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位までのたし算(型分け)

小数第2位のたし算は、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。
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} & 3.26 \\ + & 5.14 \\ \hline & 8.4\color{red}0 \end{array}


型わけによるたし算の指導順序


[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 \\ + & \hspace{0.2em}0.\square\square \\ \hline & \square.\square\square \end{array}

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

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

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

 \begin{array}{rr} & \hspace{0.2em}0.\hspace{0.2em}0\square \\ + & \hspace{0.2em}0.\square\square \\ \hline & \hspace{0.2em}0.\square\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}1\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}
[2]
 \begin{array}{rr} & \square.\square\square \\ + & \square.\square\textcolor{white}\square \\ \hline & \square.\square\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}0.\square\square \\ + & \square.\square\textcolor{white}\square \\ \hline & \square.\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}1.\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.\hspace{0.2em}0\square \\ + & \square.\square\textcolor{white}\square \\ \hline & \square.\square\square \end{array}

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

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

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

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

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

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

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

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

 \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 \\ + & \hspace{0.2em}0.\square\square \\ \hline & \square.\square\square \end{array}

 \begin{array}{rr} & \square\color{white}.\hspace{0.2em}0\square \\ + & \hspace{0.2em}0.\hspace{0.2em}0\square \\ \hline & \square.\hspace{0.2em}0\square \end{array}
[4]
 \begin{array}{rr} & \square.\square\square \\ + & \square.\square\square \\ \hline & \square.\square\color{white}\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}0.\square\square \\ + & \square.\square\square \\ \hline & \square.\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}1.\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.\square\color{white}\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.\hspace{0.2em}0\square \\ + & \square.\square\square \\ \hline & \square.\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}1.\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\color{white}\square \end{array}

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

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

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

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

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


子どもが間違いやすい箇所

 \begin{array}{rr} & \square.\square\square \\ + & \square\color{white}.\square\square \\ \hline & \square.\square\square \end{array}
6.25+5のような問題をたて書きになおす際に、小数点でそろえることを忘れる場合があります。

 \begin{array}{rr} & 6.26 \\ + & \color{white}6.2\color{black}5 \\ \hline & 6.31 \end{array}


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