{"id":191,"date":"2024-07-01T14:14:05","date_gmt":"2024-07-01T14:14:05","guid":{"rendered":"http:\/\/localhost\/teachingsecondarymathematics\/?post_type=content&#038;p=191"},"modified":"2026-08-26T12:56:51","modified_gmt":"2026-08-26T12:56:51","slug":"chapter-11-algebra-i","status":"publish","type":"content","link":"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/","title":{"rendered":"Chapter 11 &#8211; Algebra I"},"content":{"rendered":"\n<div class=\"wp-block-group alignwide has-base-background-color has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-15050843 wp-block-group-is-layout-constrained\" style=\"margin-top:0;padding-top:var(--wp--preset--spacing--60);padding-right:var(--wp--preset--spacing--60);padding-bottom:var(--wp--preset--spacing--60);padding-left:var(--wp--preset--spacing--60)\">\n<div class=\"wp-block-group alignwide has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group alignwide has-global-padding is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-54d22900 wp-block-group-is-layout-constrained\"><nav style=\"--separator: &quot;\/&quot;\" class=\"wp-block-breadcrumbs\" aria-label=\"Breadcrumbs\"><ol><li><a href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/\">Home<\/a><\/li><li><a href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/\">Resources<\/a><\/li><li><span aria-current=\"page\">Chapter 11 &#8211; Algebra I<\/span><\/li><\/ol><\/nav><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:60%\"><h1 class=\"alignwide wp-block-post-title has-large-font-size\">Chapter 11 &#8211; Algebra I<\/h1>\n\n\n<p class=\"wp-block-paragraph\">Investigate some historical foundations of algebra<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:40%\">\n<media-player  load=\"visible\" id=\"vidstack-video-block_e55e7e7bf674b46db45b7b9f14cc3a2f\" class=\"vidstack-video\" title=\"Chapter 11 - Introduction\" src=\"https:\/\/s3-eu-west-1.amazonaws.com\/s3-euw1-ap-pe-ws4-cws-documents.ri-prod\/9781032028439\/chapter-11\/Chapter11-Intro.mp4\">\n  <media-provider>\n                  <media-poster\n          class=\"vds-poster\"\n          alt=\"\">\n        <\/media-poster>\n\n  <\/media-provider>\n  <media-video-layout><\/media-video-layout>\n  <media-controls class=\"vds-controls\">\n      <media-controls-group class=\"vds-controls-group\"><\/media-controls-group>\n  <\/media-controls>\n<\/media-player><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-base-background-color has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"margin-top:0;padding-top:var(--wp--preset--spacing--70);padding-bottom:var(--wp--preset--spacing--70)\">\n<div class=\"wp-block-group alignwide is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h2 id=\"aioseo-chapter-1-exercises\" class=\"wp-block-heading\">Exercises<\/h2>\n\n\n\n<div class=\"wp-block-group has-border-color has-black-border-color has-base-element-background-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"border-width:2px;padding-top:var(--wp--preset--spacing--30);padding-right:var(--wp--preset--spacing--50);padding-bottom:var(--wp--preset--spacing--30);padding-left:var(--wp--preset--spacing--50)\">\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-1\" class=\"wp-block-heading\">Exercise 11.1<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>You are teaching algebra in your school. What will you do if another colleague teaching algebra in your school disagrees with your teaching philosophy to use technology for a particular concept or skill? Should students be impacted by different teaching philosophies in school? Should all students use the same tools in the same classes?<\/li>\n\n\n\n<li>As a professional mathematics educator, do you feel that these basic assumptions by NCTM are viable? Why or why not? Are these assumptions necessary for full development of algebraic skills during the middle grades?<\/li>\n\n\n\n<li>Make two position statements:<\/li>\n\n\n\n<li>Position 1 summarizes your recommendations for the use of technology to teach algebra in the middle school.<\/li>\n\n\n\n<li>Position 2 presents your recommendations for the use of technology to teach algebra in the high school.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Compare and contrast your two positions.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-2\" class=\"wp-block-heading\">Exercise 11.2<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Have the Common Core Standards been adopted in your state or region?&nbsp;<\/li>\n\n\n\n<li>Is there a significant difference between the objectives for Algebra I for Mississippi and Massachusetts and the Common Core? Does this surprise you? Justify your response.<\/li>\n\n\n\n<li>Is universal agreement on the content to be covered in first-year algebra important? Why or why not?<\/li>\n\n\n\n<li>What topics should form the basic framework of a first-year algebra course?<\/li>\n\n\n\n<li>Locate a copy of your state\u2019s curriculum frameworks for Algebra I. Are they similar to Mississippi and Massachusetts? Why or why not?<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-3\" class=\"wp-block-heading\">Exercise 11.3<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Describe or create an activity that could be used to show (<em>a<\/em> + <em>b<\/em>)<sup>2<\/sup> = (<em>a<\/em> + <em>b<\/em>)(<em>a<\/em> + <em>b<\/em>).<\/li>\n\n\n\n<li>Describe or create an activity that could be used to show (<em>a<\/em> \u2013 <em>b<\/em>)<sup> 2<\/sup> = (<em>a<\/em> \u2013 <em>b<\/em>)(<em>a<\/em> + <em>b<\/em>).<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-4\" class=\"wp-block-heading\">Exercise 11.4<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Develop an alternative to * that is located on the keyboard. How could this be universally implemented?<\/li>\n\n\n\n<li>Develop a new symbol for multiplication that is not currently on the keyboard. How will this key be universally accepted in the mathematics and computer community?<\/li>\n\n\n\n<li>Do you think questions about determining a key to represent multiplication on the keyboard merit time in a mathematics classroom? Why or why not?<\/li>\n\n\n\n<li>Do the differences in writing multiplication involving variables have a negative impact on the performance of students? Why or why not?<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-5\" class=\"wp-block-heading\">Exercise 11.5<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Create a paper set of manipulatives including units, <em>X<\/em>s, and X<sup>2<\/sup>s. Do an example like 5(2<em>X<\/em><sup>2<\/sup> + 3X + 4) using the manipulatives. Describe your thoughts and reactions to the manipulation in light of thinking about how this could help students understand the operation.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-6\" class=\"wp-block-heading\">Exercise 11.6<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Create a paper set of manipulatives including units, <em>X<\/em>s, and <em>X<\/em><sup>2<\/sup>s. Do an example like (<em>X<\/em> + 4)(2<em>X<\/em> + 3) using the manipulatives. Describe your thoughts and reactions to the manipulation in terms of how this could help students understand the operation.<\/li>\n\n\n\n<li>Connect a product like (3<em>X<\/em> + 4)(2<em>X<\/em> + 1) to a partial product approach used to multiply (34)(21), which would look like:<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 34<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u00d721<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; 4 from 1 \u00d7 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 30 from 1 \u00d7 30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 80 from 20 \u00d7 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 600 from 20 \u00d7 30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 714<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Describe your thoughts and reactions to the manipulation, focusing on how this could help students understand the operation.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-6\" class=\"wp-block-heading\">Exercise 11.6<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Are there any hints that help tell how many points of intersection two linear equations will have? If so, what are they and how could you describe them to students? If not, what do we do to help students?<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-7\" class=\"wp-block-heading\">Exercise 11.7<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>There are other applications of the principle used in the discussion of the speed trap in this chapter. Find at least one more and describe how it could be used to answer the typical student question, \u201cWhen am I ever going to use this?\u201d The example should be from the world as viewed by teenagers, not from your adult perspective.<\/li>\n\n\n\n<li>Like adults, children are often motivated by money. Find a real-world algebraic example that could be used during an algebra lesson that involves money.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-8\" class=\"wp-block-heading\">Exercise 11.8<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Given<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">1 + 2 = 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4 + 5 + 6 = 7 + 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">9 + 10 + 11 + 12 = 13 + 14 + 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">16 + 17 +18 + 19 + 20 = 21 + 22 + 23 + 24<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">what is the first element of the one-hundredth row? How many terms are in the row? What is the last element of that row? Describe the Nth row.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-9\" class=\"wp-block-heading\">Exercise 11.9<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>What is wrong with determining the sum of the first <em>N<\/em> even counting numbers to be <math display=\"block\" class=\"tml-display\" style=\"display:block math;\">\n  <mfrac>\n    <mrow>\n      <mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo>\n      <msup>\n        <mi>N<\/mi>\n        <mn>2<\/mn>\n      <\/msup>\n      <mo>+<\/mo>\n      <mi>N<\/mi>\n    <\/mrow>\n    <mn>2<\/mn>\n  <\/mfrac>\n<\/math> in the text? Would the approach taken to arrive at this conclusion appear logical to a student? Why or why not?<\/li>\n\n\n\n<li>Present another example of a \u201cproof\u201d that leads to an incorrect conclusion like 2 = 1.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-10\" class=\"wp-block-heading\">Exercise 11.10<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>In the text, 4 was found to be a solution to the problem \u201cSuppose 9 and 5 are two of the three digits in a three-digit number. You are to find a third digit so that an addition equation can be formed so both addends and the sum are permutations of the same three-digit number comprised of 9, 5, and the third digit you find.\u201d Is 4 the only answer?<\/li>\n\n\n\n<li>Pick any prime number greater than 3. Square it. Add 15. Divide by 12. What is the remainder? Why? Will this always occur?<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<h3 id=\"aioseo-exercise-11-11\" class=\"wp-block-heading\">Exercise 11.11<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Provide a list of five online Internet-based algebra tutorials for students. How would you rate each of these applications?<\/li>\n\n\n\n<li>Develop a lesson that would make use of an algebraic tutorial outside the classroom setting.<\/li>\n\n\n\n<li>Is it possible that mathematics tutorials could replace the importance of classroom teachers? Justify your response.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n\n\n\n<h2 id=\"aioseo-problem-solving-challenges\" class=\"wp-block-heading\">Problem Solving Challenges<\/h2>\n\n\n\n<div class=\"wp-block-group has-border-color has-black-border-color has-base-element-background-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"border-width:2px;padding-top:var(--wp--preset--spacing--30);padding-right:var(--wp--preset--spacing--50);padding-bottom:var(--wp--preset--spacing--30);padding-left:var(--wp--preset--spacing--50)\">\n<p class=\"wp-block-paragraph\"><strong>Chapter 11: Problem-solving Challenges<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Evaluate <math display=\"block\" class=\"tml-display\" style=\"display:block math;\">\n  <mfrac>\n    <mrow>\n      <mn>1001<\/mn>\n      <mo form=\"postfix\" stretchy=\"false\">!<\/mo>\n      <mo>\u2212<\/mo>\n      <mn>1000<\/mn>\n      <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">!<\/mo>\n    <\/mrow>\n    <mrow>\n      <mn>999<\/mn>\n      <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">!<\/mo>\n    <\/mrow>\n  <\/mfrac>\n<\/math><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Hint: Try a smaller problem with values such as 4, 3, and 2.<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Answer<\/summary>\n<p class=\"wp-block-paragraph\">Answer\/solution: 1,000,000<\/p>\n\n\n\n<math display=\"block\" class=\"tml-display\" style=\"display:block math;\">\n  <mtable columnalign=\"left\">\n    <mtr>\n      <mtd class=\"tml-left\" style=\"padding:0.5ex 0pt 0.5ex 0pt;\">\n        <mrow>\n          <mfrac>\n            <mrow>\n              <mn>1001<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\">!<\/mo>\n              <mo>\u2212<\/mo>\n              <mn>1000<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">!<\/mo>\n            <\/mrow>\n            <mrow>\n              <mn>999<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">!<\/mo>\n            <\/mrow>\n          <\/mfrac>\n          <mo>=<\/mo>\n          <mfrac>\n            <mrow>\n              <mn>999<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\">!<\/mo>\n              <mo form=\"prefix\" stretchy=\"false\">(<\/mo>\n              <mn>1001<\/mn>\n              <mo>\u00d7<\/mo>\n              <mn>1000<\/mn>\n              <mo>\u2212<\/mo>\n              <mn>1000<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo>\n            <\/mrow>\n            <mrow>\n              <mn>999<\/mn>\n              <mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">!<\/mo>\n            <\/mrow>\n          <\/mfrac>\n        <\/mrow>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd class=\"tml-left\" style=\"padding:0.5ex 0pt 0.5ex 0pt;\">\n        <mrow>\n          <mo>=<\/mo>\n          <mn>1001<\/mn>\n          <mo>\u00d7<\/mo>\n          <mn>1000<\/mn>\n          <mo>\u2212<\/mo>\n          <mn>1000<\/mn>\n        <\/mrow>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd class=\"tml-left\" style=\"padding:0.5ex 0pt 0.5ex 0pt;\">\n        <mrow>\n          <mo>=<\/mo>\n          <mn>1000000<\/mn>\n        <\/mrow>\n      <\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math>\n\n\n\n<p class=\"wp-block-paragraph\">The key is to factor out 999! in the numerator.<\/p>\n<\/details>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>If three hens lay four eggs in five days, how many days will it take a dozen hens to lay four dozen eggs? Please round your answers to the nearest egg!<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:&nbsp; How many eggs would a dozen chickens lay in 5 days?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Answer<\/summary>\n<p class=\"wp-block-paragraph\">Answer\/solution: 15 days<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A dozen hens would lay 16 eggs in five days. Therefore, since 48 is 3 times as many as 16 eggs, it would take 3 times as many days or 15 days to lay 48 eggs.<\/p>\n<\/details>\n<\/div>\n\n\n\n<h2 id=\"aioseo-dadditional-learning-activities\" class=\"wp-block-heading\">Additional Learning Activities<\/h2>\n\n\n\n<div class=\"wp-block-group has-border-color has-black-border-color has-base-element-background-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"border-width:2px;padding-top:var(--wp--preset--spacing--50);padding-right:var(--wp--preset--spacing--50);padding-bottom:var(--wp--preset--spacing--50);padding-left:var(--wp--preset--spacing--50)\">\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"wp-block-paragraph\">There is no Additional Learning Activities for this chapter.<\/p>\n<\/div>\n<\/div>\n\n\n\n<h2 id=\"aioseo-videos\" class=\"wp-block-heading\">Videos<\/h2>\n\n\n\n<div class=\"wp-block-group has-border-color has-black-border-color has-base-element-background-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"border-width:2px;padding-top:var(--wp--preset--spacing--50);padding-right:var(--wp--preset--spacing--50);padding-bottom:var(--wp--preset--spacing--50);padding-left:var(--wp--preset--spacing--50)\">\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-columns alignwide are-vertically-aligned-top is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-2c90304e wp-block-group-is-layout-flex\">\n<media-player  load=\"visible\" id=\"vidstack-video-block_22ddaff6093a893c7e080567f14490f7\" class=\"vidstack-video\" title=\"Problem Solving\" src=\"https:\/\/s3-eu-west-1.amazonaws.com\/s3-euw1-ap-pe-ws4-cws-documents.ri-prod\/9781032028439\/chapter-11\/Chapter11-PSC.mp4\">\n  <media-provider>\n                  <media-poster\n          class=\"vds-poster\"\n          alt=\"\">\n        <\/media-poster>\n\n  <\/media-provider>\n  <media-video-layout><\/media-video-layout>\n  <media-controls class=\"vds-controls\">\n      <media-controls-group class=\"vds-controls-group\"><\/media-controls-group>\n  <\/media-controls>\n<\/media-player>\n\n\n<h3 id=\"aioseo-problem-solving\" class=\"wp-block-heading\">Problem Solving<\/h3>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-fba139f5 wp-block-group-is-layout-flex\">\n<media-player  load=\"visible\" id=\"vidstack-video-block_8942aa46cabdff8f3bf60394f8a39a01\" class=\"vidstack-video\" title=\"Sticky Question\" src=\"https:\/\/s3-eu-west-1.amazonaws.com\/s3-euw1-ap-pe-ws4-cws-documents.ri-prod\/9781032028439\/chapter-11\/Chapter11-Sticky.mp4\">\n  <media-provider>\n                  <media-poster\n          class=\"vds-poster\"\n          alt=\"\">\n        <\/media-poster>\n\n  <\/media-provider>\n  <media-video-layout><\/media-video-layout>\n  <media-controls class=\"vds-controls\">\n      <media-controls-group class=\"vds-controls-group\"><\/media-controls-group>\n  <\/media-controls>\n<\/media-player>\n\n\n<h3 id=\"aioseo-sticky-question\" class=\"wp-block-heading\">Sticky Question<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\"><strong>On this page<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-base-background-color has-background is-horizontal is-content-justification-space-between is-nowrap is-layout-flex wp-container-core-group-is-layout-9c6c4bab wp-block-group-is-layout-flex wp-container-1 is-position-sticky\">\n<nav aria-label=\"Table of Contents\" class=\"wp-block-table-of-contents\"><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-chapter-1-exercises\">Exercises<\/a><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-1\">Exercise 11.1<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-2\">Exercise 11.2<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-3\">Exercise 11.3<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-4\">Exercise 11.4<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-5\">Exercise 11.5<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-6\">Exercise 11.6<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-6\">Exercise 11.6<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-7\">Exercise 11.7<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-8\">Exercise 11.8<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-9\">Exercise 11.9<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-10\">Exercise 11.10<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-exercise-11-11\">Exercise 11.11<\/a><\/li><\/ol><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-problem-solving-challenges\">Problem Solving Challenges<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-dadditional-learning-activities\">Additional Learning Activities<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-videos\">Videos<\/a><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-problem-solving\">Problem Solving<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-11-algebra-i\/#aioseo-sticky-question\">Sticky Question<\/a><\/li><\/ol><\/li><\/ol><\/nav>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Investigate some historical foundations of algebra Exercises Exercise 11.1 Compare and contrast your two positions. Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.5 Exercise 11.6 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 34 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u00d721 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; 4 from 1 \u00d7 4 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 30 from 1 \u00d7 30 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 80 from 20 \u00d7 4 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 600 from 20 [&hellip;]<\/p>\n","protected":false},"featured_media":0,"parent":112,"menu_order":0,"template":"no-title-2","format":"standard","meta":{"_acf_changed":false},"categories":[],"class_list":["post-191","content","type-content","status-publish","format-standard","hentry"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Investigate some historical foundations of algebra Exercises Exercise 11.1 You are teaching algebra in your school. 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