{"id":375,"date":"2024-10-05T08:08:39","date_gmt":"2024-10-05T08:08:39","guid":{"rendered":"https:\/\/urff.app\/?page_id=375"},"modified":"2026-02-05T19:35:34","modified_gmt":"2026-02-05T19:35:34","slug":"zahlenstrahl","status":"publish","type":"page","link":"https:\/\/urff.app\/en\/zahlenstrahl\/","title":{"rendered":"number line"},"content":{"rendered":"<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"404\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1024x404.jpeg\" alt=\"\" class=\"wp-image-432\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1024x404.jpeg 1024w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-300x118.jpeg 300w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-768x303.jpeg 768w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1536x607.jpeg 1536w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-2048x809.jpeg 2048w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-18x7.jpeg 18w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><!-- WP-Appbox (Version: 4.5.13 \/\/ Store: appstore \/\/ ID: 6473689075) -->\n<div class=\"wpappbox wpappbox-96d393eb62999eec1876d681b9e09380 appstore simple\">\n\t<div class=\"qrcode\"><img decoding=\"async\" src=\"https:\/\/api.qrserver.com\/v1\/create-qr-code\/?data=https%3A%2F%2Fapps.apple.com%2Fde%2Fapp%2Fzahlenstrahl%2Fid6473689075&size=200x200&ecc=M&margin=0\" alt=\"Zahlenstrahl\" \/><\/div>\n\t<div class=\"appicon\">\n\t\t<a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" aria-label=\"number line\"><img decoding=\"async\" src=\"\/\/is1-ssl.mzstatic.com\/image\/thumb\/PurpleSource221\/v4\/8c\/df\/ce\/8cdfcefc-769b-baa9-05ae-b26114241803\/Placeholder.mill\/200x200bb-75.png\" alt=\"Zahlenstrahl\" \/><\/a>\n\t<\/div>\n\t<div class=\"applinks\">\n\t\t<div class=\"appbuttons\">\n\t\t\t<a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" aria-label=\"number line\">Download<\/a>\n\t\t\t<span onmouseover=\"jQuery('.wpappbox-96d393eb62999eec1876d681b9e09380 .qrcode').show();\" onmouseout=\"jQuery('.wpappbox-96d393eb62999eec1876d681b9e09380 .qrcode').hide();\">QR code<\/span>\n\t\t<\/div>\n\t<\/div>\n\t<div class=\"appdetails\">\n\t\t<div class=\"apptitle\"><a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" title=\"number line\" aria-label=\"number line\" class=\"apptitle\">number line<\/a><\/div>\n\t\t<div class=\"developer\">\n\t\t\t<span class=\"label\">Developers: <\/span>\n\t\t\t<span class=\"value\"><a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/developer\/christian-urff\/id415894463\">Christian Urff<\/a><\/span>\n\t\t<\/div>\n\t\t<div class=\"price\">\n\t\t\t<span class=\"label\">Price: <\/span>\n\t\t\t<span class=\"value\">Free<\/span> \n\t\t\t<span class=\"rating\"><div title=\"0 out of 5 stars\" class=\"rating-stars stars-monochrome stars00\"><\/div><\/span>\n\t\t<\/div>\n\t<\/div>\n<\/div><!-- \/WP-Appbox --><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>number line<\/strong> (formerly <em>AR number line<\/em>The app has been fundamentally expanded: It has evolved from a simple augmented reality app into a comprehensive learning tool for the number line \u2013 featuring an AI tutor, an adaptive learning system, and nine different exercise types and experimental environments with and without AR. The app is based on scientific findings from trials and is the subject of ongoing research.<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"763\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1024x768.png\" alt=\"\" class=\"wp-image-763\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"758\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1024x768.png\" alt=\"\" class=\"wp-image-758\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"762\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1024x768.png\" alt=\"\" class=\"wp-image-762\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"759\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1024x768.png\" alt=\"\" class=\"wp-image-759\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"760\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1024x768.png\" alt=\"\" class=\"wp-image-760\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"761\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1024x768.png\" alt=\"\" class=\"wp-image-761\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Three experimental environments<\/strong> In addition to the augmented reality mode, there is a mode with touch controls and drawing tools, as well as a combined mode that displays AR and 2D views side-by-side. The experimental environments allow users to freely work with the different number line representations \u2013 no tasks are included here.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Learning progress reports<\/strong> \u2013 AI-generated reports show parents and teachers at a glance where a child stands: strengths, weaknesses and development over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Different types of exercises<\/strong> \u2013 they make targeted use of the possibilities of digital media and revolve around Number Line Estimation Tasks (NLET):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mark number<\/strong> \u2013 Estimate and place numbers on the number line<\/li>\n\n\n\n<li><strong>Name the number<\/strong> \u2013 Identify which number corresponds to a marked position<\/li>\n\n\n\n<li><strong>Find errors<\/strong> \u2013 Discover misplaced numbers<\/li>\n\n\n\n<li><strong>Matching numbers<\/strong> \u2013 Assign numbers to the correct positions<\/li>\n\n\n\n<li><strong>Numbers meet<\/strong> \u2013 Hit the target number by moving<\/li>\n\n\n\n<li><strong>Find excerpt<\/strong> \u2013 Find the matching section of the number line<\/li>\n\n\n\n<li><strong>Figures in the area<\/strong> \u2013 Recognize numbers in marked areas<\/li>\n\n\n\n<li><strong>neighboring numbers<\/strong> \u2013 Find predecessors and successors<\/li>\n\n\n\n<li><strong>Number puzzles<\/strong> \u2013 Solve exciting puzzles<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/urff.app\/en\/mehr-als-antworten-forschungsbasierte-anforderungen-an-ki-gestuetzte-lernbegleitung-im-mathematikunterricht\/\" data-type=\"post\" data-id=\"576\"><strong>AI Tutor<\/strong> \u2013 An intelligent learning companion<\/a> It provides child-friendly, pedagogically sound guidance when difficulties arise, recognizes error patterns, and explains things patiently. It reads out tasks and provides feedback. An internet connection is required for the AI-supported functions (costs are covered by the app purchase), but it also works offline with less detailed feedback.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Adaptive learning system<\/strong> The difficulty automatically adjusts to the child&#039;s ability. The system aims for a success rate of approximately 85%, ensuring that children are neither frustrated nor bored. Progress is saved and continued the next time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>User profiles<\/strong> \u2013 Multiple children can use the app with their own profiles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The app is suitable for use in the <strong>Primary school<\/strong>, in the <strong>Special needs school<\/strong> (e.g., in cases of dyscalculia), in the <strong>Tutoring<\/strong> and <strong>at home<\/strong>. The number ranges are flexibly selectable: 0\u201320, 0\u2013100, 0\u20131000, 0\u201310000, or a custom range. A free experimentation mode encourages discovery. Negative numbers and decimals can also be represented and practiced with these number ranges.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The app supports <strong>German, English, French, Italian and Spanish<\/strong>. It contains no advertising, no mandatory in-app purchases, and works offline. Anonymous use is possible. Optionally, anonymized data can be shared for educational research.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here&#039;s a video of the AR number line in action:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Augmented Reality Number Line App by Christian Urff\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/kIytrIxvo60?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A non-AR number line is available here as a web app to try out, but the functionality of this virtual tool is significantly reduced compared to the iPad app:<br><br><a href=\"https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/\">https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Die App Zahlenstrahl (ehemals AR Zahlenstrahl) wurde grundlegend erweitert: Aus der reinen Augmented-Reality-App ist ein umfassendes Lernwerkzeug f\u00fcr den Zahlenstrahl geworden \u2013 mit KI-Tutor, adaptivem Lernsystem und neun verschiedenen \u00dcbungstypen und Experimentierumgebungen mit und ohne AR. Die App basiert auf wissenschaftlichen Erkenntnissen aus den Erprobungen und wird weiter beforscht. Drei Experimentierumgebungen \u2013 Neben dem Augmented [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-375","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":15,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages\/375\/revisions"}],"predecessor-version":[{"id":765,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages\/375\/revisions\/765"}],"wp:attachment":[{"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/media?parent=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}