算数に強くなる!水道方式【水道方式とは何か】

算数を理解するための最善の方法

2位数×2位数のかけ算(型分け)

2位数のかけ算は、部分積の繰り上がりに注目して型分けが行われています。
これまでの型分けと違い、2-9分類法は使わず、シルエット(□)で表します。
矢印(←)はくり上がりを示します。
表の右は各型に属する問題例です。0の省略(簡便法)については×3位数の指導後にまとめて指導します。

2位数×2位数の型分け

[1]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \square\square  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 13   \\ \times &  32 \\ \hline \end{array} \begin{array}{rr} & 24   \\ \times &  12 \\ \hline \end{array} \begin{array}{rr} & 33   \\ \times &  21 \\ \hline \end{array}
[2]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em}  \\ & \square\square  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 24   \\ \times &  23 \\ \hline \end{array} \begin{array}{rr} & 14   \\ \times &  26 \\ \hline \end{array} \begin{array}{rr} & 16   \\ \times &  13 \\ \hline \end{array}
[3]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \square\square  \\ & \leftarrow\hspace*{0.3em}\hspace*{0.8em}  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 18   \\ \times &  41 \\ \hline \end{array} \begin{array}{rr} & 14   \\ \times &  62 \\ \hline \end{array} \begin{array}{rr} & 27   \\ \times &  31 \\ \hline \end{array}
[4]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em}  \\ & \square\square  \\ & \leftarrow\hspace*{0.3em}\hspace*{0.8em}  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 24   \\ \times &  33 \\ \hline \end{array} \begin{array}{rr} & 19   \\ \times &  34 \\ \hline \end{array} \begin{array}{rr} & 37   \\ \times &  22 \\ \hline \end{array}
[5]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em}\hspace*{0.8em}  \\ & \square\square\square  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 72   \\ \times &  13 \\ \hline \end{array} \begin{array}{rr} & 84   \\ \times &  12 \\ \hline \end{array} \begin{array}{rr} & 43   \\ \times &  23 \\ \hline \end{array}
[6]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \square\square  \\ & \leftarrow\hspace*{0.3em}\hspace*{0.8em}\hspace*{0.8em}  \\ & \square\square\square\hspace*{0.8em}  \\ \hline & \square\square\square\square   \\ \end{array} \begin{array}{rr} & 43   \\ \times &  32 \\ \hline \end{array} \begin{array}{rr} & 93   \\ \times &  22 \\ \hline \end{array} \begin{array}{rr} & 72   \\ \times &  31 \\ \hline \end{array}
[7]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em}\hspace*{0.8em} \\ & \square\square\square  \\ & \leftarrow\hspace*{0.3em}\hspace*{0.8em}\hspace*{0.8em}  \\ & \square\square\square\hspace*{0.8em}  \\ \hline & \square\square\square\square   \\ \end{array} \begin{array}{rr} & 61   \\ \times &  43 \\ \hline \end{array} \begin{array}{rr} & 72   \\ \times &  34 \\ \hline \end{array} \begin{array}{rr} & 42   \\ \times &  33 \\ \hline \end{array}
[8]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\leftarrow\hspace*{0.3em} \\ & \square\square\square  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 74   \\ \times &  13 \\ \hline \end{array} \begin{array}{rr} & 43   \\ \times &  26 \\ \hline \end{array} \begin{array}{rr} & 67   \\ \times &  15 \\ \hline \end{array}
[9]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \square\square \\ & \leftarrow\leftarrow\hspace*{1.1em} \\ & \square\square\square\hspace*{0.8em}  \\ \hline & \square\square\square\square   \\ \end{array} \begin{array}{rr} & 86   \\ \times &  31 \\ \hline \end{array} \begin{array}{rr} & 32   \\ \times &  72 \\ \hline \end{array} \begin{array}{rr} & 43   \\ \times &  62 \\ \hline \end{array}
[10]
 \setstretch{0.5} \begin{array}{rr} & \square\square   \\ \times &  \square \square \\ \hline & \leftarrow\leftarrow\hspace*{0.3em} \\ & \square\square\square   \\ & \leftarrow\leftarrow\hspace*{1.1em} \\ & \square\square\square\hspace*{0.8em}   \\ \hline & \square\square\square\square   \\ \end{array} \begin{array}{rr} & 34   \\ \times &  67 \\ \hline \end{array} \begin{array}{rr} & 48   \\ \times &  96 \\ \hline \end{array} \begin{array}{rr} & 87   \\ \times &  63 \\ \hline \end{array}
[11]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em} \\ & \square\square  \\ & \leftarrow\hspace*{1.1em} \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 3   \\ \times &  54 \\ \hline \end{array} \begin{array}{rr} & 7   \\ \times &  88 \\ \hline \end{array} \begin{array}{rr} & 6   \\ \times &  74 \\ \hline \end{array}
[12]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times &  \square \square \\ \hline & \leftarrow\hspace*{0.3em} \\ & \square\square  \\ & \square\hspace*{0.8em}  \\ \hline & \square\square   \\ \end{array} \begin{array}{rr} & 8   \\ \times &  16 \\ \hline \end{array} \begin{array}{rr} & 4   \\ \times &  19 \\ \hline \end{array} \begin{array}{rr} & 3   \\ \times &  28 \\ \hline \end{array}
[13]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times &  \square \square \\ \hline & \square  \\ & \leftarrow\hspace*{1.1em} \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\square   \\ \end{array} \begin{array}{rr} & 4   \\ \times &  82 \\ \hline \end{array} \begin{array}{rr} & 3   \\ \times &  53 \\ \hline \end{array} \begin{array}{rr} & 7   \\ \times &  91 \\ \hline \end{array}
[14]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times &  \square \square \\ \hline & \square  \\ & \square\hspace*{0.8em}  \\ \hline & \square\square \\ \end{array} \begin{array}{rr} & 4   \\ \times &  21 \\ \hline \end{array} \begin{array}{rr} & 2   \\ \times &  34 \\ \hline \end{array} \begin{array}{rr} & 3   \\ \times &  22 \\ \hline \end{array}
[15]
 \setstretch{0.5} \begin{array}{rr} & \square\hspace*{0.12em}0\hspace*{0.12em}  \\ \times &  \square \square \\ \hline & \square\hspace*{0.12em}0\hspace*{0.12em}  \\ & \square\hspace*{0.12em}0\hspace*{0.12em}\hspace*{0.8em}  \\ \hline & \square\square\hspace*{0.12em}0\hspace*{0.12em} \\ \end{array} \begin{array}{rr} & 20   \\ \times &  14 \\ \hline \end{array} \begin{array}{rr} & 30   \\ \times &  23 \\ \hline \end{array} \begin{array}{rr} & 20   \\ \times &  42 \\ \hline \end{array}
[16]
 \setstretch{0.5} \begin{array}{rr} & \square\square  \\ \times & \square\hspace*{0.12em}0\hspace*{0.12em}  \\ \hline & \hspace*{0.12em}0\hspace*{0.12em}\hspace*{0.12em}0\hspace*{0.12em}  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\hspace*{0.12em}0\hspace*{0.12em} \\ \end{array} \begin{array}{rr} & 32  \\ \times &  20 \\ \hline \end{array} \begin{array}{rr} & 98   \\ \times &  10 \\ \hline \end{array} \begin{array}{rr} & 21   \\ \times &  40 \\ \hline \end{array}
[17]
 \setstretch{0.5} \begin{array}{rr} & \square\hspace*{0.12em}0\hspace*{0.12em} \\ \times & \square\hspace*{0.12em}0\hspace*{0.12em}  \\ \hline & \hspace*{0.12em}0\hspace*{0.12em}\hspace*{0.12em}0\hspace*{0.12em}  \\ & \square\hspace*{0.12em}0\hspace*{0.92em}  \\ \hline & \square\hspace*{0.12em}0\hspace*{0.29em}0\hspace*{0.12em} \\ \end{array} \begin{array}{rr} & 30  \\ \times &  20 \\ \hline \end{array} \begin{array}{rr} & 40   \\ \times &  20 \\ \hline \end{array} \begin{array}{rr} & 70   \\ \times &  10 \\ \hline \end{array}
[18]
 \setstretch{0.5} \begin{array}{rr} & \square\square \\ \times & \square\hspace*{0.12em}0\hspace*{0.15em}  \\ \hline & \hspace*{0.12em}0\hspace*{0.15em}\hspace*{0.12em}0\hspace*{0.15em}  \\ & \leftarrow\hspace*{0.3em}\hspace*{1.6em}  \\ & \square\square\square\hspace*{0.8em}  \\ \hline & \square\square\square\hspace*{0.12em}0\hspace*{0.18em} \\ \end{array} \begin{array}{rr} & 56  \\ \times &  30 \\ \hline \end{array} \begin{array}{rr} & 86   \\ \times &  20 \\ \hline \end{array} \begin{array}{rr} & 62   \\ \times &  70 \\ \hline \end{array}
[19]
 \setstretch{0.5} \begin{array}{rr} & \square\hspace*{0.12em}0\hspace*{0.15em}  \\ \times & \square\hspace*{0.12em}0\hspace*{0.15em} \\ \hline & \hspace*{0.12em}0\hspace*{0.15em}\hspace*{0.12em}0\hspace*{0.15em} \\ & \leftarrow\hspace*{0.3em}\hspace*{1.6em}  \\ & \square\square\hspace*{0.12em}0\hspace*{0.95em}  \\ \hline & \square\square\hspace*{0.12em}0\hspace*{0.15em}\hspace*{0.12em}0\hspace*{0.15em} \\ \end{array} \begin{array}{rr} & 70  \\ \times &  40 \\ \hline \end{array} \begin{array}{rr} & 60   \\ \times &  80 \\ \hline \end{array} \begin{array}{rr} & 50   \\ \times &  40 \\ \hline \end{array}
[20]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times & \square\hspace*{0.12em}0\hspace*{0.15em} \\ \hline & \hspace*{0.12em}0\hspace*{0.15em} \\ & \square\hspace*{0.8em}  \\ \hline & \square\hspace*{0.12em}0\hspace*{0.15em} \\ \end{array} \begin{array}{rr} & 3  \\ \times &  30 \\ \hline \end{array} \begin{array}{rr} & 4   \\ \times &  20 \\ \hline \end{array} \begin{array}{rr} & 8   \\ \times &  10 \\ \hline \end{array}
[21]
 \setstretch{0.5} \begin{array}{rr} & \square  \\ \times & \square\hspace*{0.12em}0\hspace*{0.15em} \\ \hline & \hspace*{0.12em}0\hspace*{0.15em} \\ & \leftarrow\hspace*{0.3em}\hspace*{0.8em}  \\ & \square\square\hspace*{0.8em}  \\ \hline & \square\square\hspace*{0.12em}0\hspace*{0.15em} \\ \end{array} \begin{array}{rr} & 6  \\ \times &  90 \\ \hline \end{array} \begin{array}{rr} & 8   \\ \times &  30 \\ \hline \end{array} \begin{array}{rr} & 9   \\ \times &  80 \\ \hline \end{array}

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