[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-476791-105":3,"doc-detail-476791-en":84,"detail-sidebar-cat-0-en-105":100},{"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":77,"head_meta":79,"extra_data":81,"updated_unix":83},105,"en","proportional-reasoning-balloon-height-exercise","Proportional Reasoning - Balloon Height Exercise","","This educational document presents a mathematics problem centered on proportional reasoning, specifically focusing on the constant rate of change. The task requires students to analyze the relationship between time in seconds and the height of a rising hot-air balloon, and subsequently complete a data table provided in the exercise. This material is designed to assess student understanding of linear relationships, proportionality, and rate of change, serving as a practical practice exercise for learners seeking to improve their mathematical problem-solving skills in a classroom or assessment setting.",{"@graph":14,"@context":76},[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/proportional-reasoning-balloon-height-exercise/476791/",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/proportional-reasoning-balloon-height-exercise/476791.png","ImageObject",300,407,{"name":42,"@type":43},"Mary Man","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68,72],{"name":59,"@type":60,"acceptedAnswer":61},"What is the relationship between the time and the height of the balloon?","Question",{"text":62,"@type":63},"The balloon rises at a constant rate, meaning the height changes proportionally with time. Based on the provided data that 5 seconds equals 20 feet, the constant rate is 4 feet per second.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the missing height for 20 seconds?",{"text":67,"@type":63},"Since the rate is 4 feet per second, at 20 seconds the height of the balloon is 80 feet (20 seconds multiplied by 4 feet per second).",{"name":69,"@type":60,"acceptedAnswer":70},"What is the missing time value for the height of 160 feet?",{"text":71,"@type":63},"Given the constant rate of 4 feet per second, a height of 160 feet is reached at 40 seconds (160 feet divided by 4 feet per second).",{"name":73,"@type":60,"acceptedAnswer":74},"What is the missing height for 50 seconds?",{"text":75,"@type":63},"Following the constant rate of 4 feet per second, at 50 seconds the height of the balloon is 200 feet (50 seconds multiplied by 4 feet per second).","https://schema.org",{"og:url":32,"og:type":78,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":80,"canonical":32},"index,follow",{"doc_id":82,"site_id":7},476791,1790788558,{"code":4,"msg":85,"data":86},"success",{"doc_id":82,"user_id":87,"nickname":42,"user_avatar":88,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":89,"file_id":90,"file_url":91,"file_type":92,"file_size":93,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":94,"language":95,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":96,"faqs":97,"seo_title":98,"seo_description":12,"update_tm":83,"read_time":99},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| STAAR Released Item | Multiselect |\n| --- | --- |\n| 8.4(A) 2021 item 15\u003Cbr>[Slope]\u003Cbr>| |\n\n\n| STAAR Released Item | Inline Choice |\n| --- | --- |\n| 8.4(A) 2019 item 18 |  |\n| [Slope]\u003Cbr>| |\n\n\n| STAAR Released Item | Graphing |\n| --- | --- |\n| 8.4(B) 2019 item 20 |  |\n| [Slope]\u003Cbr>| |\n\n\n| STAAR Released Item | Drag and Drop |\n| --- | --- |\n| 8.4(B) 2016 item 5 |  |\n| [Slope]\u003Cbr>| \u003Cbr>|\n\n\n| STAAR Released Item | Inline Choice |\n| --- | --- |\n| 8.4(C) 2018 item 18 |  |\n| [Non-Proportional Reasoning]\u003Cbr>| \u003Cbr>|\n\n\n| STAAR Released Item | Equation Editor/Text Entry |\n| --- | --- |\n| 8.4(C) 2018 item 38 |  |\n| [Non-Proportional Reasoning]\u003Cbr>| \u003Cbr>|\n\n\n| STAAR Released Item | Drag and Drop |\n| --- | --- |\n| 8.4(C) 2017 item 6 |  |\n| [Non-Proportional Reasoning]\u003Cbr>| \u003Cbr>|\n\n\n| STAAR Released Item | Equation Editor/Text Entry |\n| --- | --- |\n| 8.5(A) 2018 item 14\u003Cbr>[Proportional Reasoning]\u003Cbr>| |\n\n\n| STAAR Released Item | Multiselect |\n| --- | --- |\n| 8.5(B) 2018 item 6 |  |\n| [Non-Proportional Reasoning]\u003Cbr>| |\n\n\n| STAAR Released Item | Inline Choice |\n| --- | --- |\n| 8.5(F) 2021 item 37\u003Cbr>[Proportional and Non-Proportional Recognition]\u003Cbr>| |","cbCaiixKXWYTXCpW","https://ap.wps.com/l/cbCaiixKXWYTXCpW","pdf",1735332,14,"English","# Mathematics Exercise\n## Proportional Reasoning Problem\n## Data Table Completion","[{\"question\":\"What is the relationship between the time and the height of the balloon?\",\"answer\":\"The balloon rises at a constant rate, meaning the height changes proportionally with time. Based on the provided data that 5 seconds equals 20 feet, the constant rate is 4 feet per second.\"},{\"question\":\"What is the missing height for 20 seconds?\",\"answer\":\"Since the rate is 4 feet per second, at 20 seconds the height of the balloon is 80 feet (20 seconds multiplied by 4 feet per second).\"},{\"question\":\"What is the missing time value for the height of 160 feet?\",\"answer\":\"Given the constant rate of 4 feet per second, a height of 160 feet is reached at 40 seconds (160 feet divided by 4 feet per second).\"},{\"question\":\"What is the missing height for 50 seconds?\",\"answer\":\"Following the constant rate of 4 feet per second, at 50 seconds the height of the balloon is 200 feet (50 seconds multiplied by 4 feet per second).\"}]","Proportional Reasoning - Balloon Height Exercise | PDF",35,{"code":4,"msg":85,"data":101},[102,106,110,113,118,123,128,133,138,141,145],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":111,"slug":112},70,"exam",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},5,"Comic",60,"comic",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},6,"Technology",50,"technology",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":126,"slug":127},7,"Healthcare",40,"healthcare",{"id":129,"doc_module":4,"doc_module_name":25,"category_name":130,"show_sort_weight":131,"slug":132},8,"Research & Report",30,"research-report",{"id":134,"doc_module":4,"doc_module_name":25,"category_name":135,"show_sort_weight":136,"slug":137},9,"Religion & Spirituality",20,"religion-spirituality",{"id":136,"doc_module":4,"doc_module_name":25,"category_name":139,"show_sort_weight":136,"slug":140},"World Cup","world-cup",{"id":142,"doc_module":4,"doc_module_name":25,"category_name":143,"show_sort_weight":142,"slug":144},10,"Lifestyle","lifestyle",{"id":146,"doc_module":4,"doc_module_name":25,"category_name":147,"show_sort_weight":114,"slug":148},19,"General","general"]