Prozesse: Station 6 - Lernpfad zu Matrizen und Wirtschaftliche Verpflechtungen

Didaktische Hinweise
Die folgende Station stellt einen Lernpfad vor, bei dem sich die Schülerinnen und Schüler [br]selbständig und ohne Kenntnisse der Matrizenrechnung vorausgesetzt am Beispiel einer [br]wirtschaftlichen Verflechtung mit der Darstellung mehrstufiger Prozesse auseinanderset-[br]zen. Dabei erarbeiten sie die Bedeutung einer kompakten Formulierung durch Matrizen. [br]Gleichzeitig erkennen die Schülerinnen und Schüler, dass Sie in der Lage sind Rechnun-[br]gen zu relevanten Fragestellungen z.B. Bedarfsermittlung, Kostenermittlung, Preiskalku-[br]lation mit Ihnen bekannten Mitteln zu berechnen. Darauf aufbauend kann anschließend [br]die Matrixdarstellung, das Rechnen mit Matrizen bis hin zum Lösen von Gleichungssys-[br]temen formalisiert werden.
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[/img]
Lernziele
Die Schülerinnen und Schüler[br][list][*]erkennen anhand des Sachverhaltes die Relevanz der Fragestellung.[/*][*]wenden unterschiedliche Darstellungen zur Strukturierung des Sachverhaltes an.[/*][*]diskutieren unterschiedliche Formen der Darstellung.[/*][*]wechseln zwischen den Darstellungsformen Text, Graph, Tabelle und Matrix[/*][*]erarbeiten am Beispiel die Grundlagen für das Rechnen mit Matrizen[br][/*][/list]
Ablauf
[list][*]Zunächst bearbeiten die Schülerinnen und Schüler die Aufgabe 1.[br]Die Ergebnisse werden präsentiert und die Übersichtlichkeit der Darstellungen diskutiert.[/*][*]Danach bearbeiten die Schülerinnen und Schüler in Gruppen die Aufgabe 2 ohne Kenntnisse von Matrizen.[br]Sie können die Fragen 1 - 11 ohne zusätzliche Hilfen beantworten.[br]Zu Frage 12 wird der Tipp gegeben, es mit „Probieren“ zu versuchen.[/*][*]Erst wenn alle Fragen (bis auf 12) beantwortet sind, beginnt die Arbeit mit den Lernpfadkarten.[br]Die Gruppen bearbeiten die Karten in der Reihenfolge der Nummerierung.[br]Jede Gruppe erhält zwei 2 Exemplare jeder Karte.[br][/*][/list]
Hinweis zur Diskussion nach Bearbeitung der Aufgabe 1
Hier nur die Ergebnisse vergleichen, alles andere den Schülern individuell überlassen![br]Danach unten Stehendes diskutieren[br][br]Sinn der Aufgabe: die SchülerIn soll[br][list][*]an Hand des Sachverhaltes die Relevanz der Fragestellung erkennen[/*][*]die Notwendigkeit einer übersichtlichen Darstellung erkennen[/*][*]erkennen, dass die bisherigen Lösungsmöglichkeit bei realen komplexen betrieblichen Vorgängen zeitraubend - unbrauchbar sind[/*][*]einsehen, dass ein auf den PC übertragbares Verfahren notwendig ist[/*][/list][br]weitere Punkte die auch später angesprochen werden können:[br][list][*]Verallgemeinerungen durch Abkürzungen: R,Z, E sind möglich[/*][*]der Sachverhalt kann auf unterschiedliche Weise dargestellt werden ( z.B. grafisch mit Pfeilen, mit Tabellen ...),[/*][*]das Ziel ist eine Darstellung, bei der die Berechnungen auch mit einem Computer möglich sind[br][/*][/list]
Materialien
[list][*]2 Aufgabenblätter mit Lösungen[/*][*]Arbeitsauftrag für die Gruppenarbeit mit den Lernkarten[/*][*]18 Lernkarten[br][/*][/list]
Als GeoGebraBook
[list][*][url=http://ggbtu.be/bXu3Xj25K]Die Aufgaben 1 und 2 als GeoGebraBook[/url][/*][*][url=http://ggbtu.be/bXjz4Wnlb]Die Lösungen zu den Aufgaben als GeoGebraBook[/url][/*][*][url=http://ggbtu.be/blBQLbNah]Die Lernkarten als GeoGebraBook[/url][/*][/list]
Aufgabenblätter und Lösungen
Die Lernkarten
1-18
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

Information: Prozesse: Station 6 - Lernpfad zu Matrizen und Wirtschaftliche Verpflechtungen