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

小数第1位×小数第1位のかけ算(型分け)

小数のかけ算

小数のかけ算は、整数のかけ算の理解の上に成立しますから、整数のかけ算が理解されている必要があります。
指導の順番としては、\square.\square\times\squareのような×整数を先行させると、小数点をそのまま下ろせば良いというように、加減法と混同してしまう生徒が出ても不思議ではありません。
ここでも一般から特殊へという大原則通り指導します。

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指導の道筋

小数を帯小数、真小数、整数というように型分けをしてみると、次のような8組の型分けができます。

(1) 帯 × 帯 (2) 帯 × 真 (3) 真 × 帯 (4) 真 × 真
(5) 整 × 帯 (6) 整 × 真 (7) 帯 × 整 (8) 真 × 整


小数のかけ算の型分け

(1) 帯小数×帯小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square.\square\color{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\square.\square \\ \hline \square\textcolor{white}.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square.\square\color{white}.\square \\ \end{array}
(2) 帯小数×真小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \square.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\hspace{0.2em}0.\square \\ \hline \square.\square\color{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \square\color{white}.\square.\hspace{0.1em}0\hspace{0.1em} \\ \end{array}
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\color{white}.\square \\ \end{array}
(3) 真小数×帯小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\square \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square.\square\color{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \square\textcolor{white}.\square\color{white}.\square \\ \hline \square\color{white}.\square.\square \\ \end{array}
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\square.\color{black}\square \\ \color{white}\square.\color{black}\square\color{white}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \color{white}\square.\color{black}\square\color{white}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\color{white}.\square \\ \end{array}
(4) 真小数×真小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\textcolor{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\square\color{white}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \hspace{0.1em}0\hspace{0.1em}.\hspace{0.1em}0\hspace{0.1em}\textcolor{white}.\square \\ \end{array}
(5) 整数×帯小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\square.\color{black}\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\square.\color{black}\square \\ \color{white}\square.\color{black}\square\textcolor{white}.\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\square.\color{black}\square \\ \times\textcolor{white}.\square.\square \\ \hline \color{white}\square.\color{black}\square\textcolor{white}.\hspace{0.1em}0\hspace{0.1em} \\ \color{white}\square.\color{black}\square\color{white}.\square \\ \hline \color{white}\square.\color{black}\square\color{white}.\square \\ \end{array}
(6) 整数×真小数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\square.\color{black}\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\square.\color{black}\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\square.\color{black}\square \\ \times\textcolor{white}.\hspace{0.1em}0\hspace{0.1em}.\square \\ \hline \color{white}\square.\color{black}\square\color{white}.\square \\ \end{array}
(7) 帯小数×整数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\square.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square\color{white}.\square \\ \end{array}
(8) 真小数×整数
 \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \end{array}  \setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square\color{white}.\square \\ \end{array}

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