{"id":3433,"date":"2019-03-14T15:07:16","date_gmt":"2019-03-14T15:07:16","guid":{"rendered":"https:\/\/resedblog.wpengine.com\/?p=3433"},"modified":"2021-03-26T19:47:56","modified_gmt":"2021-03-26T19:47:56","slug":"math-manipulative-roadshow-2019","status":"publish","type":"post","link":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/","title":{"rendered":"Math Manipulative Roadshow 2019"},"content":{"rendered":"<p><em><span style=\"font-weight: 400\">Written by: Michelle Callis and Heather Schoenfeld, <\/span><span style=\"font-weight: 400\">Directors of Math<\/span><\/em><\/p>\n<p><span style=\"font-weight: 400\">Everyone loves a trip to the carnival! The smell of sweet and savory treats wafting through the air, the ping-and-ding of midway games, livestock mooing and baaing, dipping their heads for a friendly, child-size pat, and big semi-trucks with trailers that have been transformed into larger-than-life amusement rides all excite the heart. In this fun and enthusiastic spirit, Michelle Callis, ResponsiveEd district math director (K-5), and Heather Schoenfeld, ResponsiveEd district math director (6-12), set out to begin the second semester of this school year inspiring classroom math instruction for <\/span><a href=\"https:\/\/responsiveed.com\/\"><span style=\"font-weight: 400\">ResponsiveEd<\/span><\/a><span style=\"font-weight: 400\"> educators. <\/span><\/p>\n<p><span style=\"font-weight: 400\">The Math Manipulative Roadshow 2019 was literally just that &#8211; a traveling roadshow. The idea was first birthed in the office of Bonnie Wimberley, director of teaching &amp; instruction, where collaborations with the district math content directors were transpiring regarding how to strategically and effectively impact student math learning with best practices across the district. Michelle and Heather worked diligently, preparing well in advance, for maximum delivery. And on Monday, January 14, 2019, the two hit the road driving 850+ miles in the course of five days for outlying school campuses. Teachers at local school campuses within an hour drive commuted to the ResponsiveEd corporate office on Monday, February 18, 2019. The purpose of the math manipulative training was four-fold: <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">To increase the use of Math manipulatives as a district<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">To demonstrate effective use of specific Math manipulatives<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">To stimulate teacher creativity with how Math manipulatives can be used<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">To bring vertical alignment K-8 with the use of Math manipulatives<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">With their arrival in each town, Michelle and Heather encountered K-8 teaching staff eager to learn new instructional methods and sharpen current skills. There were plenty of big smiles to go around and a 360-degree virtual ride on a ferris wheel while carousel music played in the background. Teachers were treated with serving-size bags of fresh popcorn and gifted with free playing cards to use as math manipulatives in their classrooms with students. And at the close of the session, they received a live web link to a \u201crefreshments\u201d math manipulative resource packet with about 100 activities organized by manipulative type and concept to bring fresh strength to math teaching.\u00a0<\/span><\/p>\n<div id=\"attachment_3435\" style=\"width: 310px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3435\" class=\"size-medium wp-image-3435\" src=\"https:\/\/resedblog.wpengine.com\/wp-content\/uploads\/2019\/03\/Math-Manipulative-2019-Group-300x183.jpg\" alt=\"\" width=\"300\" height=\"183\" srcset=\"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Group-300x183.jpg 300w, https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Group-768x468.jpg 768w, https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Group-1024x624.jpg 1024w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-3435\" class=\"wp-caption-text\">ResponsiveEd Directors of Math Heather Schoenfeld (front left) and Michelle Callis (front right) instruct a math manipulative activity.<\/p><\/div>\n<p><span style=\"font-weight: 400\">The math manipulative teacher training promoted the use of a concrete-pictorial-abstract (CPA) approach, created by Jerome Bruner (1964), a psychologist from the United States, as an essential foundation to student learning. To learn more about this approach click <\/span><a href=\"https:\/\/mathsnoproblem.com\/en\/mastery\/concrete-pictorial-abstract\/\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\">. <\/span><\/p>\n<p><span style=\"font-weight: 400\">According to the research of Steven Hedden (1986), with long term use of manipulatives in mathematics, educators have found that students make gains in the following areas: <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Putting mathematical thinking into words that can be communicated in an effective manner which in turn spurs them to work collaboratively <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Finding ways to represent real-world situations symbolically using a variety of strategies<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Owning their own learning and becoming confident in their ability to come up with creative solutions to math problems without relying on the teacher <\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Like people participating in a ride at the carnival expecting a fun and safe ride, using math manipulatives requires specific guidelines and processes for effective and enjoyable functioning. Teachers were versed on the kinds of manipulatives available, such as within the district curriculum, and other effective manipulatives that can be found within the school environment, student homes, and digitally on the internet. Teachers also learned about important guidelines unique to both the teacher and student role for working with manipulatives. Teachers examined, discussed, and made connections to math content with the \u201cBig Top Ten\u201d, the 10 most effective math manipulatives every teacher should have access to for teaching math. <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Base 10 blocks\/algebra tiles<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Uni\/Unifix snap cubes<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Pattern blocks or attribute tiles<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Geometric solids<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Measurement devices<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Dice<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Playing cards <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Individual dry erase boards<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Plain paper &amp; graph paper<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Colored highlighters or pencils<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Hands-on, Socratic-style math lessons, like the ones listed below, were modeled with teacher participation (as students), as well as, tangible ways to make connections that bridge physical concept realities to more symbolic representations. It was during this part of the training session that Ashley Giuseppetti, response to intervention (RTI) coordinator at <\/span><a href=\"https:\/\/foundersclassical.com\/schertz\/\"><span style=\"font-weight: 400\">Founders Classical Academy of Schertz<\/span><\/a><span style=\"font-weight: 400\">, felt like it really hit home for her in \u201chow to address students with misunderstandings of mathematical concepts.\u201d <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The Colors of the Carnival Skittles Activity <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Base Ten Blocks Roll &amp; Race Gaming Activity <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Fantasy Figures Geometry Activity <\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Socratic learning emphasizes, \u201cletting students explore (in this case, math manipulatives) first and letting them tell you what they observe,\u201d said Julia Russell, sixth-grade math &amp; science teacher at <\/span><a href=\"https:\/\/tyler-classical.responsiveed.com\/\"><span style=\"font-weight: 400\">Tyler Classical Academy<\/span><\/a><span style=\"font-weight: 400\">. Teacher responses to student observations is a critical element of creating a math-safe classroom, where every student can feel confident they are valued as a person and can make mistakes (and learn from them) without shame. Math manipulatives at every age are an important element in math-safe classrooms. Julia Russell went on to say that, \u201cEven the middle and high school students still need manipulatives on some things; and, we need to teach them how to use them and have them available.\u201d Ronald Morris, Tyler Classical Academy campus director grades 7-12, said he would support school staff by \u201cencouraging teachers to use manipulatives and praising them when I see it in action.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400\">Teaching staff also became more familiar with 21st-century hands-on math materials, digital manipulatives, \u00a0such as the ones found in the online version of the math curriculum and other online components with free public access like the <\/span><a href=\"http:\/\/nlvm.usu.edu\/\"><span style=\"font-weight: 400\">National Library of Virtual Manipulatives<\/span><\/a><span style=\"font-weight: 400\">.<\/span><\/p>\n<p><span style=\"font-weight: 400\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-3436 alignleft\" src=\"https:\/\/resedblog.wpengine.com\/wp-content\/uploads\/2019\/03\/Math-Manipulative-2019-Activity-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Activity-300x225.jpg 300w, https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Activity-768x576.jpg 768w, https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Activity-1024x768.jpg 1024w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>Teachers left the training inspired and enthusiastic about getting back to their classrooms and putting what they had learned into practice with their students. Jacquelyn Tabor, a fifth and sixth-grade math &amp; science teacher at <\/span><a href=\"https:\/\/crockett-classical.responsiveed.com\/\"><span style=\"font-weight: 400\">Crockett Classical Academy<\/span><\/a><span style=\"font-weight: 400\">, took a proactive approach saying that she would be \u201cincorporating manipulatives into my lesson plans\u201d. Precious Hicks, a fifth-grade math &amp; science teacher at Tyler Classical Academy, said she\u2019d be, \u201cusing items outside of the classroom as math manipulatives to make the lesson more real world for the students.\u201d Jaime West, a second-grade teacher at <\/span><a href=\"https:\/\/jasper-classical.responsiveed.com\/\"><span style=\"font-weight: 400\">Jasper Classical Academy<\/span><\/a><span style=\"font-weight: 400\"> shared, \u201cThe different types and ways to use math manipulatives was very helpful.\u201d Tina Drab, kindergarten teacher at <\/span><a href=\"https:\/\/austin-classical.responsiveed.com\/\"><span style=\"font-weight: 400\">Austin Classical Academy<\/span><\/a><span style=\"font-weight: 400\"> declared that the experience was a win-win for all!\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400\">In conclusion, a carnival is a place of fun and fantasy, a place of wild imaginings, an atmosphere of thrill and curiosities. Math experiences, too, should be oozing with intrigue and opportunities for discovery and creativity. Yet, students should not be left in a fantasy world where math is only in their head. Students need tangible math, understanding that happens in their hands\u2026. doing math rather than just thinking about doing Math. <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Additional Resources:<\/strong><\/p>\n<p><span style=\"font-weight: 400\">Bruner, J. (1964). \u201cThe Cognitive Course for Growth\u201d. American Psychologist, 19, <\/span><\/p>\n<p><span style=\"font-weight: 400\">1: 1-15.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Heddens, S. (1986). \u201cBridging the Gap Between the Concrete and Abstract\u201d. The Arithmetic Teacher, 33: 14-17. DOI 10.1037\/h0044160<\/span><\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_3433\" class=\"pvc_stats all  \" data-element-id=\"3433\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Written by: Michelle Callis and Heather Schoenfeld, Directors of Math Everyone loves a trip to the carnival! The smell of sweet and savory treats wafting through the air, the ping-and-ding&#8230;<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_3433\" class=\"pvc_stats all  \" data-element-id=\"3433\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":2,"featured_media":4190,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,52],"tags":[464,591,612,615],"class_list":{"0":"post-3433","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-featured","8":"category-home-office","9":"tag-math","10":"tag-professional-development","11":"tag-responsive-education-solutions","12":"tag-responsiveed"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Math Manipulative Roadshow 2019 - ResponsiveEd Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math Manipulative Roadshow 2019 - ResponsiveEd Blog\" \/>\n<meta property=\"og:description\" content=\"Written by: Michelle Callis and Heather Schoenfeld, Directors of Math Everyone loves a trip to the carnival! The smell of sweet and savory treats wafting through the air, the ping-and-ding...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/\" \/>\n<meta property=\"og:site_name\" content=\"ResponsiveEd Blog\" \/>\n<meta property=\"article:published_time\" content=\"2019-03-14T15:07:16+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-03-26T19:47:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"350\" \/>\n\t<meta property=\"og:image:height\" content=\"350\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"responsiveed\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"responsiveed\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/\"},\"author\":{\"name\":\"responsiveed\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/#\\\/schema\\\/person\\\/b48b02593408736187aa4017146698ca\"},\"headline\":\"Math Manipulative Roadshow 2019\",\"datePublished\":\"2019-03-14T15:07:16+00:00\",\"dateModified\":\"2021-03-26T19:47:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/\"},\"wordCount\":1160,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2019\\\/03\\\/Math-Manipulative-2019-Cover-350x350-1.jpg\",\"keywords\":[\"Math\",\"Professional Development\",\"Responsive Education Solutions\",\"ResponsiveEd\"],\"articleSection\":[\"Featured\",\"Home Office\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/\",\"url\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/\",\"name\":\"Math Manipulative Roadshow 2019 - ResponsiveEd Blog\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2019\\\/03\\\/Math-Manipulative-2019-Cover-350x350-1.jpg\",\"datePublished\":\"2019-03-14T15:07:16+00:00\",\"dateModified\":\"2021-03-26T19:47:56+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/#\\\/schema\\\/person\\\/b48b02593408736187aa4017146698ca\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#primaryimage\",\"url\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2019\\\/03\\\/Math-Manipulative-2019-Cover-350x350-1.jpg\",\"contentUrl\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2019\\\/03\\\/Math-Manipulative-2019-Cover-350x350-1.jpg\",\"width\":350,\"height\":350},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/2019\\\/03\\\/14\\\/math-manipulative-roadshow-2019\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Math Manipulative Roadshow 2019\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/#website\",\"url\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/\",\"name\":\"ResponsiveEd Blog\",\"description\":\"Just another ResponsiveEd Sites site\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/#\\\/schema\\\/person\\\/b48b02593408736187aa4017146698ca\",\"name\":\"responsiveed\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g\",\"caption\":\"responsiveed\"},\"sameAs\":[\"http:\\\/\\\/responsiveed.wpengine.com\"],\"url\":\"https:\\\/\\\/responsiveed.com\\\/responsiveed-blog\\\/author\\\/responsiveed\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Math Manipulative Roadshow 2019 - ResponsiveEd Blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/","og_locale":"en_US","og_type":"article","og_title":"Math Manipulative Roadshow 2019 - ResponsiveEd Blog","og_description":"Written by: Michelle Callis and Heather Schoenfeld, Directors of Math Everyone loves a trip to the carnival! The smell of sweet and savory treats wafting through the air, the ping-and-ding...","og_url":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/","og_site_name":"ResponsiveEd Blog","article_published_time":"2019-03-14T15:07:16+00:00","article_modified_time":"2021-03-26T19:47:56+00:00","og_image":[{"width":350,"height":350,"url":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg","type":"image\/jpeg"}],"author":"responsiveed","twitter_card":"summary_large_image","twitter_misc":{"Written by":"responsiveed","Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#article","isPartOf":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/"},"author":{"name":"responsiveed","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/#\/schema\/person\/b48b02593408736187aa4017146698ca"},"headline":"Math Manipulative Roadshow 2019","datePublished":"2019-03-14T15:07:16+00:00","dateModified":"2021-03-26T19:47:56+00:00","mainEntityOfPage":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/"},"wordCount":1160,"commentCount":0,"image":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#primaryimage"},"thumbnailUrl":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg","keywords":["Math","Professional Development","Responsive Education Solutions","ResponsiveEd"],"articleSection":["Featured","Home Office"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/","url":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/","name":"Math Manipulative Roadshow 2019 - ResponsiveEd Blog","isPartOf":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#primaryimage"},"image":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#primaryimage"},"thumbnailUrl":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg","datePublished":"2019-03-14T15:07:16+00:00","dateModified":"2021-03-26T19:47:56+00:00","author":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/#\/schema\/person\/b48b02593408736187aa4017146698ca"},"breadcrumb":{"@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#primaryimage","url":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg","contentUrl":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-content\/uploads\/sites\/2\/2019\/03\/Math-Manipulative-2019-Cover-350x350-1.jpg","width":350,"height":350},{"@type":"BreadcrumbList","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/2019\/03\/14\/math-manipulative-roadshow-2019\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/responsiveed.com\/responsiveed-blog\/"},{"@type":"ListItem","position":2,"name":"Math Manipulative Roadshow 2019"}]},{"@type":"WebSite","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/#website","url":"https:\/\/responsiveed.com\/responsiveed-blog\/","name":"ResponsiveEd Blog","description":"Just another ResponsiveEd Sites site","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/responsiveed.com\/responsiveed-blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/responsiveed.com\/responsiveed-blog\/#\/schema\/person\/b48b02593408736187aa4017146698ca","name":"responsiveed","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/12d9cb235c3c2d940a786a481dad7e69889c72fb070e2cbef1d46a0407002506?s=96&d=mm&r=g","caption":"responsiveed"},"sameAs":["http:\/\/responsiveed.wpengine.com"],"url":"https:\/\/responsiveed.com\/responsiveed-blog\/author\/responsiveed\/"}]}},"a3_pvc":{"activated":true,"total_views":438,"today_views":0},"_links":{"self":[{"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/posts\/3433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/comments?post=3433"}],"version-history":[{"count":0,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/posts\/3433\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/media\/4190"}],"wp:attachment":[{"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/media?parent=3433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/categories?post=3433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/responsiveed.com\/responsiveed-blog\/wp-json\/wp\/v2\/tags?post=3433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}