[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-263964-105":53,"doc-detail-263964-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","tools-of-algebra-expressions-equations-and-inequalities-part-1-fast-track-grasp-math-packet","Tools of Algebra: Expressions, Equations, and Inequalities - Part 1 - Fast Track GRASP Math Packet","","Fast Track GRASP Math Packet Part 1 develops algebraic reasoning by teaching how to use expressions and equations as problem-solving tools. The packet guides learners through mathematical equality, evaluating expressions, creating and solving equations with visual models such as area models, hanger diagrams, and balance scales, and applying order of operations. It also covers balancing equations, using the distributive property, and translating real-life situations into equations, supported by assessment questions, answer keys, vocabulary, and a glossary.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/tools-of-algebra-expressions-equations-and-inequalities-part-1-fast-track-grasp-math-packet/263964/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/tools-of-algebra-expressions-equations-and-inequalities-part-1-fast-track-grasp-math-packet/263964.png","ImageObject",442,249,{"name":88,"@type":89},"Bill Black","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-11-03","2026-09-14",true,{"@type":98,"interactionType":99,"userInteractionCount":40},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What topics are covered in Part 1 of the Fast Track GRASP Math Packet?","Question",{"text":108,"@type":109},"Part 1 covers mathematical equality, evaluating expressions, creating and solving equations, and using visual models like area models, hanger diagrams, and balance scales. It also includes the distributive property and order of operations, plus writing equations for real-life situations.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Are there prerequisites for working through this packet?",{"text":113,"@type":109},"The packet states there are no prerequisites. As long as learners can read the packet independently, they do not need to study other math packets first.",{"name":115,"@type":106,"acceptedAnswer":116},"How does the packet help learners understand equations?",{"text":117,"@type":109},"It uses step-by-step strategies and visual representations such as area models, hanger diagrams, and balance scales. Learners practice balancing equations, applying inverse operations, and writing equations from situations.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},263964,1791722579,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":40,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141,"preview_page_count":4},24189269381491,"https://ap-avatar.wpscdn.com/avatar/160000cf11732dd8392?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788146458752108895","Tools of Algebra: Expressions, Equations & Inequalities  \nFast Track GRASP Math Packet  \nPart 1  \nVersion 1.11 Updated 02/12/2024  \nThis Fast Track GRASP Math Packet was made possible through support from the New York State Education Department, Office of Adult Career and Continuing Education Services. The Fast Track GRASP Math packets use a Creative Commons license of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), which means that they can be shared, copied andredistributed in any form, as long as the document retains attribution to CUNY/NYSED for their creation.  \n[http://www.collectedny.org/ftgmp](http://www.collectedny.org/ftgmp)  \nTools of Algebra: Expressions, Equations, and Inequalities (Part 1)  \nTable of Contents  \nOverview 4  \nAssessment Questions 5  \nAnswer Key 7  \nRecommendations 8  \nWelcome! 9  \nIntroduction 10  \nHistory of Algebra 10  \nWhat is Algebra? 11  \nAlgebra as a Tool 13  \nVocabulary 14  \nSkills Practice 16  \nThe Multiplication Table 16  \nMagic Triangle 20  \nAnswer Key-Skills Practice 22  \nEquations and Expressions 24  \nEquality 24  \nEquations 27  \nNotes from a Math Class 30  \nCreating and Solving Equations I 32  \nArea Models for Multiplication 33  \nOrder of Operations 42  \nFix These Equations! 46  \nMatching Equivalent Expressions 48  \nFour 4’s 49  \nReview-Expressions and Order of Operations 50  \nAnswer Key-Equations and Expressions 53  \nThinking in an Algebraic Way 62  \nA Magic Trick 62  \nGuess My Number 63  \nOpen Number Sentences 64  \nMatching Statements and Open Number Sentences 65  \nSolving Equations 66  \nHow Many Values Make the Equation True? 67  \nEvaluate Expressions 69  \n©2024 The City University of New York Adult Literacy/HSE/ESL Program ([http://l](http://l)[iteracy.cuny.edu](iteracy.cuny.edu)). This work is licensed 2  \nunder Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) . V.1.11 , 02/ 12/2024  \nTools of Algebra: Expressions, Equations, and Inequalities (Part 1)  \nAnswer Key-Thinking in an Algebraic Way 70  \nBalancing Equations 73  \nHanger Diagrams 73  \nStrategies for Solving Equations 83  \nInverse Operations 85  \nCreating and Solving Equations II 87  \nWriting the Steps to Solve a Linear Equation 88  \nWriting an Equation for a Situation 89  \nThe Distributive Property and the Order of Operations 91  \nThe Math Behind the Magic Trick 98  \nBalance Scales 100  \nRestaurant Pricing 105  \nAnswer Key-Balancing Equations 106  \nVocabulary Review 113  \nGlossary 113  \nUsing Graphic Organizers to Learn Vocabulary 116  \nSources 119  \n©2024 The City University of New York Adult Literacy/HSE/ESL Program ([http://l](http://l)[iteracy.cuny.edu](iteracy.cuny.edu)). This work is licensed 3 under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) . V.1.11 , 02/ 12/2024  \nTools of Algebra: Expressions, Equations, and Inequalities (Part 1)  \nOverview  \nIn this packet you will develop your algebraic reasoning and learn how to use algebra as a tool in problem-solving. You will also learn about mathematical symbols and how they are used.  \n\n| Prerequisites | There are no prerequisites to this packet. As long as you are able to read this packet independently, you don't have to study any other math packets first. |\n| --- | --- |\n| Optional | You may find it helpful to complete the Fast Track GRASP Math Packets, Two-Dimensional Figures, Part 1: Area & Perimeter and Three-Dimensional Figures, Part 1: Surface Area and Volume for an in-depth introduction to some of the geometry concepts explored in Part 2 of this packet. |\n\nIn Part 1, you will study the following topics:  \n● Mathematical equality  \n● How to evaluate equations and expressions and solve equations using visual models like area models, hanger diagrams, and balance scales  \n● The distributive property of multiplication and the order of operations  \n● How to write equations to describe real-life situations  \nIn Part 2, you will build on what you learned in Part 1, and study the following topics:  \n● ","cbCaiof4CqMGjzQy","https://ap.wps.com/l/cbCaiof4CqMGjzQy","pdf",14139697,119,"English","# Overview\n# Assessment Questions\n# Answer Key\n# Recommendations\n# Welcome!\n# Introduction\n## History of Algebra\n## What is Algebra?\n## Algebra as a Tool\n# Vocabulary\n## Skills Practice\n## The Multiplication Table\n## Magic Triangle\n# Equations and Expressions\n## Equality\n## Equations\n# Notes from a Math Class\n## Creating and Solving Equations I\n## Order of Operations\n# Solving Equations\n## Evaluate Expressions\n# Thinking in an Algebraic Way\n## Guess My Number\n## Open Number Sentences\n# Balancing Equations\n## Strategies for Solving Equations\n# Creating and Solving Equations II\n## Writing the Steps to Solve a Linear Equation\n## Distributive Property and Order of Operations\n# Vocabulary Review\n# Glossary\n# Sources","[{\"question\":\"What topics are covered in Part 1 of the Fast Track GRASP Math Packet?\",\"answer\":\"Part 1 covers mathematical equality, evaluating expressions, creating and solving equations, and using visual models like area models, hanger diagrams, and balance scales. It also includes the distributive property and order of operations, plus writing equations for real-life situations.\"},{\"question\":\"Are there prerequisites for working through this packet?\",\"answer\":\"The packet states there are no prerequisites. As long as learners can read the packet independently, they do not need to study other math packets first.\"},{\"question\":\"How does the packet help learners understand equations?\",\"answer\":\"It uses step-by-step strategies and visual representations such as area models, hanger diagrams, and balance scales. Learners practice balancing equations, applying inverse operations, and writing equations from situations.\"}]","Tools of Algebra: Expressions, Equations, and Inequalities - Part 1 - Fast Track GRASP Math Packet | PDF",1789376091,42]