Entdecken3 (Multiplikation mit mehrstelligen Zahlen)

DB6114

$\textsf{\vphantom{Äg}Neue Rechnung}$

$\textsf{\vphantom{Äg}Zurück}$

$\textsf{\vphantom{Äg}Weiter}$

\textsf{Die beiden Produkte werden addiert.}

$\textsf{Los geht's!}$

\textsf{Hier wird eine schriftliche Multiplikation ausgeführt.
\\vphantom{Äg}Beobachte die einzelnen Schritte.}

|
|
|
|
|
|
|
|
|
|

questionCount = 1 (slider from 0 to 120, step 1)
randomNosB2 = Join(Sequence[Shuffle[{1, 2, 3, 4, 5, 6, 7, 8, 9}], m, 1, 9])
randomNosA3 = Join(Sequence[Shuffle[{1, 2, 3, 4, 5, 6, 7, 8, 9}], m, 1, 9])
randomNosA2 = Join(Sequence[Shuffle[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}], m, 1, 9])
randomNosB1 = Join({{Random[1, 9]}, Join[Sequence[Shuffle[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}], m, 1, 9]]})
b1: randomNosB1(Mod[questionCount, 70] + 1)
randomNosA1 = Join({{Random[1, 9]}, Join[Sequence[Shuffle[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}], m, 1, 9]]})
a1: randomNosA1(Mod[questionCount, 70] + 1)
s21: (a1 * b1)
ü21: floor(s21 / 10)
a2: randomNosA2(Mod[questionCount, 70] + 1)
s22a: (a2 * b1)
s22b: s22a + ü21
ü22: floor(s22b / 10)
d2: s22b - (10 * ü22)
a3: randomNosA3(Mod[questionCount, 70] + 1)
s23a: (a3 * b1)
s23b: s23a + ü22
d32: floor(s23b / 10)
d31: s23b - (10 * d32)
b2: randomNosB2(Mod[questionCount, 70] + 1)
s11: (a1 * b2)
ü11: floor(s11 / 10)
c1: s11 - (10 * ü11)
t1: c1 + d2
tm1: floor(t1 / 10)
s12a: (a2 * b2)
s12b: s12a + ü11
ü12b: floor(s12b / 10)
c2b: s12b - (10 * ü12b)
s13a: (a3 * b2)
s13b: s13a + ü12b
c32: floor(s13b / 10)
c31: s13b - (10 * c32)
numA: (100 * a3) + (10 * a2) + a1
numB: (10 * b2) + b1
multy: (numB * numA)
step = 0 (slider from 0 to 11, step 1)
S11 = (4, 4.5)
S12: (-4, 4.5)
f = Segment(S11, S12)
A1: (-0.1643, 6.7)
A2: (1.60433, 6.7)
k2 = Semicircle(A1, A2)
B1: (-1.27788, 6.7)
k3 = Semicircle(B1, A2)
C1: (-2.3587, 6.7)
k4 = Semicircle(C1, A2)
A3: (2.68516, 6.7)
text2: "" + (LaTeX[a1]) + "\cdot" + (LaTeX[b2]) + "=" + (LaTeX[s11]) + ""
text3: "" + (LaTeX[a2]) + "\cdot" + (LaTeX[b2]) + "=" + (LaTeX[s12a]) + ""
text4: "" + (LaTeX[a3]) + "\cdot" + (LaTeX[b2]) + "=" + (LaTeX[s13a]) + ""
text5: "" + (LaTeX[a1]) + "\cdot" + (LaTeX[b1]) + "=" + (LaTeX[s21]) + ""
text7: "" + (LaTeX[a3]) + "\cdot" + (LaTeX[b1]) + "=" + (LaTeX[s23a]) + ""
text6: "" + (LaTeX[a2]) + "\cdot" + (LaTeX[b1]) + "=" + (LaTeX[s22a]) + ""
S21: (1.60433, 0)
S22: (-3.99632, -0)
i = Segment(S21, S22)
d1: s21 - (10 * ü21)
tl1: t1 - (10 * tm1)
t2: c2b + d31 + tm1
tm2: floor(t2 / 10)
tl2: t2 - (10 * tm2)
t3: c31 + d32 + tm2
tm3: floor(t3 / 10)
tl3: t3 - (10 * tm3)
t4: c32 + tm3
AAA = (6.4, 6.5)
ü12a: floor(s12a / 10)
c2a: s12a - (10 * ü12a)
k7 = Semicircle(A1, A3)
k8 = Semicircle(B1, A3)
k9 = Semicircle(C1, A3)
czehner: "" + (If[step ∈ {3, 8}, color, "000000"]) + ""
ctausender: "" + (If[step ∈ {4, 10}, color, "000000"]) + ""
chunderter: "" + (If[step ∈ {4, 9}, color, "000000"]) + ""
ceiner: "" + (If[step ∈ {2, 7}, color, "000000"]) + ""
Text6: "\text{Nun wird die \textcolor{" + (LaTeX[ceiner]) + "}{Einerstelle} des 2. Faktors}\\\\\text{mit dem 1. Faktor multipliziert.} "
textd4: "\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[d32]) + "}"
textd1: "\textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[d1]) + "}"
textd2: "\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[d2]) + "}"
textd3: "\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[d31]) + "}"
Text11b: "\text{Das Ergebnis lautet}  \textcolor{}{" + (LaTeX[tl3]) + "~" + (LaTeX[tl2]) + "" + (LaTeX[tl1]) + "" + (LaTeX[d1]) + "}."
textc2: "\textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[c2b]) + "}"
textc4: "\textcolor{" + (LaTeX[If[step ∈ {4}, color, "000000"]]) + "}{" + (LaTeX[c32]) + "}"
textc3: "\textcolor{" + (LaTeX[If[step ∈ {4}, color, "000000"]]) + "}{" + (LaTeX[c31]) + "}"
textc0: "\textcolor{" + (LaTeX[If[step ∈ {5}, color, "000000"]]) + "}0"
textc1: "\textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[c1]) + "}"
textü11: "\textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[ü11]) + "}"
textü12: "\textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[ü12b]) + "}"
textü21: "\textcolor{" + (LaTeX[If[step ∈ {7}, color, "000000"]]) + "}{" + (LaTeX[ü21]) + "}"
textü22: "\textcolor{" + (LaTeX[If[step ∈ {8}, color, "000000"]]) + "}{" + (LaTeX[ü22]) + "}"
text22: "\textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[d1]) + "}"
text23: "\textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[tl1]) + "}"
text24: "\textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[tl2]) + "}"
text25: "\textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[tl3]) + "}"
text26: "\textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[t4]) + "}"
step2 = 1
showPart1 = false
showÜbertrag: step < 10
Text0: "\textsf{" + (LaTeX[a3]) + " " + (LaTeX[a2]) + " " + (LaTeX[a1]) + " \cdot \textcolor{" + (LaTeX[If[step ∈ {1}, color, If[showPart1, "#b00020", "000000"]]]) + "}" + (LaTeX[b2]) + " \textcolor{" + (LaTeX[If[step ∈ {6}, color, If[showPart1, color, "000000"]]]) + "}{" + (LaTeX[b1]) + "}"
Text5: "\textsf{\vphantom{Äg}Da eigentlich mit " + (LaTeX[(b2 * 10)]) + " multipliziert wurde, wird
\\\vphantom{Äg}in der ersten Zeile eine \textcolor{" + (LaTeX[color]) + "}{0} angehängt.
\\\\\vphantom{Äg}Die 0 steht für die Einerstelle \textcolor{" + (LaTeX[color]) + "}{(E)}.}"
Text11: "\text{Das Ergebnis lautet}  \textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[t4]) + "" + (LaTeX[tl3]) + "~" + (LaTeX[tl2]) + "" + (LaTeX[tl1]) + "" + (LaTeX[d1]) + "}."
text43: "" + (LaTeX[s23a]) + "+" + (LaTeX[ü22]) + "=" + (LaTeX[d31]) + " \rightarrow " + (LaTeX[d31]) + "\text{ anschreiben}"
Text1: "\textsf{Zuerst wird die \textcolor{" + (LaTeX[If[step ∈ {1}, color, "000000"]]) + "}{Zehnerstelle}\\\\des 2. Faktors mit dem ersten\\\\Faktor multipliziert. }"
Text3: "\textsf{\vphantom{Äg}Die Zahl " + (LaTeX[b2]) + "" + (LaTeX[b1]) + " hat \textcolor{#b00020}{" + (LaTeX[b2]) + "Z} und \textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[b1]) + "E}.
\\\vphantom{Ä}Es gilt also " + (LaTeX[b2]) + "" + (LaTeX[b1]) + " = \textcolor{#b00020}{" + (LaTeX[(b2 * 10)]) + "} + \textcolor{" + (LaTeX[color]) + "}{" + (LaTeX[b1]) + "}.}"
Text2a: "\textsf{" + (LaTeX[a1]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a1 * b2)]) + "\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[(a1 * b2)]) + "Z} = \textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[ü11]) + "H} \textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[c1]) + "Z}\\\\\textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[c1]) + "Z} anschreiben und \textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[ü11]) + "H} (Übertrag) weiter"
Text3d: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a2 * b2)]) + "\\\\" + (LaTeX[(a2 * b2)]) + "H + " + (LaTeX[ü11]) + "H =  " + (LaTeX[(a2 * b2) + ü11]) + "H\\\\
\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[(a2 * b2) + ü11]) + "H} anschreiben\\\\\\
Weil " + (LaTeX[(a2 * b2) + ü11]) + " kleiner als 10 ist,\\\\schreibst du keinen Übertrag."
Text7a: "\textsf{" + (LaTeX[a1]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a1 * b1)]) + "\\\\\textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[(a1 * b1)]) + "E} = \textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[ü21]) + "Z} \textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[d1]) + "E}
\\\\\textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[d1]) + "E} anschreiben und \textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[ü21]) + "Z} (Übertrag) weiter\\"
Text8a: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a2 * b1)]) + "\\\\" + (LaTeX[(a2 * b1)]) + "Z + " + (LaTeX[ü21]) + "Z = " + (LaTeX[(a2 * b1) + ü21]) + "Z\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[ü22]) + "" + (LaTeX[d2]) + "Z} = \textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[ü22]) + "H} \textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[d2]) + "Z}
\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[d2]) + "Z} anschreiben und \textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[ü22]) + "H} (Übertrag) weiter}"
Text9b: "\textsf{" + (LaTeX[a3]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a3 * b1)]) + "\\\\" + (LaTeX[s23a]) + "H + " + (LaTeX[ü22]) + "H = " + (LaTeX[d32]) + "" + (LaTeX[d31]) + "H\\\\\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[d32]) + "" + (LaTeX[d31]) + "H} anschreiben"
Text3a: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a2 * b2)]) + "\\\\" + (LaTeX[s12a]) + "H + " + (LaTeX[ü11]) + "H = " + (LaTeX[ü12b]) + "" + (LaTeX[c2b]) + "H\\\\
\textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[ü12b]) + "" + (LaTeX[c2b]) + "H} = \textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[ü12b]) + "T} 
\textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[c2b]) + "H}\\\\

\textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[c2b]) + "H} anschreiben und \textcolor{" + (LaTeX[If[step ∈ {3}, color, "000000"]]) + "}{" + (LaTeX[ü12b]) + "T} (Übertrag) weiter"
Text4a: "\textsf{" + (LaTeX[a3]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a3 * b2)]) + "\\\\" + (LaTeX[s13a]) + "T + " + (LaTeX[ü12b]) + "T = " + (LaTeX[s13a + ü12b]) + "T \\\\\textcolor{" + (LaTeX[ctausender]) + "}{" + (LaTeX[c32]) + "" + (LaTeX[c31]) + "T} anschreiben"
Text7b: "\textsf{" + (LaTeX[a1]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a1 * b1)]) + "\\\\\\\textcolor{" + (LaTeX[ceiner]) + "}{" + (LaTeX[(a1 * b1)]) + "E} anschreiben \\\\\\
Weil " + (LaTeX[d1]) + " kleiner als 10 ist,\\\\
schreibst du keinen Übertrag."
Text8c: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a2 * b1)]) + "\\\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[(a2 * b1)]) + "Z} anschreiben \\\\\\
Weil " + (LaTeX[d2]) + " kleiner als 10 ist,\\\\
schreibst du keinen Übertrag."
Text9a: "\textsf{" + (LaTeX[a3]) + " \cdot " + (LaTeX[b1]) + " =  " + (LaTeX[(a3 * b1)]) + "\\\\\\\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[(a3 * b1)]) + "H} anschreiben \\\\\\"
Text2b: "\textsf{" + (LaTeX[a1]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a1 * b2)]) + "\\\\\\\textcolor{" + (LaTeX[If[step ∈ {2}, color, "000000"]]) + "}{" + (LaTeX[(a1 * b2)]) + "Z} anschreiben \\\\\\
Weil " + (LaTeX[(a1 * b2)]) + " kleiner als 10 ist,\\\\
schreibst du keinen Übertrag."
Text3b: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a2 * b2)]) + "\\\\\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[(a2 * b2)]) + "H} = \textcolor{" + (LaTeX[ctausender]) + "}{" + (LaTeX[ü12b]) + "T} \textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[c2b]) + "H}\\\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[c2b]) + "H} anschreiben und \textcolor{" + (LaTeX[ctausender]) + "}{" + (LaTeX[ü12b]) + "T} (Übertrag) weiter}"
Text4b: "\textsf{" + (LaTeX[a3]) + " \cdot " + (LaTeX[b2]) + " = " + (LaTeX[(a3 * b2)]) + "\\\\\textcolor{" + (LaTeX[ctausender]) + "}{" + (LaTeX[s13a]) + "T} anschreiben"
Text8d: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a2 * b1)]) + "\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[(a2 * b1)]) + "Z} = \textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[ü22]) + "H} \textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[d2]) + "Z}\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[d2]) + "Z} anschreiben und \textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[ü22]) + "H} (Übertrag) weiter"
Text3c: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b2]) + " =  " + (LaTeX[(a2 * b2)]) + "\\\\\\\textcolor{" + (LaTeX[chunderter]) + "}{" + (LaTeX[(a2 * b2)]) + "H} anschreiben\\\\\\
Weil " + (LaTeX[(a2 * b2)]) + " kleiner als 10 ist,\\\\
schreibst du keinen Übertrag.}"
Text8b: "\textsf{" + (LaTeX[a2]) + " \cdot " + (LaTeX[b1]) + " = " + (LaTeX[(a2 * b1)]) + "\\\\" + (LaTeX[(a2 * b1)]) + "Z + " + (LaTeX[ü21]) + "Z = " + (LaTeX[(a2 * b1) + ü21]) + "Z\\\\\textcolor{" + (LaTeX[czehner]) + "}{" + (LaTeX[s22b]) + "Z} anschreiben\\\\\\
Weil " + (LaTeX[s22b]) + " kleiner als 10 ist,\\\\schreibst du keinen Übertrag."

Tool: SpeechBubble
SpeechBubble[ <Point>, <Point TextCorner1>, <Point TextCorner2>, <Point TextCorner3> ]
Input: A, B, C, D
Output: SB1

C: (4.94, 3.37)
D: (4.94, 3.92)
height: y(D) - y(C)
B: (2.45, 3.37)
width: x(C) - x(B)
E1: B + (0, height / 2)
E2: E1 + (width, 0)
E3: (0.5 * (E1 + E2)) + (0, (1.1 * height))
b: y(E3) - y(E2)
a: sqrt(width^(2) / 4 + b^(2))
M: (0.5 * (E1 + E2))
SB1 = If(x(A) < x(M), {PolyLine[M + ((a * cos((6 / 5 * pi))), (b * sin((6 / 5 * pi)))), A, M + ((a * cos((2 / 3 * pi))), ((-b) * sin((2 / 3 * pi))))], CurveCartesian[M + ((a * cos(t)), ((-b) * sin(t))), t, 0, (2 / 3 * pi)], CurveCartesian[M + ((a * cos(t)), (b * sin(t))), t, 0, (6 * pi / 5)]}, {PolyLine[M + ((a * cos((5 / 3 * pi))), (b * sin((5 / 3 * pi)))), A, M + ((a * cos((1 / 5 * pi))), ((-b) * sin((1 / 5 * pi))))], CurveCartesian[M + ((a * cos(t)), ((-b) * sin(t))), t, 0, (1 / 5 * pi)], CurveCartesian[M + ((a * cos(t)), (b * sin(t))), t, 0, (5 * pi / 3)]})

Tool: SpeechBubble (command SpeechBubble1)
SpeechBubble[ <Point>, <Point TextCorner1>, <Point TextCorner2>, <Point TextCorner3> ]
Input: A, B, C, D
Output: SB1

C: (4.94, 3.37)
D: (4.94, 3.92)
height: y(D) - y(C)
B: (2.45, 3.37)
width: x(C) - x(B)
E1: B + (0, height / 2)
E2: E1 + (width, 0)
E3: (0.5 * (E1 + E2)) + (0, (1.1 * height))
b: y(E3) - y(E2)
a: sqrt(width^(2) / 4 + b^(2))
M: (0.5 * (E1 + E2))
SB1 = If(x(A) < x(M), {PolyLine[M + ((a * cos((6 / 5 * pi))), (b * sin((6 / 5 * pi)))), A, M + ((a * cos((2 / 3 * pi))), ((-b) * sin((2 / 3 * pi))))], CurveCartesian[M + ((a * cos(t)), ((-b) * sin(t))), t, 0, (2 / 3 * pi)], CurveCartesian[M + ((a * cos(t)), (b * sin(t))), t, 0, (6 * pi / 5)]}, {PolyLine[M + ((a * cos((5 / 3 * pi))), (b * sin((5 / 3 * pi)))), A, M + ((a * cos((1 / 5 * pi))), ((-b) * sin((1 / 5 * pi))))], CurveCartesian[M + ((a * cos(t)), ((-b) * sin(t))), t, 0, (1 / 5 * pi)], CurveCartesian[M + ((a * cos(t)), (b * sin(t))), t, 0, (5 * pi / 3)]})