{"id":143,"date":"2026-02-20T20:44:44","date_gmt":"2026-02-20T20:44:44","guid":{"rendered":"https:\/\/metisarchive.com\/?p=143"},"modified":"2026-02-23T00:25:53","modified_gmt":"2026-02-23T00:25:53","slug":"how-i-teach-algebra-pt1-introduction","status":"publish","type":"post","link":"https:\/\/metisarchive.com\/?p=143","title":{"rendered":"How I teach Algebra: Pt1 Introduction"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"271\" height=\"157\" src=\"https:\/\/metisarchive.com\/wp-content\/uploads\/2026\/02\/Algebra1-1.png\" alt=\"\" class=\"wp-image-151\"\/><\/figure>\n\n\n\n<p>Until now, your math class has been working with numbers. These numbers have taken many different forms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Whole numbers: 1, 2, 3<\/li>\n\n\n\n<li>Negative Integers: -1, -4, -5, -6<\/li>\n\n\n\n<li>Fraction: 3\/4, 8\/9<\/li>\n\n\n\n<li>Decimals: 4.08, 7.6, 3.14159<\/li>\n\n\n\n<li>Percentages: 43%, 68%<\/li>\n<\/ul>\n\n\n\n<p>In math, we call these numbers &#8220;<strong>constants<\/strong>.&#8221;<\/p>\n\n\n\n<p>Algebra introduces a new concept called &#8220;<span style=\"text-decoration: underline;\">variables<\/span>&#8221; that we use letters and names to represent: x, y, z, a, b, c, k, etc). These variables are tools that make solving complicated math problems easier.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What are Variables?<\/h3>\n\n\n\n<p>Basically, we use variables to represent things that we don&#8217;t know. With that, we can create equations that help us talk about things in mathematical language. Let me give an example:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">Let&#8217;s say we bought a pack of Oreo cookies&#8211;a family pack&#8211;to enjoy over the course of a week. However, before we can get to it, our brother Tom gets into it and consumes a number of the cookies. <span style=\"text-decoration: underline;\">We want to know how many cookies he ate<\/span>. <br>We weren&#8217;t around to watch him eat the cookies, so don&#8217;t immediately know how many cookies he ate. In this case, we assign a variable for that unknown: &nbsp; <br><strong>x= &#8220;Number of cookies Tom ate.&#8221;<\/strong> &nbsp; <br>Luckily, we happen to know a family pack of Oreos has 48 cookies, and were able to count 13 cookies remaining.&nbsp; Since Tom was presumably the only one to eat the cookies, we have a nice equation:&nbsp; &nbsp; <br><strong>&#8220;Number of cookies Tom ate&#8221; + &#8220;Number of cookies left&#8221;= &#8220;Cookies originally in the pack&#8221;<\/strong><br><strong>x+13=48<\/strong> &nbsp; <br>From here, we can work backward.&nbsp;<br>Some number (x) plus 13 results in 48. We can find that number by working backward from 48. <br><strong>x=48-13=35 <br>x=35 <br>Tom ate 35 cookies. <\/strong><br>Tom owes us almost a whole normal pack of Oreos&#8230;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The key to using Algebra effectively is creating mathematical equations using variables, and solving backward.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">You&#8217;ve secretly been using variables<\/h3>\n\n\n\n<p>If you think about it, you&#8217;ve actually been using variables in arithmetic. But back then we used to use a (blank) to represent the unknown.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>For example: <br><strong>Arithmetic<\/strong>: 4+5= _(blank)_ 9 <br><strong>Algebra<\/strong>: 4+5=x x=9<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>In this case, we might say that either 4+5=9, or 9=x.&nbsp;<\/p>\n\n\n\n<p>We use variables because they give us more flexibility and help us talk about more complicated problems.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Arithmetic:<\/strong> 4* _(blank)_+4= 16<\/li>\n\n\n\n<li><strong>Algebra<\/strong>: 4x+4=16<\/li>\n<\/ul>\n\n\n\n<p>Later on, we end up working with more than one unknown number. With Algebra, we assign these unknowns to different variables. Unfortunately our _(blanks)_ don&#8217;t offer us the same flexibility and can cause confusion.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Jack and Jill ate a pack of Oreos (48 cookies). We don&#8217;t know how many each ate, but we know that Jack ate twice as many as Jill. <br><strong>x= Number of cookies that Jack ate.<\/strong> <br><strong>y= Number of cookies that Jill ate.<\/strong> <br><strong>48= total number of cookies in the pack<\/strong> <br>We might be able to guess our way to the solution with numbers, but it can be solved more consistently with algebra.&nbsp; Because Jack ate twice as many cookies as Jill, we know that x=2 times y.&nbsp; <br><strong>x=2y<\/strong> <br>We know that x+y=48 because they at the whole pack. <br><strong>x+y=48<\/strong> <br>We can replace x with 2y, because they are the same amount: <br><strong>2y + y = 48.<\/strong> <br>We combine the bundles (Think &#8220;I have 2 bananas, and I add a banana. Now I have 3 bananas) <br><strong>3y=48<\/strong><br>This basically says jill&#8217;s number times 3 is 48. We work backward and divide 48 by 3. <br><strong>y=48\/3<\/strong> <br><strong>y=16 cookies.&nbsp;<\/strong><br><strong>Jill ate 16 cookies of the cookies.<\/strong> <br>Based on everything we discussed before, we know that Jack ate the rest, so Jack ate 32 cookies. (This is how we solved it.<br><strong>x+16=48<\/strong> <br><strong>x=48-16<\/strong> <br><strong>x=32<\/strong><br><strong>Jack ate 32 cookies.<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>If you&#8217;re new to Algebra, you may not have followed all of that. Just know that some problems are more difficult to solve without the tools that Algebra provides us.<\/p>\n\n\n\n<p>In the following sections we will discuss how to solve algebra questions in more detail.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Until now, your math class has been working with numbers. These numbers have taken many different forms: In math, we call these numbers &#8220;constants.&#8221; Algebra introduces a new concept called &#8220;variables&#8221; that we use letters and names to represent: x, y, z, a, b, c, k, etc). These variables are tools that make solving complicated [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[23,15,24,25],"class_list":["post-143","post","type-post","status-publish","format-standard","hentry","category-education","tag-algebra","tag-learning-2","tag-math","tag-variables"],"_links":{"self":[{"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/posts\/143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/metisarchive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=143"}],"version-history":[{"count":5,"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/posts\/143\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/metisarchive.com\/index.php?rest_route=\/wp\/v2\/posts\/143\/revisions\/152"}],"wp:attachment":[{"href":"https:\/\/metisarchive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/metisarchive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/metisarchive.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}