[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-631377-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-631377-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","brunos-bones-4th-grade-math-challenge","Bruno's Bones - 4th Grade Math Challenge","","This educational document presents a mathematical logic puzzle centered on a character named Bruno the bulldog, designed for fourth-grade students. The challenge requires students to determine the number of bones collected by Bruno based on specific remainders when divided into piles of four and seven. The document provides two separate scenarios: one where the total bone count is between 30 and 50, and another where it ranges between 50 and 80. Comprehensive answers and a step-by-step breakdown of the logical process are included to help students verify their calculations and understand modular arithmetic concepts in a simplified, approachable format suitable for elementary mathematics learning.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/brunos-bones-4th-grade-math-challenge/631377/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/brunos-bones-4th-grade-math-challenge/631377.png","ImageObject",300,407,{"name":42,"@type":43},"Lucas Martin","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-26","2026-10-22",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How many bones did Bruno have if the count was between 30 and 50?","Question",{"text":62,"@type":63},"Bruno had 43 bones, which satisfies the condition of having 3 left over when grouped by 4s and 1 left over when grouped by 7s.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the answer if Bruno had between 50 and 80 bones?",{"text":67,"@type":63},"If the total number of bones was between 50 and 80, Bruno would have 71 bones.",{"name":69,"@type":60,"acceptedAnswer":70},"How does the provided table assist in solving the problem?",{"text":71,"@type":63},"The table lists the possible bone counts that satisfy each condition separately, allowing students to identify the common number that fits both criteria.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},631377,1792984923,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":95},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","BRUNO’S BONES  \nBruno the bulldog collects bones and buries them in the yard. Every so often, he digs them all up again and counts them.  \nBruno digs them up one day and finds that he has between 30 and 50 bones.  \nHe counts his bones by putting them into piles of 4 bones, and finds he has 3 bones left over.  \nHe counts them by putting them into piles of 7 bones and finds that he only has 1 bone left over.  \nHow many bones did he have?  \nWhat if he had between 50 and 80 bones?  \nBRUNO’S BONES ANSWERS  \nBruno the bulldog collects bones and buries them in the yard. Every so often, he digs them all up again and counts them.  \nBruno digs them up one day and finds that he has between 30 and 50 bones.  \nHe counts his bones by putting them into piles of 4 bones, and finds he has 3 bones left over.  \nHe counts them by putting them into piles of 7 bones and finds that he only has 1 bone left over.  \nHow many bones did he have?  \nHe had 43 bones.  \n\n| piles of 4 with 3 left | piles of 7 with 1 left |\n| --- | --- |\n| 7 | 8 |\n| 11 | 15 |\n| 15 | 22 |\n| 19 | 29 |\n| 23 | 36 |\n| 27 | 43 |\n| 31 | 50 |\n| 35 |  |\n| 39 |  |\n| 43 |  |\n| 47 |  |\n| 51 |  |\n\nWhat if he had between 50 and 80 bones?  \nHe would have 71 bones.","cbCaifqtI2D26kMp","https://ap.wps.com/l/cbCaifqtI2D26kMp","pdf",241329,"English","# Problem Description\n## Bruno's Challenges\n# Answer Key\n## Solutions and Calculations","[{\"question\":\"How many bones did Bruno have if the count was between 30 and 50?\",\"answer\":\"Bruno had 43 bones, which satisfies the condition of having 3 left over when grouped by 4s and 1 left over when grouped by 7s.\"},{\"question\":\"What is the answer if Bruno had between 50 and 80 bones?\",\"answer\":\"If the total number of bones was between 50 and 80, Bruno would have 71 bones.\"},{\"question\":\"How does the provided table assist in solving the problem?\",\"answer\":\"The table lists the possible bone counts that satisfy each condition separately, allowing students to identify the common number that fits both criteria.\"}]","Bruno's Bones - 4th Grade Math Challenge | PDF",1792669018]