{"id":375,"date":"2024-10-05T08:08:39","date_gmt":"2024-10-05T08:08:39","guid":{"rendered":"https:\/\/urff.app\/?page_id=375"},"modified":"2026-09-05T17:01:06","modified_gmt":"2026-09-05T17:01:06","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<div class=\"urff-appbox\" style=\"display:flex;flex-wrap:wrap;align-items:center;gap:1rem;padding:1rem 1.25rem;margin:1.5rem 0;border:1px solid rgba(0,0,0,.12);border-radius:18px;background:rgba(0,0,0,.035)\">\n<a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"flex:0 0 auto;line-height:0\"><img decoding=\"async\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/09\/appicon-zahlenstrahl-6473689075.jpg\" alt=\"App-Icon Zahlenstrahl\" width=\"96\" height=\"96\" loading=\"lazy\" style=\"width:96px;height:96px;border-radius:22%;box-shadow:0 1px 4px rgba(0,0,0,.15)\"><\/a>\n<div style=\"flex:1 1 12rem;min-width:0\">\n<div style=\"font-weight:700;font-size:1.15em;line-height:1.3\"><a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"text-decoration:none\">number line<\/a><\/div>\n<div style=\"font-size:.9em;opacity:.75;margin-top:.15em\">Christian Urff \u00b7 iPad, iPhone<\/div>\n<\/div>\n<a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"flex:0 0 auto;display:inline-block;padding:.55em 1.1em;border-radius:999px;background:#0071e3;color:#fff;font-weight:600;font-size:.95em;text-decoration:none;white-space:nowrap\">Download from the App Store<\/a>\n<\/div>\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> \u2013 Neben dem Augmented-Reality-Modus gibt es einen mit Touch-Bedienung und Zeichenwerkzeugen sowie einen kombinierten Modus, der AR- und 2D-Ansicht synchron nebeneinander zeigt. In den Experimentierumgebungen kann mit den unterschiedlichen Zahlenstrahldarstellungen frei gearbeitet werden \u2013 hier sind keine Aufgabenstellungen enthalten.<\/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> gibt kindgerechte, fachdidaktisch fundierte Hinweise bei Schwierigkeiten, erkennt Fehlermuster und erkl\u00e4rt geduldig. Er spricht Aufgaben und R\u00fcckmeldungen vor. Er ben\u00f6tigt f\u00fcr die KI-gest\u00fctzten Funktionen eine Internetverbindung (ohne zus\u00e4tzliche Kosten), aber funktioniert auch offline mit weniger fundierten R\u00fcckmeldungen.<\/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>. Sie enth\u00e4lt keine Werbung, keine In-App-K\u00e4ufe und funktioniert offline. Die Nutzung ist anonym m\u00f6glich. Optional k\u00f6nnen anonymisierte Daten f\u00fcr die Bildungsforschung freigegeben werden.<\/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\">Einen Zahlenstrahl ohne AR gibt es hier als Webapp zum Ausprobieren, der Funktionsumfang des virtuellen Arbeitsmittels ist aber deutlich reduziert gegen\u00fcber der iPad-App:<br><br><a href=\"https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/\">https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Zahlenstrahl Christian Urff \u00b7 iPad, iPhone Im App Store laden 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 [&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":20,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages\/375\/revisions"}],"predecessor-version":[{"id":1352,"href":"https:\/\/urff.app\/en\/wp-json\/wp\/v2\/pages\/375\/revisions\/1352"}],"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}]}}