{"id":4496,"date":"2026-01-16T17:29:18","date_gmt":"2026-01-16T17:29:18","guid":{"rendered":"https:\/\/www.terc.edu\/adultnumeracycenter\/?page_id=4496"},"modified":"2026-02-02T15:11:54","modified_gmt":"2026-02-02T15:11:54","slug":"exploring-10","status":"publish","type":"page","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/exploring-10\/","title":{"rendered":"Exploring 10%"},"content":{"rendered":"\n<h2 class=\"wp-block-heading is-style-highlight-purple\"><strong>Benchmark Percent Review<\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size\">On this page, you will explore and learn about how to use 10% as a benchmark. Before you do, take a few minutes to practice with the benchmark percents you have already learned about. Here is the model you&#8217;ve been working with and some warm-up questions. Try to use the things you have learned about benchmark percents and their relationships to answer the questions before you investigate them on the model. You can also try drawing your own pictures!<\/p>\n\n\n\n<center>\n\n<iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/qapbwhu5dw?embed\" width=\"750px\" height=\"300px\" style=\"border: 1px solid #ccc\" frameborder=0><\/iframe>\n\n<\/center>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Warm up questions:<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">What is 25% of 200?<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">If 50% of a number is 75, what is the number?<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">What percent of 140 is 105%<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">What is 75% of 116?<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">If 75% of the people in a group wear glasses, what percent of the people do not wear glasses?<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">If you get a 25% discount on a gym membership that normally costs $200, how much do you pay for it?<\/li>\n\n\n\n<li class=\"has-medium-font-size\" style=\"font-style:normal;font-weight:700\">There were 8 students enrolled in a math class. Then enrollment went up by 75%. How many students are there now?<\/li>\n<\/ol>\n\n\n\n<p class=\"has-medium-font-size\"><a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/warmupanswers_acc.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Click here for answers to these warm up questions.<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading is-style-highlight-purple\"><strong>Introducing 10%<\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size\">Here is a new model. Play with it a little to see how it works.<\/p>\n\n\n\n<center>\n\n<iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/qakuwqhaqy?embed\" width=\"730px\" height=\"300px\" style=\"border: 1px solid #ccc\" frameborder=0><\/iframe>\n\n<\/center>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\">As you play with the model, write down what you notice and what you wonder about. Here are some things you might want to think about:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">How does 10% compare with the other benchmark percents that you&#8217;ve been working with?<\/li>\n\n\n\n<li class=\"has-medium-font-size\">The shaded part is 10%. What percent is unshaded?<\/li>\n\n\n\n<li class=\"has-medium-font-size\">What fraction do you think is equal to 10%?<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Use the model to fill in the blanks in these sentences:<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>8. 10% of 100 is ____.<br><br>9. 15 is 10% of ____.<br><br>10. 10% of 50 is ____.<br><br>11. 20 is 10% of ____.<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Look at the four percents you&#8217;ve figured out so far. Can you figure out what fraction 10% is equal to? (Hint: try to figure out what you have to divide a number by to get 10% of it. Or see if you can figure out how many times 10% fits in to the whole.)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/exploring-10\/some-answers-and-explanations-of-10\/\">If you&#8217;re not sure what fraction 10% is, click&nbsp;here&nbsp;to find out.<\/a> If you feel pretty sure you know, try filling in the missing numbers in the table that follows. Use a calculator if you need to. (The first row is filled in for you.) What patterns do you notice?<\/p>\n\n\n\n<figure style=\"font-size:24px\" class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">10%<\/th><th class=\"has-text-align-center\" data-align=\"center\">100%<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><td class=\"has-text-align-center\" data-align=\"center\">100<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">120<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">180<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">3500<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">350<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">35<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-medium-font-size\"><a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/warmupanswers_10percent100percent-acc.docx\" target=\"_blank\" rel=\"noreferrer noopener\">Click here for the filled in table if you want to check your answers.<\/a><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>What patterns did you notice in the table?<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading is-style-highlight-purple\"><strong>Investigating Patterns<\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size\">Below are&nbsp;<strong>two special calculators<\/strong>. The first one finds 10% of a number. The second one tells you what the whole number is if you know 10%. Play with both calculators. Put in any number you want and try to predict what the calculator will say before you click the button. Can you figure out any patterns that can help you think about 10%?<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<center>\n<b>Calculator to find 10%<\/b>\n<br><br>\n<label>The whole is <\/label><input type=\"text\" id=\"billInput\" value=100>\n<br><br>\n<button class=\"tenPercent\">Find 10%<\/button>\n<br>\n\n<p id=\"tipAmount\"><\/p>\n<\/center>\n<script>\nvar tenPerBtn = document.querySelector('.tenPercent');\nvar bill = document.getElementById('billInput');\nvar tipSuggestion = document.getElementById('tipAmount');\n\nfunction calcTen() {\n  var billInput = bill.value;\n  var tipAmount = billInput \/ 10;\n  tipSuggestion.innerHTML = '10% of ' + billInput + ' is ' + tipAmount;\n}\n\ntenPerBtn.addEventListener('click', calcTen)\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<center>\n<b>Calculator to find the whole<\/b>\n<br><br>\n<label>10% is <\/label><input type=\"text\" id=\"billInput2\" value=10>\n<br><br>\n<button class=\"tenPercent2\">Find the Whole<\/button>\n<br>\n\n<p id=\"tipAmount2\"><\/p>\n<\/center>\n<script>\nvar tenPerBtn2 = document.querySelector('.tenPercent2');\nvar bill2 = document.getElementById('billInput2');\nvar tipSuggestion2 = document.getElementById('tipAmount2');\n\nfunction calcTen2() {\n  var billInput2 = bill2.value;\n  var tipAmount2 = billInput2 * 10;\n  tipSuggestion2.innerHTML = 'If ' + billInput2 + ' is 10%, then the whole is ' + tipAmount2;\n}\n\ntenPerBtn2.addEventListener('click', calcTen2)\n<\/script>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-medium-font-size\">What strategies do you have for thinking about 10%? Here are some numbers to try in the calculators to check your strategies. If your strategies work for all of these numbers, they will probably work for any number! Remember to make a prediction before you click the button! If you strategy doesn&#8217;t give you the right answer, can you make your strategy better?<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Numbers to try:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\" style=\"font-size:24px;font-style:normal;font-weight:700\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>30<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>3<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.3<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.30<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.0300<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>1234<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>123.4<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>12.34<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1.234<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.1234<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-medium-font-size\">(Did something weird happen with zeros?<a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/exploring-10\/zeros-in-decimals\/\" target=\"_blank\" rel=\"noreferrer noopener\"> If you&#8217;re confused about the zeros, click&nbsp;here.<\/a>)<\/p>\n\n\n\n<h2 class=\"wp-block-heading is-style-highlight-purple\"><strong>Pictures of Percents<\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size\">Below are some pictures that show percents. For each one, pick the answer choice that best describes the colored part. <a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/picures_of_percents_acc.docx\" target=\"_blank\" rel=\"noreferrer noopener\">An alternative version that is more accessible to those with visual impairments is available.<\/a><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"663\" height=\"800\" src=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/pictures-of-percents_orig.jpg\" alt=\"set of 9 visualizations representing different percents.\" class=\"wp-image-4733\" style=\"width:840px;height:auto\" srcset=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/pictures-of-percents_orig.jpg 663w, https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/pictures-of-percents_orig-249x300.jpg 249w\" sizes=\"auto, (max-width: 663px) 100vw, 663px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-left has-medium-font-size\"><strong><a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/picures_of_percents_ak.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Click here to check your answers.<\/a><\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/picures_of_percents_ak_acc.docx\" target=\"_blank\" rel=\"noreferrer noopener\">An accessible version of the answer key is available.<\/a><\/p>\n\n\n\n<h5 class=\"wp-block-heading is-style-highlight-purple\"><strong>Creative Challenge!<\/strong><\/h5>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-medium-font-size\">Here is a website where you can make your own pictures of percents:&nbsp;<a href=\"https:\/\/www.visnos.com\/demos\/percentage-fraction-decimals-grid\" target=\"_blank\" rel=\"noreferrer noopener\">www.visnos.com\/demos\/percentage-fraction-decimals-grid<\/a><\/p>\n\n\n\n<p class=\"has-medium-font-size\">This picture that follows shows what some of the buttons do. If you want to find out what the other ones do, try them out!  Some challenges to try follow the picture.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"978\" height=\"734\" src=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/visnosinstructions2_orig.jpg\" alt=\"screenshot from Visnos online percentage maker website\" class=\"wp-image-4736\" srcset=\"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/visnosinstructions2_orig.jpg 978w, https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/visnosinstructions2_orig-300x225.jpg 300w, https:\/\/www.terc.edu\/adultnumeracycenter\/wp-content\/uploads\/sites\/28\/2026\/01\/visnosinstructions2_orig-768x576.jpg 768w\" sizes=\"auto, (max-width: 978px) 100vw, 978px\" \/><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<h5 class=\"wp-block-heading is-style-highlight-purple\"><strong>Challenges:<\/strong><\/h5>\n\n\n\n<p class=\"has-medium-font-size\">Here are some creative challenges. Make your picture first and then click on the fraction, decimal, and percent buttons to see if you were successful. (And then click them again before you start the next challenge.)<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<ol start=\"1\" class=\"wp-block-list has-medium-font-size\">\n<li><strong>Make a picture on a square grid that is more than 25% orange but less than 50% orange.<\/strong><\/li>\n\n\n\n<li><strong>&nbsp;Make a picture on a square grid that is exactly 10% orange, but don&#8217;t have any of the orange boxes touch each other!<\/strong><\/li>\n\n\n\n<li><strong>Make a picture on a circle with slices that is more than 10% orange but less than 25% orange.<\/strong><\/li>\n\n\n\n<li><strong>Make a picture on a circle that is 10% white.&nbsp;<\/strong>(You can also click and drag to color in a bunch of pieces at once.)&nbsp;<strong>What percent orange is your picture?<\/strong><\/li>\n<\/ol>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns has-medium-font-size is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"font-size:24px\">\n<div class=\"wp-block-buttons has-custom-font-size is-layout-flex wp-block-buttons-is-layout-flex\" style=\"font-size:28px\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-custom-font-size wp-element-button\" href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/exploring-75\/\" style=\"border-radius:20px;font-size:22px\"><strong>Go back to the 75% page<\/strong><\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"font-size:26px\">\n<div class=\"wp-block-buttons has-custom-font-size is-content-justification-right is-layout-flex wp-container-core-buttons-is-layout-765c4724 wp-block-buttons-is-layout-flex\" style=\"font-size:28px;font-style:normal;font-weight:700\">\n<div class=\"wp-block-button is-style-fill\"><a class=\"wp-block-button__link has-custom-font-size wp-element-button\" href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/percent-building-blocks\/\" style=\"border-radius:20px;font-size:22px\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Continue to Percent Building Blocks<\/strong><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Benchmark Percent Review<\/p>\n<p>On this page, you will explore and learn about how to use 10% as a benchmark. Before you do, take a few minutes to practice with the benchmark percents you have already learned about. Here is the model you&#8217;ve been working with and some warm-up questions. Try to use the things you have learned about benchmark percents and their relationships to answer the questions before you investigate them on the model. You can also try drawing your own pictures!  <a href=\"https:\/\/www.terc.edu\/adultnumeracycenter\/resources-for-teacher-growth-and-support\/learn-about-percents\/exploring-10\/\">&nbsp;&raquo;&nbsp;Read more<\/a><\/p>\n","protected":false},"author":16,"featured_media":0,"parent":4428,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-fullwidth.php","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"720,1582,1656,2359,2371,2934","_relevanssi_noindex_reason":"","footnotes":""},"class_list":["post-4496","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/pages\/4496","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/comments?post=4496"}],"version-history":[{"count":40,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/pages\/4496\/revisions"}],"predecessor-version":[{"id":5108,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/pages\/4496\/revisions\/5108"}],"up":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/pages\/4428"}],"wp:attachment":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/media?parent=4496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}