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2位までのひき算(型分け)

小数第2位のたし算同様、位取りの仕組みが理解できていれば、特にタイルを用いず指導できます。
たし算と同じように整数との違いは次の2点です。

  • 小数点をそろえて計算すること。
  • 0を想定したり(頭の中で補う)、後0を処理すること。
 \begin{array}{rr} & 4.1\color{red}0 \\ - & 1.87 \\ \hline \end{array}  \begin{array}{rr} & 5.26 \\ - & 2.16 \\ \hline & 3.1\color{red}0 \end{array}


型わけによるひき算の指導順序

\boxtimesは、0の場合も含むことを示します。


[1]水源地
\begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}
\begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

\begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \square.\square\textcolor{white}\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\square\textcolor{white}\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \boxtimes\color{white}.\square\square \end{array}

\begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}.\square\square \\ \hline & \square.\square\square \end{array}

\begin{array}{rr} & \hspace{0.2em}1.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

\begin{array}{rr} & \hspace{0.2em}1.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \square.\square\color{white}\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\color{white}\square \\ \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \square\color{white}.\square\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\color{white}\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0\color{white}.\square\square \\ \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \square.\square\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\square\square \\ \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \square.\square\color{white}\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\square\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\hspace{0.2em}1\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\square\color{white}\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\hspace{0.2em}0\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\hspace{0.2em}0\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0\color{white}.\hspace{0.2em}0\square \\ \end{array}
[2]
 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\textcolor{white}\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\textcolor{white}\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\textcolor{white}\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\square \\ - & \hspace{0.2em}0.\square\textcolor{white}\square \\ \hline & \square.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\square \\ - & \hspace{0.2em}0.\square\textcolor{white}\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\textcolor{white}\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\square \\ - & \hspace{0.2em}0.\square\textcolor{white}\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}
[3]
 \begin{array}{rr} & \square.\square\square \\ - & \square\color{white}.\square\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & \square.\square\square \\ - & \square\color{white}.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}
[4]
 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \square .\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\color{white}\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\color{white}\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\color{white}\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\color{white}\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \square.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1.\square\color{white}\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\square\color{white}\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}0.\hspace{0.2em}1\color{white}\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}
[5]
 \begin{array}{rr} & \square\color{white}.\square\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & \square\color{white}.\square\square \\ - & \square.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \square\color{white}.\square\square \\ - & \square.\hspace{0.2em}9\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square\color{white}.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \square.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1\color{white}.\square\square \\ - & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1\color{white}.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}9\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}

 \begin{array}{rr} & \square\color{white}.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \square.\hspace{0.2em}9\square \end{array}

 \begin{array}{rr} & \hspace{0.2em}1\color{white}.\square\square \\ - & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \hspace{0.2em}0.\hspace{0.2em}0\square \end{array}


子どもが間違いやすい箇所

 \begin{array}{rr} & \square.\square\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & 0.26 \\ - & 0.26 \\ \hline & 0.00 \end{array} 左の答えは0.00と書いていますが、0.\cancel{0}\cancel{0}とするか、0と直します。

 \begin{array}{rr} & 0.94 \\ - & 0.84 \\ \hline & 0.10 \end{array} この答えも、0.10と書かずに、0.1\cancel{0}と書くか、0.1とします。
 \begin{array}{rr} & \square.\square\color{white}\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}  \begin{array}{rr} & \square\color{white}.\square\square \\ - & \square.\square\square \\ \hline & \square.\square\square \end{array}
 \begin{array}{rr} & 5\color{white}.38 \\ - & 4.38 \\ \hline & 1.38 \end{array} 減数の小数部分をそのままおろしてしまっています。5.00から4.38を引くように指導します。

 \begin{array}{rr} & 8\color{white}.00 \\ - & 4.75 \\ \hline & 3.75 \end{array} くり下がりの処理が不完全です。

 \begin{array}{rr} & 1\color{white}.00 \\ - & 0.32 \\ \hline & 68 \end{array} 小数点と整数の0をつけ忘れています。

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