Zahlen und Stellenwerte

– ein virtuelles Arbeitsmittel um das dezimale Stellenwertsystem besser zu verstehen.

Mit dieser App können große und kleine Zahlen und die Bedeutung der Stellenwerte interaktiv erforscht werden. Es ist keine klassische Übungsapp, sondern eine Experimentierumgebung.

‎Zahlen und Stellenwerte
‎Zahlen und Stellenwerte
Developer: Christian Urff
Price: 1,99 €

Wenn du verstanden hast, wie Stellenwerte funktionieren, hast du einen der wichtigsten Fähigkeiten für den Mathematikunterricht erworben. Das Verständnis der Zahlen und der Stellenwerte ist die Grundlage für viele weiterführende Inhalte wie nichtzählende Rechenstrategien, halbschriftliche und schriftliche Rechenverfahren, Dezimalzahlen usw.

App „Zahlen und Stellenwerte“ für iOS und iPadOS in Aktion!

Bedienung und Handlungsmöglichkeiten in der App

  • Verändere die einzelnen Stellenwerte durch hoch- und herunterziehen mit dem Finger. Wenn du über die 9 hinausgehst, kannst du beobachten wie die Menge überläuft und 10 in der nächsthöheren Stelle gebündelt werden. Wenn du die Zahl unter 0 bewegst, kannst du sehen, wie von der nächsthöhere Stelle die Menge „entbündelt“ wird.
  • Streiche oder tippe auf die Menge unter einer Zahl, um sie zu verändern.
  • Unten am Bildschirmrand kannst du auswählen, wie die Stellenwertmenge dargestellt werden soll, zum Beispiel als Zahlplättchen, Dienes-Material, Euro-Geld uvm.
  • An der rechten Bildschirmseite gibt es einige Knöpfe, mit denen du Aktivitäten auslösen kannst:
    • Mit dem Lautsprecher kannst du dir die Zahl vorlesen lassen.
    • Mit der Sprechblase mit Haken kannst du die dargestellte Zahl vorlesen und überprüfen, ob du richtig vorgelesen hast.
    • Mit dem Symbol zum Auseinanderziehen der Zahlen wird beispielsweise die Zahl 142 aus den Zahlen 100, 40 und 2 dargestellt.
    • Mit den Würfeln kannst du eine zufällige neue Zahl würfeln, die du dann beispielsweise danach vorlesen oder verändern kannst.
    • Mit der Sprechblase mit drei Punkten kannst du selbst eine neue Zahl einsprechen. Die Zahl wird dann direkt beim Sprechen (mit kleiner Verzögerung) angezeigt. Bitte achte auch hier darauf, laut und deutlich zu sprechen und Hintergrundgeräusche zu vermeiden.
    • Mit dem Fragezeichen werden einzelne Stellenwerte abgedeckt, die Zahl wird vorgelesen und du musst die passenden Zahlen eintragen.

Dann gibt es noch weitere Anpassungsmöglichkeiten in der App:

  • mit den grauen Pfeilen auf der linken Seite der Zahl kannst du zusätzliche Stellen ein- oder ausblenden und so den Zahlenraum verändern. Du kannst Zahlen bis zu 100 Billionen darstellen und erkunden.
  • mit dem grauen Pfeil rechts neben den Einern kannst du das Komma verschieben und so auch Dezimalzahlen / Kommazahlen darstellen.
  • Du kannst die Farben der Zahlziffern verändern, indem du bei den Einern, Zehnern oder Hundertern auf die Bezeichnung „E“, „Z“ bzw. „H“ tippst und eine neue Farbe auswählst.
  • Wenn du bei einer Zahl von links nach rechts streichst, wird die Zahl abgedeckt. Wenn du in das Abdeckfeld tippst, kannst du eine Lösung eingeben und du bekommst eine Rückmeldung, ob deine Lösung richtig war.
  • Zudem kannst du in den globalen Einstellungen einige Darstellungen individuell vorkonfigurieren.

Beispielhafte Aktivitäten

Damit mit der Experimentierumgebung das Zahl- und Stellenwertverständnis effektiv gefördert wird, bedarf es passender Aufgabenstellungen, die zum Erkunden und Nachdenken von Zusammenhängen herausfordern wie beispielsweise:

  • Zahlendiktat: Stelle die Zahl 3469 dar, …
  • Erhöhe die Einer um immer um eins mehr. Beschreibe was passiert, wenn du die 9 um eins erhöhst?
  • Stelle die Zahl 340 dar. Was passiert, wenn du die Einer um eins verringerst?
  • Warum funktioniert dies nicht, wenn du die Zahl 0 um eins verringern möchtest?
  • Stelle die Zahl 5216 dar. Klappe die Zahlen mit dem Ausklappen-Knopf auf. Aus welchen Zahlen setzt sich die Zahl zusammen (5000 + 200 + 10 + 6). Überlege, aus welchen Zahlen sich dann die Zahl 5316 zusammensetzt.
  • Lass dir eine Zahl vorlesen. Nun verändere eine Stelle. Kannst du die Zahl richtig vorlesen? Überprüfe mit der Spracheingabe-Funktion, ob du die richtige Zahl gelesen hast.
  • Decke eine Stelle ab (indem du mit dem Finger von links nach rechts wischst). Verändere nun eine andere Stelle so, dass die abgedeckte Stelle um Eins (Vier) höher (niedriger) ist. Erkläre, wie dies funktioniert.
    Zusatzfrage: Warum kannst du nicht mit der Stelle nächsthöheren Stelle die abgedeckte Zahl verändern?
  • Tippe auf den Fragezeichen-Knopf und löse einige Aufgaben. Zeige danach dem Lehrer, wie viele Aufgaben du gerechnet hast (die Anzahl der Aufgaben wird mitgezählt und lässt sich durch Klick auf die Zahl zurücksetzen).
  • Warum verschwindet bei der Zahl 0453 die vordere Null? Warum verändert sich dadurch nichts an der Zahl? Warum bleibt die Null bei der Zahl 204 oder 240 stehen?
  • Überlege dir eine Erklärung anhand der App, warum die Zahl 567 und die Zahl 765 unterschiedlich sind obwohl die gleichen Zahlen dastehen.
  • Schriftliches Addieren und Subtrahieren: Rechne die Aufgabe 5498 – 2345 schriftlich aus und stelle jeden Schritt in der App dar. Was passiert bei bei der Aufgabe 5328 – 3619? Überlege anhand der App, warum du bei manchen Stellen Überträge notieren musst.

Viel Spaß beim Ausprobieren und Lernen mit der App!

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