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

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+<div class="aussen"><div class="menutag">[[P-Seminar/Mathematik_2010-12|Hauptmenü]]</div>
+;-----------------------------------------------------------------------------------
+<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]]
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+<popup name="II. Addition und Subtraktion natürlicher Zahlen ">
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+<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]]
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+<popup name="III. Die ganzen Zahlen; Addition und Subtraktion ">
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+<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]]
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+</popup>
+<popup name="IV. Geometrische Grundbegriffe ">
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+<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]]
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+<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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+<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]]
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+<popup name="VII. Größen und ihre Einheiten ">
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+<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]]
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+</popup>
+<popup name="VIII. Flächen und Flächenmessung ">
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+<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]]
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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 />
-'''Hier das Kommutativgesetz zum Ausprobieren:'''
+'''Zum besseren Verständnis kannst du auch noch einmal selbst das Kommutativgesetz erproben. Ziehe die Schieberegler!'''<br />
+'''Man sieht: a + b = b + a'''
+<br /><br />
+<ggb_applet width="596" height="258"  version="3.2" ggbBase64="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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 />
+'''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 />
-<ggb_applet height="300" width="550" showMenuBar="false" showResetIcon="true" filename="Kommutativgesetz.ggb" />
+<ggb_applet width="660" height="341"  version="3.2" 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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"/>
 </div>
@@ Zeile 26: / Zeile 203: @@
 |<div style="font: 10pt Verdana; font-weight:bold; padding:5px; border-bottom:1px solid #AAAAAA;">&nbsp;<big> <colorize> Aufgaben </colorize> </big>
 </div>
-Aufgaben
+&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>