{"id":4594,"date":"2020-04-21T00:19:04","date_gmt":"2020-04-21T00:19:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-whole-numbers\/"},"modified":"2025-09-02T22:49:16","modified_gmt":"2025-09-02T22:49:16","slug":"adding-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-whole-numbers\/","title":{"raw":"Adding Whole Numbers: Notation and Modeling","rendered":"Adding Whole Numbers: Notation and Modeling"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use symbols and words to describe addition of single and double digit numbers<\/li>\r\n \t<li>Model addition of single and double digit numbers using base-10 blocks, or shapes<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2>Use Addition Notation<\/h2>\r\nA college student has a part-time job. Last week he worked [latex]3[\/latex] hours on Monday and [latex]4[\/latex] hours on Friday. To find the total number of hours he worked last week, he added [latex]3[\/latex] and [latex]4[\/latex].\r\n\r\nThe operation of addition combines numbers to get a sum. The notation we use to find the sum of [latex]3[\/latex] and [latex]4[\/latex] is:\r\n<p style=\"text-align: center;\">[latex]3+4[\/latex]<\/p>\r\nWe read this as <em>three plus four<\/em> and the result is the sum of three and four. The numbers [latex]3[\/latex] and [latex]4[\/latex] are called the addends. A math statement that includes numbers and operations is called an expression.\r\n\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Addition Notation<\/h3>\r\nTo describe addition, we can use symbols and words.\r\n<table id=\"fs-id2711498\" class=\"unnumbered\" style=\"width: 40%;\" summary=\"This is a table with two rows and five columns. The top row is a header row. Each column from left to right is labeled accordingly: Operation, Notation, Expressions, Read as, and result. In the second row, from left to right is addition, the plus sign, the expression 3 plus four, the statement three plus four and the sum of 3 and 4.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Operation<\/th>\r\n<th>Notation<\/th>\r\n<th>Expression<\/th>\r\n<th>Read as<\/th>\r\n<th>Result<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Addition<\/td>\r\n<td>[latex]+[\/latex]<\/td>\r\n<td>[latex]3+4[\/latex]<\/td>\r\n<td>three plus four<\/td>\r\n<td>the sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAfter talking to her counselor, Esmeralda needs to determine how many classes she has taken so far at Blue Sky College. Last year she took [latex]6[\/latex] classes, and this year will complete [latex]8[\/latex] classes. She needs to determine the sum of [latex]6[\/latex] and [latex]8[\/latex]. First translate the sentence into math notation and then calculate the results.\r\n\r\nTranslate from words to math: [latex]6+8[\/latex]\r\n\r\n<em>The operation of addition combines numbers to get a sum<\/em>\r\n\r\nWe read this as <em>six plus eight<\/em>\u00a0and the result is the sum of six and eight.\r\n\r\n[latex]6+8=14[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]143045[\/ohm_question]\r\n\r\n[ohm_question hide_question_numbers=1]143046[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Model Addition of Whole Numbers<\/h2>\r\nAddition is really just counting. We will model addition with [latex]\\text{base - 10}[\/latex] blocks. Remember, a block represents [latex]1[\/latex] and a rod represents [latex]10[\/latex]. Let\u2019s start by modeling the addition expression we just considered, [latex]3+4[\/latex].\r\nEach addend is less than [latex]10[\/latex], so we can use ones blocks.\r\n<table id=\"eip-167\" class=\"unnumbered unstyled\" summary=\"This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states \">\r\n<tbody>\r\n<tr>\r\n<td>We start by modeling the first number with 3 blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215314\/CNX_BMath_Figure_01_02_019_img-02.png\" alt=\"CNX_BMath_Figure_01_02_019_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Then we model the second number with 4 blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215315\/CNX_BMath_Figure_01_02_019_img-03.png\" alt=\"CNX_BMath_Figure_01_02_019_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the total number of blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215316\/CNX_BMath_Figure_01_02_019_img-04.png\" alt=\"CNX_BMath_Figure_01_02_019_img-04.png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThere are [latex]7[\/latex] blocks in all. We use an equal sign [latex]\\text{(=)}[\/latex] to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that. [latex]3+4=7[\/latex].\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nModel the addition [latex]2+6[\/latex].\r\n[reveal-answer q=\"771692\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"771692\"]\r\n\r\nSolution\r\n[latex]2+6[\/latex] means the sum of [latex]2[\/latex] and [latex]6[\/latex]\r\nEach addend is less than [latex]10[\/latex], so we can use ones blocks.\r\n<table id=\"eip-951\" class=\"unnumbered unstyled\" summary=\"This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states \">\r\n<tbody>\r\n<tr>\r\n<td>Model the first number with [latex]2[\/latex] blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215317\/CNX_BMath_Figure_01_02_016_img-02.png\" alt=\"CNX_BMath_Figure_01_02_016_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Model the second number with [latex]6[\/latex] blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215318\/CNX_BMath_Figure_01_02_016_img-03.png\" alt=\"CNX_BMath_Figure_01_02_016_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the total number of blocks<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215319\/CNX_BMath_Figure_01_02_016_img-04.png\" alt=\"CNX_BMath_Figure_01_02_016_img-04.png\" \/>There are [latex]8[\/latex] blocks in all, so [latex]2+6=8[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nModel: [latex]3+6[\/latex].\r\n[reveal-answer q=\"498397\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"498397\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215321\/CNX_BMath_Figure_01_02_006_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\nModel: [latex]5+1[\/latex].\r\n[reveal-answer q=\"677857\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"677857\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215322\/CNX_BMath_Figure_01_02_007_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWhen the result is [latex]10[\/latex] or more ones blocks, we will exchange the [latex]10[\/latex] blocks for one rod.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nModel the addition [latex]5+8[\/latex].\r\n[reveal-answer q=\"557360\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"557360\"]\r\n\r\nSolution\r\n[latex]5+8[\/latex] means the sum of [latex]5[\/latex] and [latex]8[\/latex].\r\n<table id=\"eip-555\" class=\"unnumbered unstyled\" summary=\"This image is two columns. The left column is annotations and the right column are base blocks. The first line on the left says \">\r\n<tbody>\r\n<tr>\r\n<td>Each addend is less than [latex]10[\/latex], se we can use ones blocks.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Model the first number with [latex]5[\/latex] blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215322\/CNX_BMath_Figure_01_02_017_img-02.png\" alt=\"CNX_BMath_Figure_01_02_017_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Model the second number with [latex]8[\/latex] blocks.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215324\/CNX_BMath_Figure_01_02_017_img-03.png\" alt=\"CNX_BMath_Figure_01_02_017_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the result. There are more than [latex]10[\/latex] blocks so we exchange [latex]10[\/latex] ones blocks for [latex]1[\/latex] tens rod.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215325\/CNX_BMath_Figure_01_02_017_img-04.png\" alt=\"CNX_BMath_Figure_01_02_017_img-04.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now we have [latex]1[\/latex] ten and [latex]3[\/latex] ones, which is [latex]13[\/latex].<\/td>\r\n<td>[latex]5+8=13[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nNotice that we can describe the models as ones blocks and tens rods, or we can simply say <em>ones<\/em> and <em>tens<\/em>. From now on, we will use the shorter version but keep in mind that they mean the same thing.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nModel the addition: [latex]5+7[\/latex].\r\n[reveal-answer q=\"489565\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"489565\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215326\/CNX_BMath_Figure_01_02_010_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\nModel the addition: [latex]6+8[\/latex].\r\n[reveal-answer q=\"772557\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"772557\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215327\/CNX_BMath_Figure_01_02_011_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nNext we will model adding two digit numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nModel the addition: [latex]17+26[\/latex].\r\n[reveal-answer q=\"118621\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"118621\"]\r\n\r\nSolution\r\n[latex]17+26[\/latex] means the sum of [latex]17[\/latex] and\u00a0[latex]26[\/latex].\r\n<table id=\"eip-93\" class=\"unnumbered unstyled\" summary=\"This is an image with three columns: the left column states \">\r\n<tbody>\r\n<tr>\r\n<td>Model the [latex]17[\/latex].<\/td>\r\n<td>[latex]1[\/latex] ten and[latex]7[\/latex] ones<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215328\/CNX_BMath_Figure_01_02_018_img-02.png\" alt=\"CNX_BMath_Figure_01_02_018_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Model the [latex]26[\/latex].<\/td>\r\n<td>[latex]2[\/latex] tens and [latex]6[\/latex] ones<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215330\/CNX_BMath_Figure_01_02_018_img-03.png\" alt=\"CNX_BMath_Figure_01_02_018_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine.<\/td>\r\n<td>[latex]3[\/latex] tens and [latex]13[\/latex] ones<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215331\/CNX_BMath_Figure_01_02_018_img-04.png\" alt=\"CNX_BMath_Figure_01_02_018_img-04.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Exchange [latex]10[\/latex] ones for[latex]1[\/latex] ten.<\/td>\r\n<td>[latex]4[\/latex] tens and [latex]3[\/latex] ones [latex]40+3=43[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215333\/CNX_BMath_Figure_01_02_018_img-05.png\" alt=\"CNX_BMath_Figure_01_02_018_img-05.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We have shown that [latex]17+26=43[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nModel each addition: [latex]15+27[\/latex].\r\n[reveal-answer q=\"586067\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"586067\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215334\/CNX_BMath_Figure_01_02_014_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\nModel each addition: [latex]16+29[\/latex].\r\n[reveal-answer q=\"421353\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"421353\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215336\/CNX_BMath_Figure_01_02_015_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWatch the video below for another example of how to use base [latex]10[\/latex] blocks to model the sum of two whole numbers.\r\n\r\nhttps:\/\/youtu.be\/_smXQAPbygQ","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use symbols and words to describe addition of single and double digit numbers<\/li>\n<li>Model addition of single and double digit numbers using base-10 blocks, or shapes<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Use Addition Notation<\/h2>\n<p>A college student has a part-time job. Last week he worked [latex]3[\/latex] hours on Monday and [latex]4[\/latex] hours on Friday. To find the total number of hours he worked last week, he added [latex]3[\/latex] and [latex]4[\/latex].<\/p>\n<p>The operation of addition combines numbers to get a sum. The notation we use to find the sum of [latex]3[\/latex] and [latex]4[\/latex] is:<\/p>\n<p style=\"text-align: center;\">[latex]3+4[\/latex]<\/p>\n<p>We read this as <em>three plus four<\/em> and the result is the sum of three and four. The numbers [latex]3[\/latex] and [latex]4[\/latex] are called the addends. A math statement that includes numbers and operations is called an expression.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Addition Notation<\/h3>\n<p>To describe addition, we can use symbols and words.<\/p>\n<table id=\"fs-id2711498\" class=\"unnumbered\" style=\"width: 40%;\" summary=\"This is a table with two rows and five columns. The top row is a header row. Each column from left to right is labeled accordingly: Operation, Notation, Expressions, Read as, and result. In the second row, from left to right is addition, the plus sign, the expression 3 plus four, the statement three plus four and the sum of 3 and 4.\">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Notation<\/th>\n<th>Expression<\/th>\n<th>Read as<\/th>\n<th>Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Addition<\/td>\n<td>[latex]+[\/latex]<\/td>\n<td>[latex]3+4[\/latex]<\/td>\n<td>three plus four<\/td>\n<td>the sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>After talking to her counselor, Esmeralda needs to determine how many classes she has taken so far at Blue Sky College. Last year she took [latex]6[\/latex] classes, and this year will complete [latex]8[\/latex] classes. She needs to determine the sum of [latex]6[\/latex] and [latex]8[\/latex]. First translate the sentence into math notation and then calculate the results.<\/p>\n<p>Translate from words to math: [latex]6+8[\/latex]<\/p>\n<p><em>The operation of addition combines numbers to get a sum<\/em><\/p>\n<p>We read this as <em>six plus eight<\/em>\u00a0and the result is the sum of six and eight.<\/p>\n<p>[latex]6+8=14[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143045\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143045&theme=oea&iframe_resize_id=ohm143045\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm143046\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143046&theme=oea&iframe_resize_id=ohm143046\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Model Addition of Whole Numbers<\/h2>\n<p>Addition is really just counting. We will model addition with [latex]\\text{base - 10}[\/latex] blocks. Remember, a block represents [latex]1[\/latex] and a rod represents [latex]10[\/latex]. Let\u2019s start by modeling the addition expression we just considered, [latex]3+4[\/latex].<br \/>\nEach addend is less than [latex]10[\/latex], so we can use ones blocks.<\/p>\n<table id=\"eip-167\" class=\"unnumbered unstyled\" summary=\"This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states\">\n<tbody>\n<tr>\n<td>We start by modeling the first number with 3 blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215314\/CNX_BMath_Figure_01_02_019_img-02.png\" alt=\"CNX_BMath_Figure_01_02_019_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Then we model the second number with 4 blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215315\/CNX_BMath_Figure_01_02_019_img-03.png\" alt=\"CNX_BMath_Figure_01_02_019_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the total number of blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215316\/CNX_BMath_Figure_01_02_019_img-04.png\" alt=\"CNX_BMath_Figure_01_02_019_img-04.png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>There are [latex]7[\/latex] blocks in all. We use an equal sign [latex]\\text{(=)}[\/latex] to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that. [latex]3+4=7[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the addition [latex]2+6[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q771692\">Show Solution<\/span><\/p>\n<div id=\"q771692\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n[latex]2+6[\/latex] means the sum of [latex]2[\/latex] and [latex]6[\/latex]<br \/>\nEach addend is less than [latex]10[\/latex], so we can use ones blocks.<\/p>\n<table id=\"eip-951\" class=\"unnumbered unstyled\" summary=\"This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states\">\n<tbody>\n<tr>\n<td>Model the first number with [latex]2[\/latex] blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215317\/CNX_BMath_Figure_01_02_016_img-02.png\" alt=\"CNX_BMath_Figure_01_02_016_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Model the second number with [latex]6[\/latex] blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215318\/CNX_BMath_Figure_01_02_016_img-03.png\" alt=\"CNX_BMath_Figure_01_02_016_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the total number of blocks<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215319\/CNX_BMath_Figure_01_02_016_img-04.png\" alt=\"CNX_BMath_Figure_01_02_016_img-04.png\" \/>There are [latex]8[\/latex] blocks in all, so [latex]2+6=8[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Model: [latex]3+6[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q498397\">Show Solution<\/span><\/p>\n<div id=\"q498397\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215321\/CNX_BMath_Figure_01_02_006_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<p>Model: [latex]5+1[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q677857\">Show Solution<\/span><\/p>\n<div id=\"q677857\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215322\/CNX_BMath_Figure_01_02_007_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>When the result is [latex]10[\/latex] or more ones blocks, we will exchange the [latex]10[\/latex] blocks for one rod.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the addition [latex]5+8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q557360\">Show Solution<\/span><\/p>\n<div id=\"q557360\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n[latex]5+8[\/latex] means the sum of [latex]5[\/latex] and [latex]8[\/latex].<\/p>\n<table id=\"eip-555\" class=\"unnumbered unstyled\" summary=\"This image is two columns. The left column is annotations and the right column are base blocks. The first line on the left says\">\n<tbody>\n<tr>\n<td>Each addend is less than [latex]10[\/latex], se we can use ones blocks.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Model the first number with [latex]5[\/latex] blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215322\/CNX_BMath_Figure_01_02_017_img-02.png\" alt=\"CNX_BMath_Figure_01_02_017_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Model the second number with [latex]8[\/latex] blocks.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215324\/CNX_BMath_Figure_01_02_017_img-03.png\" alt=\"CNX_BMath_Figure_01_02_017_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the result. There are more than [latex]10[\/latex] blocks so we exchange [latex]10[\/latex] ones blocks for [latex]1[\/latex] tens rod.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215325\/CNX_BMath_Figure_01_02_017_img-04.png\" alt=\"CNX_BMath_Figure_01_02_017_img-04.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Now we have [latex]1[\/latex] ten and [latex]3[\/latex] ones, which is [latex]13[\/latex].<\/td>\n<td>[latex]5+8=13[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Notice that we can describe the models as ones blocks and tens rods, or we can simply say <em>ones<\/em> and <em>tens<\/em>. From now on, we will use the shorter version but keep in mind that they mean the same thing.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Model the addition: [latex]5+7[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q489565\">Show Solution<\/span><\/p>\n<div id=\"q489565\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215326\/CNX_BMath_Figure_01_02_010_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<p>Model the addition: [latex]6+8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q772557\">Show Solution<\/span><\/p>\n<div id=\"q772557\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215327\/CNX_BMath_Figure_01_02_011_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Next we will model adding two digit numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the addition: [latex]17+26[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q118621\">Show Solution<\/span><\/p>\n<div id=\"q118621\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n[latex]17+26[\/latex] means the sum of [latex]17[\/latex] and\u00a0[latex]26[\/latex].<\/p>\n<table id=\"eip-93\" class=\"unnumbered unstyled\" summary=\"This is an image with three columns: the left column states\">\n<tbody>\n<tr>\n<td>Model the [latex]17[\/latex].<\/td>\n<td>[latex]1[\/latex] ten and[latex]7[\/latex] ones<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215328\/CNX_BMath_Figure_01_02_018_img-02.png\" alt=\"CNX_BMath_Figure_01_02_018_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Model the [latex]26[\/latex].<\/td>\n<td>[latex]2[\/latex] tens and [latex]6[\/latex] ones<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215330\/CNX_BMath_Figure_01_02_018_img-03.png\" alt=\"CNX_BMath_Figure_01_02_018_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine.<\/td>\n<td>[latex]3[\/latex] tens and [latex]13[\/latex] ones<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215331\/CNX_BMath_Figure_01_02_018_img-04.png\" alt=\"CNX_BMath_Figure_01_02_018_img-04.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Exchange [latex]10[\/latex] ones for[latex]1[\/latex] ten.<\/td>\n<td>[latex]4[\/latex] tens and [latex]3[\/latex] ones [latex]40+3=43[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215333\/CNX_BMath_Figure_01_02_018_img-05.png\" alt=\"CNX_BMath_Figure_01_02_018_img-05.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>We have shown that [latex]17+26=43[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Model each addition: [latex]15+27[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q586067\">Show Solution<\/span><\/p>\n<div id=\"q586067\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215334\/CNX_BMath_Figure_01_02_014_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<p>Model each addition: [latex]16+29[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q421353\">Show Solution<\/span><\/p>\n<div id=\"q421353\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215336\/CNX_BMath_Figure_01_02_015_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Watch the video below for another example of how to use base [latex]10[\/latex] blocks to model the sum of two whole numbers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Model Addition of Two Digit Whole Numbers Using Base Ten Blocks\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_smXQAPbygQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4594\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Authored by<\/strong>: Deborah Devlin. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Model Addition of Two Digit Whole Numbers Using Base Ten Blocks. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_smXQAPbygQ\">https:\/\/youtu.be\/_smXQAPbygQ<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 143045, 143046. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"Deborah Devlin\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Model Addition of Two Digit Whole Numbers Using Base Ten Blocks\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/_smXQAPbygQ\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Question ID: 143045, 143046\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4594","chapter","type-chapter","status-publish","hentry"],"part":4588,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4594","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4594\/revisions"}],"predecessor-version":[{"id":5737,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4594\/revisions\/5737"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4588"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4594\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4594"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4594"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4594"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}