小数第１位×小数第１位のかけ算

Posted2024年11月24日

Updated2024年11月24日

By水道方式教育図書管理人

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
$\setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square.\square \\ \end{array}$	$\setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \end{array}$	$\setstretch{0.75} \begin{array}{rr} \color{white}\square.\color{black}\hspace{0.1em}0\hspace{0.1em}.\square \\ \times \color{white}.\square.\color{black}\square \\ \hline \color{white}\square.\color{black}\square\color{white}.\square \\ \end{array}$