Translations

Code	Language		Translator	Run

Credits

lookang; Francisco Esquembre; Felix J. Garcia Clemente

 Add to Twenty Game 

Briefing Document: Target Math (Race to 20) Game & Open Source Physics Resources

1. Overview

This document reviews the "Target Math (Race to 20)" game, a card-based mathematics activity designed by Theresa Heng and implemented as a JavaScript HTML5 applet. The source also highlights the broader Open Educational Resources / Open Source Physics @ Singapore project, which provides numerous interactive educational simulations and tools, primarily in physics and mathematics.

2. Target Math (Race to 20) Game

• Core Concept: The game is designed to help students understand the logic of reaching a target number (default 20) through addition. It encourages strategic thinking and an understanding of number relationships, particularly in the context of winning strategies.
• Gameplay: Two players (or a player vs. AI) take turns adding numbers (represented by cards) to a running total, aiming to be the first to reach the target number.
• Customization: The game offers customizable parameters for increased difficulty:
• Target Number: Can be varied from the default 20 (e.g., to 40).
• Starting Number: Can be changed from the default of 0 (e.g., to 10).
• Number of Cards: The range of numbers on cards available to players can be adjusted (default is 11, or numbers 1 to 11).
• Card Type: Can be restricted to odd or even numbers for either player, adding to the challenge.
• Winning Strategy: The key to winning is to reach a specific number before your opponent to force their moves and guarantee a final landing on the target number. The document outlines the underlying math for the win using formulas:
• "The hint is to always win, you need to reach (end-start) - n -1 , which is 8 so that whatever the next move by the opponent ranging from 1 to 11, you can place your next card to reach end =20!" (Where 'end' is the target number, 'start' is the starting number, and 'n' is the largest card number)
• Another example: "So the AI step is = end - i*(n+1), so stepAI[0https://iwant2study.org/lookangejss/math/ejss_model_racetotwentywithStartNumber/racetotwentywithStartNumber_Simulation.xhtml" target="_blank" rel="noopener noreferrer" style="box-sizing: border-box; color: rgb(0, 102, 204); text-decoration: underline;">https://iwant2study.org/lookangejss/math/ejss_model_racetotwentywithStartNumber/racetotwentywithStartNumber_Simulation.xhtml
• A Progressive Web App (PWA): https://iwant2study.org/lookangejss/math/ejss_pwa_racetotwentywithStartNumber/
• Mobile Apps for Android and iOS (links provided)

3. Open Educational Resources / Open Source Physics @ Singapore

• Project Focus: This is a larger initiative providing freely accessible educational resources, with a strong emphasis on interactive simulations and applets developed using Easy JavaScript Simulations (EjsS).
• Subject Coverage: While the "Target Math" game is included under mathematics, the project is primarily focused on physics, offering a wide variety of simulations and tools for various physics concepts.
• Resource Types: The project provides:
• Interactive applets (JavaScript/HTML5) covering diverse topics.
• Tracker-based simulations that use video analysis.
• 3D models and WebGL implementations of physical phenomena.
• Tools that include virtual labs.
• Open Source Physics based software development
• Development and Collaboration: The project has been collaborative in nature, acknowledging contributions from multiple individuals and institutions within the Open Source Physics community, including Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian and Felix J. Garcia Clemente.
• Accessibility: Resources are hosted on https://sg.iwant2study.org/ospsg/
• Licensing: Content is licensed under a Creative Commons Attribution-Share Alike 4.0 Singapore License. However, the EasyJavaScriptSimulations Library has separate commercial licensing terms.
• Recognition: The project and its contributors have received various awards, showcasing its impact in education.

4. Key Themes and Important Ideas

• Open Educational Resources (OER): The project strongly emphasizes the use of OER to improve education accessibility and facilitate learning using interactive technology.
• Interactive Learning: A strong focus on interactive simulations and applets to enhance learning, allowing students to experiment, explore, and develop conceptual understanding.
• Computational Modeling: The use of simulations that enable students to build and test models of mathematical and physical systems.
• Technology Integration: Emphasizes the use of technology, especially JavaScript/HTML5, for creating and deploying educational resources and the use of open source based tools.
• Collaborative Development: The resources are a result of the efforts of many in the Open Source Physics community.
• Teacher Resources: Provides resources for teachers including sample learning goals and software requirements.
• Multiple Platforms: The project has resources available on web, mobile and app store platforms.

5. Quotes from Source

• "This card game designed to help understand how to always be the first person to reach 20 by allowing students to develop their own thinking about the rules of reaching twenty."
• "The hint is to always win, you need to reach (end-start) - n -1 , which is 8 so that whatever the next move by the opponent ranging from 1 to 11, you can place your next card to reach end =20!"
• "This app is created to support playing of adding up in creative and challenging ways."
• "My sincere gratitude for the tireless contributions of Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian, Félix Jesús García Clemente, Anne Cox, Andrew Duffy, Todd Timberlake and many more in the Open Source Physics community."
• "Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License."

6. Conclusion

The "Target Math (Race to 20)" game and the broader Open Educational Resources / Open Source Physics @ Singapore project demonstrate a commitment to leveraging technology to enhance mathematics and science education. The resources provide a wealth of interactive learning tools that can benefit both students and educators.

This briefing document offers a starting point for understanding these valuable resources. Further exploration of the website and the various links provided would be beneficial for those seeking more detailed information.

 

Target Math (Race to 20) Study Guide

Quiz

Instructions: Answer the following questions in 2-3 sentences each.

1. What is the primary purpose of the "Target Math (Race to 20)" game?
2. In the game, what does the "end" number represent, and what is its default value?
3. How does the game incorporate the concept of a "start" number? What is its default value?
4. What does "n" represent in the game's rules, and what does it determine?
5. According to the hint provided, what is the key number a player needs to reach to guarantee a win, given an "end" and "start" number, and the maximum card number "n?"
6. Explain the formula "end - i*(n+1)" and what it calculates.
7. Describe how varying the target end number can change the game.
8. Besides the default, what other parameters of the game can be changed to alter the difficulty of the gameplay?
9. What acknowledgement does the game's description provide, and to whom is credit given?
10. What are some other educational resources you might find on the site hosting this game?

Quiz Answer Key

1. The primary purpose of the "Target Math (Race to 20)" game is to help students understand the strategy of reaching a target number, specifically 20, through addition, by encouraging them to develop their own winning strategies. It's based on a card game and helps with strategic thinking.
2. The "end" number represents the final target number players are trying to reach. The default value is 20.
3. The game incorporates a "start" number as the initial number from which the players begin to add; it allows for variability in game play. The default "start" number is 0.
4. "n" represents the largest card number available to each player. It determines the maximum amount a player can increase the running total on each turn.
5. To guarantee a win, a player needs to reach the number equal to (end-start) - n -1, as it forces a win on the subsequent turn. This is strategically advantageous as it limits the other player's ability to reach the end number.
6. The formula "end - i*(n+1)" calculates the target numbers that guarantee a win, with "i" representing the sequence of steps in reaching the end number. This formula is specific to this game's strategy.
7. Varying the target end number increases or decreases the complexity of the game by adjusting the total sum to reach. Increasing the end number generally leads to longer, more strategic game play.
8. The difficulty can be altered by changing the target end number, the start number, the number of cards available, and card limitations such as odd or even cards. This allows for a lot of customization in game play.
9. The game description acknowledges Theresa Heng for originally showing and conceptualizing the physical card game this simulation is based on. It also thanks contributors in the Open Source Physics community.
10. You can find other interactive resources for math and science, including physics simulations, games, and learning tools. The site includes material for various grade levels from primary to junior college.

Essay Questions

Instructions: Write an essay addressing each of the following questions.

1. Discuss the pedagogical value of the "Target Math (Race to 20)" game. How can it be used effectively in an educational setting to improve students' understanding of mathematical concepts and problem-solving strategies?
2. Analyze the strategic thinking involved in the "Target Math (Race to 20)" game. How can players use the provided hint to develop a guaranteed winning strategy, and what mathematical principles does this reveal?
3. Compare and contrast the various ways that the parameters of the "Target Math (Race to 20)" game can be modified to increase or decrease its difficulty. How do changes to parameters like the target number, starting number, and card limitations impact gameplay?
4. Explore the design principles of the "Target Math (Race to 20)" applet simulation model. What elements of the design contribute to its accessibility, usability, and overall effectiveness as a learning tool?
5. Considering the game's connection to the Open Source Physics community, discuss the importance of open educational resources and collaborative development in creating innovative learning materials. How does the "Target Math (Race to 20)" project exemplify this?

Glossary of Key Terms

• End Number: The target number that players aim to reach through addition in the game. Default is 20.
• Start Number: The number from which players begin adding to reach the end number. Default is 0.
• n: The largest numerical value available on a card, representing the maximum addition possible in a single turn by a player.
• (end-start) - n -1: The strategic target number that guarantees a win for the player who reaches it first. It's derived from the end, start and the largest card number.
• Open Educational Resources (OER): Educational materials that are freely available for use, adaptation, and distribution, often promoting collaboration and innovation.
• Open Source Physics (OSP): A community-driven movement that promotes open-source tools for physics education, focusing on interactive simulations and models.
• Applet Simulation Model: An interactive computer simulation, in this case, using JavaScript/HTML5, that models the rules and gameplay of the "Target Math (Race to 20)" game.
• Pedagogical Value: The educational benefit or learning potential of a resource or activity; in this case, the value of the game as a learning tool.
• Strategic Thinking: The process of thinking through a problem and developing a plan to achieve a goal; crucial in this game for understanding how to guarantee a win.
• Parameter: A variable that determines the characteristics or behavior of a system or game. In this case, game parameters include the start number, end number, and card limitations.

App

https://iwant2study.org/lookangejss/math/ejss_pwa_racetotwentywithStartNumber/ PWA

 

 https://play.google.com/store/apps/details?id=com.ionicframework.raceto20 

https://itunes.apple.com/us/app/race-to-twenty-card-game-for-fun-learning-addition/id1272553809?ls=1&mt=8

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About

About
This card game designed to help understand how to always be the first person to reach 20 by allowing students to develop their own thinking about the rules of reaching twenty.

Let assume end in the last number, say 20
Start is the beginning number say 0
largest card number is say, n = 11 for both RED and BLUE players.

The hint is to always win, you need to reach (end-start) - n -1 , which is 8 so that whatever the next move by the opponent ranging from 1 to 11, you can place your next card to reach end =20!

Another example is
Let assume end in the last number, say 20
Start is the beginning number say 0
largest card number is say, n = 5 for both RED and BLUE players.
So the AI step is = end - i*(n+1),
so stepAI[0] = 20 -0*(5+1) = 20
stepAI[1] = 20-1*(5+1) = 14
stepAI[2] = 20-2*(5+1) = 8
stepAI[3] = 20-3*(5+1) = 2
so to win, try to land on 2, followed by 8, followed by 14 and lastly to win 20!
enjoy!

Game play can be made more challenging by varying target end number from default 20 to 40 for example.
start number from default of 0 to 10 for example
number of cards available to players, default is 11
odd numbers card only for player 1 or 2
even numbers cards only for player 1 or 2

more resources can be found here
https://sg.iwant2study.org/ospsg/index.php/interactive-resources/mathematics

Interesting Fact
This app is created to support playing of adding up in creative and challenging ways.

Acknowledgement
This physical card game was originally shown to me and conceptualized by Theresa Heng.

My sincere gratitude for the tireless contributions of Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian, Félix Jesús García Clemente, Anne Cox, Andrew Duffy, Todd Timberlake and many more in the Open Source Physics community.

Network Learn together?
FaceBook Fan Page: https://www.facebook.com/Open-Source-Physics-Easy-Java-Simulation-Tracker-132622246810575/
Twitter: https://twitter.com/lookang
YouTube: https://www.youtube.com/user/lookang/videos
Blog: http://weelookang.blogspot.sg/
Digital Library: https://sg.iwant2study.org/ospsg/

 

Sample Learning Goals

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For Teachers

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Software Requirements

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Translation

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Research

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Credits

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Version:

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Other Resources

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Frequently Asked Questions

1. What is the "Target Math (Race to 20)" game about? The "Target Math (Race to 20)" game is a card-based math game designed to help players develop strategic thinking about addition. The goal is to be the first player to reach a designated target number (e.g., 20) by adding card values to a running total. The game is intended to teach number relationships, strategic planning, and an understanding of how to manipulate the rules to reach the target first. The initial version was conceptualized by Theresa Heng.
2. How do you play the "Race to 20" game strategically to win? A winning strategy involves understanding the math behind the game. If 'end' is the target number, 'start' is the beginning number and 'n' is the highest card value, you should try to land on the number (end - start) - n -1. Then whatever number your opponent adds (between 1 and n) you can add your next card and reach 'end'. For example, with a target of 20, a starting number of 0 and max card of 11, you should try to reach 8. This guarantees that you can always reach 20. For a target of 20, starting number of 0 and max card of 5, try to reach 2, then 8, then 14 and finally 20. In other words, your winning steps are end - i*(n+1) where i = 0, 1, 2, 3...
3. Can the "Race to 20" game be customized, and how? Yes, the game can be customized in several ways to increase challenge and variation. These customizations include changing the target number (e.g., from 20 to 40), varying the starting number (e.g., from 0 to 10), altering the number of available cards for each player, or restricting players to using only odd or even-numbered cards. These options allow for a wide range of gameplay experiences.
4. Is the "Target Math (Race to 20)" game available as an app? Yes, the game is available as a Progressive Web App (PWA) accessible through a browser and has dedicated mobile apps on the Google Play Store and Apple App Store, ensuring accessibility across different devices and platforms.
5. What resources are available for educators to use the "Target Math (Race to 20)" game? The page has an embedded simulation model of the game, which teachers can use in the classroom, as well as links to app store versions. The Open Source Physics community provides learning goals, teaching guides and software requirements, and acknowledges various contributors to this and other educational resources. There is a network to interact via social media.
6. What is Open Source Physics @ Singapore? Open Source Physics @ Singapore (OSP@SG) is an organization that develops and shares interactive learning resources such as simulations and models for educational purposes, specifically in mathematics, physics, and other sciences. These resources are often based on the Easy Java/JavaScript Simulations (EjsS) tool. The site includes a variety of models such as the "Target Math (Race to 20)" game, physics simulations, and tools designed for educators to facilitate hands-on learning experiences. OSP@SG is associated with the Ministry of Education.
7. What other types of interactive resources does Open Source Physics @ Singapore provide? Besides the "Target Math" game, OSP@SG offers a wide array of interactive resources, including simulations for physics topics (e.g., mechanics, electromagnetism, optics), chemistry (e.g., acid-base titrations), and various math concepts. These resources often use models, simulations and trackers that allow users to visualize and explore different scientific and mathematical concepts interactively. There are 1176 articles and about 10 million views of these materials.
8. What technologies are used to develop these interactive resources, and how can they be accessed? Many resources are developed using Easy Java/JavaScript Simulations (EjsS), which allows for cross-platform compatibility and accessibility. These interactive simulations are typically web-based, utilizing JavaScript and HTML5 and thus easily accessible through standard web browsers on various devices. There are also a number of apps built based on these resources. The resources are available under a Creative Commons license, and there are some commercial restrictions for use of the library.