss/math/ejss_model_knight_intro/knight_intro_Simulation.xhtml. This link allows users to directly run the simulation in their web browser.

Q8: For whom is this game intended? While described under a mathematics section and with a focus on critical thinking, this game is likely intended for students of various levels who want to engage in a fun and challenging puzzle that promotes strategic planning. The availability of different board sizes makes it accessible for both younger and older students to explore the principles of movement and problem-solving within a constrained environment.

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