Numberama: Recreational Number Theory In The School System

Games of Recreational Number Theory: Skill Levels Through Addition, Subtraction, and Multiplication

Author(s): Elliot Benjamin

Pp: 69-80 (12)

DOI: 10.2174/9781681085128117010007

* (Excluding Mailing and Handling)

Abstract

Chapter 2 consists of the games that require the skill levels through addition, subtraction, and multiplication. These games consist of The Tri Game, The Fib-Tri Game, The Multiplicative Persistence Game, The Tri-Square Game, The Tri-Squar- -Cube Game, and The Kaprekar Number Game. These games are in general appropriate for children in grades 1, 2, and 3, depending on the children's arithmetic skills level. However, they can be used as enjoyable recreational games for children of all ages, inclusive of mathematically gifted children. See the sections “Introduction to the Games” and “Game Ideas from Teachers at Numberama Teacher Workshops” in the beginning of this book, and some of the teacher and teacher education Numberama workshop participant responses in the Appendix for relevant information about playing these games effectively with children, as well as how these games were developed.


Keywords: Recreational number theory games, The Fib-Tri game, The kaprekar number game, The multiplicative persistence game, The Tri game, The Tri-square game, The Tri-square-cube game.

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      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2236 and `b`.`banner_from_date` <= 1740526358 and `b`.`banner_to_date` >= 1740526358 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.03msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2236
      • 3: 1740526358
      • 4: 1740526358
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='16dcc8b47809e2337cc801e93f5869cb'
      190μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    7Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
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        uc_cart_id
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        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/10533" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
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        status_code
        200
        
        status_text
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        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IjMzNDJKMldLMjU4L1NSd2QrbEJsT2c9PSIsInZhbHVlIjoiZ25YbmkvU3B3cVA0MHpUMmtwWW1LYXJ1Q0dPVytxSE9VaCtTK2E2a0NuMD0iLCJtYWMiOiI3ODQyNmIwNGU3YWNiMzM4MjAxYTcyOTJmOWU4NDczNTY4ZDJmZjUxMjc4YmU2ZDlhNzc5YjFiMGUzZDg0YTc4IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IjMzNDJKMldLMjU4L1NSd2QrbEJsT2c9PSIsInZhbHVlIjoiZ25YbmkvU3B3cVA0MHpUMmtwWW1LYXJ1Q0dPVytxSE9VaCtTK2E2a0NuMD0iLCJtYWMiOiI3ODQyNmIwNGU3YWNi" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 23:32:38 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImIrZVJlSlFidnJsQ0s0OW5IWEFsQ2c9PSIsInZhbHVlIjoiMG4yemVOUklvWGZhbUpGZ1dnZVd4Mmd6V3p6ci9IL0VFcUhhTjlXY2plK0htOTl3c3dma1VoanAzVkZoKzc1TVpOUGlaZFh5dHFXTVRORTk1dVJRU2RrMzFCaE1CdFROY0tpeDN2UHVSVlc2SFJZNGpkWWEzbUxlcEd0SFlEOVIiLCJtYWMiOiJlZDk2OGRiZTk3MWFiZjgzZThjZGVmYWU1MTc0ZDM1MDZjOTQ4NTJlNWEyNWZkZmUxMWU0NTgxMDA3NmRhNGY1IiwidGFnIjoiIn0%3D; expires=Fri, 28 Feb 2025 11:32:38 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6ImIrZVJlSlFidnJsQ0s0OW5IWEFsQ2c9PSIsInZhbHVlIjoiMG4yemVOUklvWGZhbUpGZ1dnZVd4Mmd6V3p6ci9IL0VFcUhhTjlXY2plK0htOTl3c3dma1VoanAzVkZoKzc1TVpOUGlaZ" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImZEYnhqeGltVnpPS2J5RTJ5bk9hSlE9PSIsInZhbHVlIjoiZU1xcUltT3p3dnArV3Y4QmY3RUowWDRyRmdDRjVQdnc0disvNzVCVCszR2t2dnpXUlFvNHY3WmxSVW1PUDE1OGZ1VThvL2J6OHR0cGRqV1hGZlVhV3R4MWN6NEwyM0RDVGJEbmZZVmsySlZEQUJvR2xBSExCMHVYMlBITlpiNjgiLCJtYWMiOiIxODdlMGFjZTc0OWJlY2YxYTVhM2RlYTQwNWFjMjNhMTAwMTMxZDE2ZmRlNzM4ZDczNzY3M2MyNmU3Nzk1YmNmIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6ImZEYnhqeGltVnpPS2J5RTJ5bk9hSlE9PSIsInZhbHVlIjoiZU1xcUltT3p3dnArV3Y4QmY3RUowWDRyRmdDRjVQdnc0disvNzVCVCszR2t2dnpXUlFvNHY3Wmx" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImIrZVJlSlFidnJsQ0s0OW5IWEFsQ2c9PSIsInZhbHVlIjoiMG4yemVOUklvWGZhbUpGZ1dnZVd4Mmd6V3p6ci9IL0VFcUhhTjlXY2plK0htOTl3c3dma1VoanAzVkZoKzc1TVpOUGlaZFh5dHFXTVRORTk1dVJRU2RrMzFCaE1CdFROY0tpeDN2UHVSVlc2SFJZNGpkWWEzbUxlcEd0SFlEOVIiLCJtYWMiOiJlZDk2OGRiZTk3MWFiZjgzZThjZGVmYWU1MTc0ZDM1MDZjOTQ4NTJlNWEyNWZkZmUxMWU0NTgxMDA3NmRhNGY1IiwidGFnIjoiIn0%3D; expires=Fri, 28-Feb-2025 11:32:38 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6ImIrZVJlSlFidnJsQ0s0OW5IWEFsQ2c9PSIsInZhbHVlIjoiMG4yemVOUklvWGZhbUpGZ1dnZVd4Mmd6V3p6ci9IL0VFcUhhTjlXY2plK0htOTl3c3dma1VoanAzVkZoKzc1TVpOUGlaZ" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImZEYnhqeGltVnpPS2J5RTJ5bk9hSlE9PSIsInZhbHVlIjoiZU1xcUltT3p3dnArV3Y4QmY3RUowWDRyRmdDRjVQdnc0disvNzVCVCszR2t2dnpXUlFvNHY3WmxSVW1PUDE1OGZ1VThvL2J6OHR0cGRqV1hGZlVhV3R4MWN6NEwyM0RDVGJEbmZZVmsySlZEQUJvR2xBSExCMHVYMlBITlpiNjgiLCJtYWMiOiIxODdlMGFjZTc0OWJlY2YxYTVhM2RlYTQwNWFjMjNhMTAwMTMxZDE2ZmRlNzM4ZDczNzY3M2MyNmU3Nzk1YmNmIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6ImZEYnhqeGltVnpPS2J5RTJ5bk9hSlE9PSIsInZhbHVlIjoiZU1xcUltT3p3dnArV3Y4QmY3RUowWDRyRmdDRjVQdnc0disvNzVCVCszR2t2dnpXUlFvNHY3Wmx" ] ]
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 23:32:38GET/chapter/10533112189