II.2. Rechengesetze und Rechenvorteile: Unterschied zwischen den Versionen

@@ Zeile 1: / Zeile 1: @@
-<u>Kommutativgesetz der Addition</u>
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-Für alle natürliche Zahlen a,b gilt:
+<div class="aussen"><div class="menutag">[[P-Seminar/Mathematik_2010-12|Hauptmenü]]</div>
-<br /> a+b=<strong> b+a </strong>
+;-----------------------------------------------------------------------------------
+<popup name="I.Natürliche Zahlen ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''I.Natürliche Zahlen'''</div>
+*[[P-Seminar/Mathematik_2010-12/I.1._Zählen_und_Ordnen|Zählen und Ordnen]]
+*[[P-Seminar/Mathematik_2010-12/I.2._Veranschaulichung_von_Zahlen|Veranschaulichung von Zahlen]]
+*[[P-Seminar/Mathematik_2010-12/I.3._Das_Dezimalsystem|Das Dezimalsystem]]
+*[[P-Seminar/Mathematik_2010-12/I.4._Römische_Zahlen|Römische Zahlen]]
+*[[P-Seminar/Mathematik_2010-12/I.5._Zahlenmengen|Zahlenmengen]]
+*[[P-Seminar/Mathematik_2010-12/I.6._Runden|Runden]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="II. Addition und Subtraktion natürlicher Zahlen ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''II. Addition und Subtraktion natürlicher Zahlen'''</div>
+*[[P-Seminar/Mathematik_2010-12/II.1._Addieren_und_Subtrahieren|1.Addieren und Subtrahieren]]
+*[[P-Seminar/Mathematik_2010-12/II.2._Rechengesetze_und_Rechenvorteile|2.Rechengesetze und Rechenvorteile]]
+*[[P-Seminar/Mathematik_2010-12/II.3._Terme|3.Terme]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="III. Die ganzen Zahlen; Addition und Subtraktion ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''III. Die ganzen Zahlen; Addition und Subtraktion'''</div>
+*[[P-Seminar/Mathematik_2010-12/III.1._Negative_Zahlen|1.Negative Zahlen]]
+*[[P-Seminar/Mathematik_2010-12/III.2._Vorzeichenschreibweise|2.Vorzeichenschreibweise]]
+*[[P-Seminar/Mathematik_2010-12/III.3._Anordnung_und_Betrag|3.Anordnung und Betrag]]
+*[[P-Seminar/Mathematik_2010-12/III.4._Addieren|4.Addieren]]
+*[[P-Seminar/Mathematik_2010-12/III.5._Subtrahieren|5.Subtrahieren]]
+*[[P-Seminar/Mathematik_2010-12/III.6._Rechnen_mit_Summen_und_Differenzen|6.Rechnen mit Summen und Differenzen]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="IV. Geometrische Grundbegriffe ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''IV. Geometrische Grundbegriffe'''</div>
+*[[P-Seminar/Mathematik_2010-12/IV.1._Geometrische_Körper|1. Geometrische Körper]]
+*[[P-Seminar/Mathematik_2010-12/IV.2._Geraden|2. Geraden]]
+*[[P-Seminar/Mathematik_2010-12/IV.3._Abstände|3. Abstände]]
+*[[P-Seminar/Mathematik_2010-12/IV.4._Parallelogramme_-_Umfang|4. Parallelogramme - Umfang]]
+*[[P-Seminar/Mathematik_2010-12/IV.5._Kreise|5. Kreise]]
+*[[P-Seminar/Mathematik_2010-12/IV.6._Winkel|6. Winkel]]
+*[[P-Seminar/Mathematik_2010-12/IV.7._Achsensymmetrie|7. Achsensymmetrie]]
+*[[P-Seminar/Mathematik_2010-12/IV.8._Netze_geometrischer_Körper|8. Netze geometrischer Körper]]
+*[[P-Seminar/Mathematik_2010-12/IV.9._Schrägbilder|9. Schrägbilder]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="V. Multiplikation und Division natürlicher Zahlen ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''V. Multiplikation und Division natürlicher Zahlen'''</div>
+*[[P-Seminar/Mathematik_2010-12/V.1._Multiplizieren_und_Dividieren|1. Multiplizieren und Dividieren]]
+*[[P-Seminar/Mathematik_2010-12/V.2._Rechnen_mit_Null_und_Eins|2. Rechnen mit Null und Eins]]
+*[[P-Seminar/Mathematik_2010-12/V.3._Schriftliches_Multiplizieren_und_Dividieren|3. Schriftliches Multiplizieren und Dividieren]]
+*[[P-Seminar/Mathematik_2010-12/V.4._Verbindung_der_Grundrechenarten|4. Verbindung der Grundrechenarten]]
+*[[P-Seminar/Mathematik_2010-12/V.5._Rechengesetze_und_Rechenvorteile|5. Rechengesetze und Rechenvorteile]]
+*[[P-Seminar/Mathematik_2010-12/V.6._Potenzieren|6. Potenzieren]]
+*[[P-Seminar/Mathematik_2010-12/V.7._Faktorisieren_von_Zahlen|7. Faktorisieren von Zahlen]]
+*[[P-Seminar/Mathematik_2010-12/V.8._Terme|8. Terme]]
+*[[P-Seminar/Mathematik_2010-12/V.9._Abzählen_am_Baumdiagramm|9. Abzählen am Baumdiagramm]]
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+</popup>
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+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''VI. Multiplikation und Division ganzer Zahlen'''</div>
+*[[P-Seminar/Mathematik 2010-12/VI.1. Multiplikation | 1. Multiplikation]]
+*[[P-Seminar/Mathematik 2010-12/VI.2 Division | 2. Division]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="VII. Größen und ihre Einheiten ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''VII. Größen und ihre Einheiten'''</div>
+*[[P-Seminar/Mathematik_2010-12/VII.1._Messen|1. Messen]]
+*[[P-Seminar/Mathematik_2010-12/VII.2._Längen|2. Längen]]
+*[[P-Seminar/Mathematik_2010-12/VII.3._Rechnen_mit_Größen|3. Rechnen mit Größen]]
+*[[P-Seminar/Mathematik_2010-12/VII.4._Maßstab|4. Maßstab]]
+*[[P-Seminar/Mathematik_2010-12/VII.5._Massen|5. Massen]]
+*[[P-Seminar/Mathematik_2010-12/VII.6._Geld|6. Geld]]
+*[[P-Seminar/Mathematik_2010-12/VII.7._Zeit|7. Zeit]]
+</div>
+</div>
+</div>
+</popup>
+<popup name="VIII. Flächen und Flächenmessung ">
+<div class="menuebox"><div class="menue">
+<div class="aussen"><div class="menutag">'''VIII. Flächen und Flächenmessung'''</div>
+*[[P-Seminar/Mathematik_2010-12/VIII.1._Flächeninhalte_vergleichen_und_messen|1. Flächeninhalte vergleichen und messen]]
+*[[P-Seminar/Mathematik_2010-12/VIII.2._Flächeneinheiten|2. Flächeneinheiten]]
+*[[P-Seminar/Mathematik_2010-12/VIII.3._Flächeninhalt_des_Rechtecks|3. Flächeninhalt des Rechtecks]]
+*[[P-Seminar/Mathematik_2010-12/VIII.4._Flächeninhalte_verschiedener_Figuren|4. Flächeninhalte verschiedener Figuren]]
+*[[P-Seminar/Mathematik_2010-12/VIII.5._Oberflächeninhalt_des_Quaders|5. Oberflächeninhalt des Quaders]]
+</div>
+</div>
+</div>
+</popup>
+<br><br><br><br>
+</div>
+</div>
+</div>
+<br>
+<br>
+<div style="font: 10pt Comic Sans MS; padding:5px; border-bottom:1px solid #AAAAAA;">&nbsp;
+<div style="margin:0; margin-right:4px; margin-left:0px; border:1px solid  #6C7B8B; padding: 0em 0em 0em 1em; background-color:#FFB90F;">
+''II. Addition und Subtraktion natürlicher Zahlen:''
+[[P-Seminar/Mathematik 2010-12/II.1. Addieren und Subtrahieren|1. Addieren und Subtrahieren]] - [[P-Seminar/Mathematik 2010-12/II.2. Rechengesetze und Rechenvorteile|2. Rechengesetze und Rechenvorteile]] - [[P-Seminar/Mathematik 2010-12/II.3. Terme| 3. Terme]]</div>
+<br />
+<div style="border: 5px solid #1D17AE; background-color:#FFEC8B; padding:7px;">
+<big> <colorize> Erklärung </colorize> </big>
+<br />
+<br />
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framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" useLocalJar = "true" />
+<br />
+<br />
+'''Zum besseren Verständnis kannst du auch noch einmal selbst das Kommutativgesetz erproben. Ziehe die Schieberegler!'''<br />
+'''Man sieht: a + b = b + a'''
+<br /><br />
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+<br /><br />
+'''Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!'''<br />
+'''Man sieht: (a + b) + c = a + (b + c)'''<br />
+::&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''(a + b) + c = a + b + c'''
+<br />
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+</div>
+{| border="0" cellpadding="5" cellspacing="2" style="border-left: 15px solid {{{RandLinks|#049128}}}; border-top: 5px solid {{{RandOben|#049128}}}; border-bottom: 5px solid {{{RandUnten|#049128}}}; border-right: 5px solid {{{RandRechts|#049128}}}; margin-bottom: 0.4em; margin-left: auto; margin-right: auto; width: {{{Breite|100%}}}; background-color: {{{Hintergrund|#FFFBE9}}}"
+|-
+|<div style="font: 10pt Verdana; font-weight:bold; padding:5px; border-bottom:1px solid #AAAAAA;">&nbsp;<big> <colorize> Aufgaben </colorize> </big>
+</div>
+&nbsp;
+<quiz display="simple">
+{ Forme den Text in eine Rechnung um, rechne es dann aus und gib das Ergebnis ein.
+| type="{}"}
+'''Beispiel'''
+Die Summe der Zahlen 228 und 454 wird addiert zur Zahl 368
+(228+454)+368=1050
+&nbsp;
+'''a.''' Addiere zu der Differenz aus 450 und 302 die Zahl 169.
+={ 317 }
+'''b.''' Addiere die Summe der Zahlen  155 und 71 zur Zahl 24.
+={ 250 }
+{ Achte auf die richtige Reihenfolge!
+| type="{}"}
+'''Beispiel'''
+(5 + 5) - 2 = 10 - 2 = 8<br /><br />
+'''Aufgaben'''
+(13 + 17) + 25 =
+{ 30 } + { 25 } = { 55 }
++ (27 - 8) =
+{ 45 } + { 19 } = { 64 }
+- (13 + 8) =
+{ 32 } - { 21 } = { 11 }
+- (36 - 22) =
+{ 68 } - { 14 } =  { 54 }
+- (15 + 34) =
+{ 82 } - { 49 } = { 33 }
+{
+| type="{}"}
+- (30 + 18) =
+{ 58 } - { 48 } = { 10 }
+(58 - 30) + 18 =
+{ 28 } + { 18 } = { 46 }
+(82 - 15) + 34 =
+{ 67 } + { 34 } = { 101 }
+(82 + 15) - 34 =
+{ 97 } - { 34 } = { 63 }
+(80 - 32) + (42 + 60) =
+{ 48 } + { 102 } = { 150 }
+{ Rechne geschickt.
+| type="{}"}
++ 56 - (14 + 56) = { 86 } <br />
+- 44 - ( 15 - 14 - 30) = { 60 }
+</quiz>
+|}<noinclude>
+<div style="margin:0; margin-right:4px; margin-left:0px; border:1px solid  #6C7B8B; padding: 0em 0em 0em 1em; background-color:#FFB90F;">
+''II. Addition und Subtraktion natürlicher Zahlen:''
+<br />
+[[P-Seminar/Mathematik 2010-12/II.1. Addieren und Subtrahieren|1. Addieren und Subtrahieren]] - [[P-Seminar/Mathematik 2010-12/II.2. Rechengesetze und Rechenvorteile|2. Rechengesetze und Rechenvorteile]] - [[P-Seminar/Mathematik 2010-12/II.3. Terme| 3. Terme]]</div></div>