GWM5
Inhaltsverzeichnis
- 1 Grundwissen Mathematik 5. Klasse
- 1.1 GWM 5.1 Zahlenmengen
- 1.2 GWM 5.2 Fachbegriffe beim Rechnen
- 1.3 GWM 5.3 Potenzen
- 1.4 GWM 5.4 Rechengesetze und die Bedeutung der Null
- 1.5 GWM 5.5 Ganze Zahlen
- 1.6 GWM 5.6 Rechnen mit ganzen Zahlen: Addition und Subtraktion
- 1.7 GWM 5.7 Rechnen mit ganzen Zahlen: Multiplikation und Division
- 1.8 GWM 5.8 Größen und Maßstab
- 1.9 GWM 5.9 Kreis Vierecke
- 1.10 GWM 5.10 Körper
- 1.11 GWM 5.11 Umfang, Flächeninhalt, Oberflächen
- 1.12 GWM 5.12 Strecken, Geraden, Winkel
- 1.13 GWM 5.13 Koordinatensystem
- 1.14 GWM 5.14 Zählprinzip, Baumdiagramm
- 1.15 Web-Links
Grundwissen Mathematik 5. Klasse
GWM 5.1 Zahlenmengen
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Menge der natürlichen Zahlen mit Null
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Primzahlen: Eine Zahl die genau zwei Teiler hat, heißt Primzahl.
Menge der Primzahlen
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Primfaktorzerlegung: Jede Zahl lässt sich eindeutig in ein Produkt von Primzahlen zerlegen.
Beispiel:
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Menge der Quadratzahlen
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Römische Zahlen:
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werden beim Voranstellen einmal abgezogen.
Beispiel:
GWM 5.2 Fachbegriffe beim Rechnen
Addition:
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Subtraktion:
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Multiplikation:
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Division:
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GWM 5.3 Potenzen
Potenz:
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Beispiel:
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Merke:
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Potenz:
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GWM 5.4 Rechengesetze und die Bedeutung der Null
Reihenfolge: „Klammer vor Potenz vor Punkt vor Strich!“
Was noch nicht zum Rechnen dran ist, schreibt man unverändert an!
Kommutativgesetz:
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Assoziativgesetz:
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Distributivgesetz:
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Null bei der Multiplikation:
Ist ein Faktor Null, so ist auch der Produktwert Null.
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Ist der Produktwert Null, so muss mindestens ein Faktor Null sein!
Aus
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Null bei der Division:
Allgemein:
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Die Division durch Null ist nicht erlaubt!
GWM 5.5 Ganze Zahlen
Zahlengerade:
Betrag: Der Betrag einer Zahl ist ihre Entfernung vom Nullpunkt.
Beispiel:
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Zahlen, die gleichen Betrag aber verschiedene Vorzeichen haben, heißen Gegenzahlen.
Beispiel:
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GWM 5.6 Rechnen mit ganzen Zahlen: Addition und Subtraktion
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GWM 5.7 Rechnen mit ganzen Zahlen: Multiplikation und Division
Regel: Gleiche Vorzeichen ergeben beim Multiplizieren und Dividieren "
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GWM 5.8 Größen und Maßstab
Länge:
Umrechnungszahl
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Fläche:
Umrechnungszahl
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Masse:
Umrechnungszahl
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Zeit:
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Maßstab:
Der Maßstab
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Beispiel:
Eine
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GWM 5.9 Kreis Vierecke
Alle Punkte, die von einem Punkt M aus gleich weit entfernt sind, liegen auf einem Kreis.
GWM 5.10 Körper
GWM 5.11 Umfang, Flächeninhalt, Oberflächen
|
| ||||
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| ||||
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GWM 5.12 Strecken, Geraden, Winkel
Eine Strecke ist die kürzeste Verbindung zweier Punkte.
Die Schreibweise
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Der Abstand von Anfangs- und Endpunkt ist die Länge der Strecke.
Mit der Schreibweise
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IP address: 188.64.62.105 gibt man die Länge der Stecke an.
Verlängert man eine Strecke über einen Punkt bzw. über beide Punkte hinaus, so einsteht eine Halbgerade bzw. Gerade.
Beispiele:
g ist parallel zu h:
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IP address: 188.64.62.105. g ist senkrecht zu l (g ist Lot zu l):
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Der Abstand d eines Punktes P von einer Geraden ist die Länge der senkrechten Verbindungsstrecke.
Zwei Halbgeraden mit demselben Anfangspunkt S teilen die Ebene in zwei Teile. Jeder Teil (mit Rand) heißt Winkel.
Bezeichnungen:
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IP address: 188.64.62.105 oder kleine griechische Buchstaben:
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beta,
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Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 epsilon,
Request served via cp3066 cp3066, Varnish XID 594638678
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 eta,
theta,
Request served via cp3066 cp3066, Varnish XID 630399288
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 my,
Request served via cp3066 cp3066, Varnish XID 605048269
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 sigma,
Request served via cp3066 cp3066, Varnish XID 622873549
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 tau,
phi,
omega
Winkelarten:
- Nullwinkel:
Wikimedia Error If you report this error to the Wikimedia System Administrators, please include the details below.
Request served via cp3066 cp3066, Varnish XID 614220655
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 - spitze Winkel:
Wikimedia Error If you report this error to the Wikimedia System Administrators, please include the details below.
Request served via cp3066 cp3066, Varnish XID 592273640
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 - rechter Winkel:
Wikimedia Error If you report this error to the Wikimedia System Administrators, please include the details below.
Request served via cp3066 cp3066, Varnish XID 592273643
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 - stumpfe Winkel:
Wikimedia Error If you report this error to the Wikimedia System Administrators, please include the details below.
Request served via cp3066 cp3066, Varnish XID 592273645
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 - gestreckter Winkel:
Wikimedia Error If you report this error to the Wikimedia System Administrators, please include the details below.
Request served via cp3066 cp3066, Varnish XID 614776945
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 - überstumpfe Winkel:
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Request served via cp3066 cp3066, Varnish XID 611926287
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105
GWM 5.13 Koordinatensystem
Ein Koordinatensystem besteht aus zwei senkrechten Zahlenstrahlen mit gemeinsamem Nullpunkt. Die x-Achse heißt auch Abszisse, die y-Achse auch Ordinate.
Ein Punkt P(x/y) ist durch seine Koordinaten festgelegt.
Die Ebene wird in vier Quadranten unterteilt.
GWM 5.14 Zählprinzip, Baumdiagramm
Veranschaulichung am Baumdiagramm:
Jeder Pfad durch den Baum steht für eine Kombinationsmöglichkeit.
Hat die erste Verzeigung If you report this error to the Wikimedia System Administrators, please include the details below. Äste und die zweite
Äste, so gibt es
Request served via cp3066 cp3066, Varnish XID 630399291
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 Möglichkeiten.
Beispiel:
Es gibt rote (r), grüne (g) und blaue (b) Schuluniformen. Sie sind als T-Shirt T oder Sweatshirt S erhältlich.
Es gibt
If you report this error to the Wikimedia System Administrators, please include the details below.Request served via cp3066 cp3066, Varnish XID 634128376
Upstream caches: cp3066 int
Error: 429, Too many requests (f061ab2) at Thu, 26 Mar 2026 23:28:16 GMTSensitive client information
IP address: 188.64.62.105 Möglichkeiten, nämlich:
rT, gT, bT, rS, gS, bS.
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