II.2. Rechengesetze und Rechenvorteile: Unterschied zwischen den Versionen
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+ | Bild:Erklärbär.PNG|30px|left| | ||
+ | rect 0 0 0 0 [[P-Seminar/Mathematik_2010-12]] | ||
+ | default [[P-Seminar/Mathematik_2010-12]] | ||
+ | desc none | ||
+ | </imagemap> | ||
− | <div class=" | + | <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]] | ||
+ | </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> | ||
+ | </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]] | ||
+ | </div> | ||
+ | </div> | ||
+ | </div> | ||
+ | |||
+ | </popup> | ||
+ | |||
+ | |||
+ | |||
+ | <popup name="VI. Multiplikation und Division ganzer Zahlen "> | ||
+ | |||
+ | <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;"> | ||
+ | <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 /> | ||
+ | :: '''(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;"> <big> <colorize> Aufgaben </colorize> </big> | ||
+ | </div> | ||
+ | | ||
+ | |||
+ | <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 | ||
+ | | ||
+ | '''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 } | ||
+ | |||
+ | 45 + (27 - 8) = | ||
+ | { 45 } + { 19 } = { 64 } | ||
+ | |||
+ | 32 - (13 + 8) = | ||
+ | { 32 } - { 21 } = { 11 } | ||
+ | |||
+ | 68 - (36 - 22) = | ||
+ | { 68 } - { 14 } = { 54 } | ||
+ | |||
+ | 82 - (15 + 34) = | ||
+ | { 82 } - { 49 } = { 33 } | ||
+ | |||
+ | { | ||
+ | | type="{}"} | ||
+ | |||
+ | 58 - (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="{}"} | ||
+ | |||
+ | 100 + 56 - (14 + 56) = { 86 } <br /> | ||
+ | |||
+ | 75 - 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> |
Aktuelle Version vom 23. Oktober 2013, 00:03 Uhr
II. Addition und Subtraktion natürlicher Zahlen:
1. Addieren und Subtrahieren - 2. Rechengesetze und Rechenvorteile - 3. Terme
Erklärung
Zum besseren Verständnis kannst du auch noch einmal selbst das Kommutativgesetz erproben. Ziehe die Schieberegler!
Man sieht: a + b = b + a
Und hier kannst du das Assoziativgesetz besser verstehen. Ziehe die Schieberegler!
Man sieht: (a + b) + c = a + (b + c)
- (a + b) + c = a + b + c
Aufgaben
|
II. Addition und Subtraktion natürlicher Zahlen: