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

@@ Zeile 1: / Zeile 1: @@
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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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+</div>
+</div>
+</popup>
+<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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+</div>
+</div>
+</popup>
+<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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+</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]]
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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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+</div>
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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" />
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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 />
@@ Zeile 17: / Zeile 188: @@
 '''Man sieht: a + b = b + a'''
 <br /><br />
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-<br />
+<br /><br />
-<br />
+'''Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!'''<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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framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" useLocalJar = "true" />
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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 34: / Zeile 204: @@
 </div>
 &nbsp;
-AUFGABEN:
 <quiz display="simple">
 { Forme den Text in eine Rechnung um, rechne es dann aus und gib das Ergebnis ein.
@@ Zeile 41: / Zeile 211: @@
 Die Summe der Zahlen 228 und 454 wird addiert zur Zahl 368
 (228+454)+368=1050
+&nbsp;
-Addiere zu der Differenz aus 450 und 302 die Zahl 169.
+'''a.''' Addiere zu der Differenz aus 450 und 302 die Zahl 169.
 ={ 317 }
-Addiere die Summe der Zahlen  155 und 71 zur Zahl 24.
+'''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 }
@@ Zeile 64: / Zeile 238: @@
 - (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>