[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-632059-105":59,"doc-detail-632059-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","magic-square-4-mathematical-puzzle-sheet","Magic Square 4 - Mathematical Puzzle Sheet","","This educational document provides two magic square challenges designed for 4th-grade mathematics students. A magic square is defined as a grid where the numbers in each horizontal, vertical, and diagonal row sum to the same constant value. The first puzzle requires arranging specific integers from -4 to 4 to achieve a sum of 0, while the second challenge tasks students with using integers from -6 to 2 to reach a total sum of -6. The document includes empty grid templates for student practice and provides verified answer keys, noting that multiple rotational or reflective solutions may exist for each puzzle. This resource is suitable for developing logical reasoning and arithmetic skills with positive and negative integers in a classroom or home-learning environment.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/magic-square-4-mathematical-puzzle-sheet/632059/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/magic-square-4-mathematical-puzzle-sheet/632059.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the definition of a magic square according to the document?","Question",{"text":112,"@type":113},"A magic square is a grid where each vertical, horizontal, and diagonal line of three numbers adds up to the same total amount.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the specific numbers required to solve the first magic square puzzle?",{"text":117,"@type":113},"The first puzzle requires using the numbers -4, -3, -2, -1, 1, 2, 3, and 4 to ensure each line sums to 0.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the document imply there is only one correct way to arrange the numbers in the magic squares?",{"text":121,"@type":113},"No, the document notes that there are several possible solutions for each puzzle, as different arrangements can be achieved through rotations or reflections of the base solutions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},632059,1793056340,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","Name  \nMAGIC SQUARE 4  \nDate  \nA magic square is a square where each line of 3 numbers (vertical, horizontal and diagonal) adds up to the same amount.  \n1) Write the numbers-4, -3, -2, -1, 1, 2, 3 and 4 in the correct place so that each line (vertical, horizontal and diagonal) adds up to 15.  \n-4 -3 -2 -1 1 2 3 4  \nTotal must be 0   \n2) Can you make a new magic square using the digits-6, -5, -4, -3,-2, -1, 1, 2 so that each line adds up to-6?  \n-6 -5 -4 -3 -2 -1 1 2 Total must be-6   \n\n|  |  |  |\n| --- | --- | --- |\n|  | 0 |  |\n|  |  |  |\n\n\n|  |  |  |\n| --- | --- | --- |\n| 0 |  |  |\n|  |  |  |\n\nName Date  \nMAGIC SQUARE 4 ANSWERS  \nPlease note that there are several solutions for each square puzzle. Each solution will be a reflection or a rotation of one of the solutions below.  \nOne solution for each challenge is given. 1)  \n-4 -3 -2 -1 1 2 3 4 Total must be 0  \n2)  \n-6 -5 -4 -3 -2 -1 1 2 Total must be-6   \n\n| -1 | -2 | 3 |\n| --- | --- | --- |\n| 4 | 0 | -4 |\n| -3 | 2 | 1 |\n\n\n| -5 | 2 | -3 |\n| --- | --- | --- |\n| 0 | -2 | -4 |\n| -1 | -6 | 1 |","cbCaid5a8iV8QYf0","https://ap.wps.com/l/cbCaid5a8iV8QYf0","pdf",142583,"English","# Magic Square Challenges\n## Puzzle 1: Sum to 0\n## Puzzle 2: Sum to -6\n## Answer Keys","[{\"question\":\"What is the definition of a magic square according to the document?\",\"answer\":\"A magic square is a grid where each vertical, horizontal, and diagonal line of three numbers adds up to the same total amount.\"},{\"question\":\"What are the specific numbers required to solve the first magic square puzzle?\",\"answer\":\"The first puzzle requires using the numbers -4, -3, -2, -1, 1, 2, 3, and 4 to ensure each line sums to 0.\"},{\"question\":\"Does the document imply there is only one correct way to arrange the numbers in the magic squares?\",\"answer\":\"No, the document notes that there are several possible solutions for each puzzle, as different arrangements can be achieved through rotations or reflections of the base solutions.\"}]","Magic Square 4 - Mathematical Puzzle Sheet | PDF",1792669871]