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

3位数÷1位数[商2位数](型分け)

次に商が2位数の問題に進みます。最初に立てる商が百位に立たず、十位に立つことに気づかせるよう指導します。
これは素過程  \setstretch{0.7} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square \\ \end{array} の複合になるので、生徒が戸惑う場合は、素過程に分解して見せることで解決するでしょう。
商を立てる位置決めは、÷2位数のアルゴリズムに発展します。

3位数÷1位数[商2位数]の指導

[1] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\square \\ \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\square \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em2& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 137 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 258 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em6& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 345 \\ \end{array}

[2] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\square \\ \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.8em}0 \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 152 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em2& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 174 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 180 \\ \end{array}

[3] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\square \\ \ &\ &\hspace{0.6em}\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\square \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 131 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 160 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em7& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 361 \\ \end{array}

[4][5] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-0.9em}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\square \\ \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\boxtimes \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 119 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 103 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em7& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 130 \\ \end{array}


 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 111 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em6& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 108 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 104 \\ \end{array}

[6] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{0.6em}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\square \\ \ &\ &\hspace{0.6em}\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\square \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 100 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em9& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 104 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 101 \\ \end{array}

[7][8] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\square \\ \ &\ &\hspace{0.6em}\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\boxtimes \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em2& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 147 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 278 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 289 \\ \end{array}


 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 216 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 248 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em6& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 546 \\ \end{array}

[9]一次退化 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\hspace{0.2em}0 \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\square \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\square \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em2& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 121 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 212 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 283 \\ \end{array}

[11] 問題
 \setstretch{0.8} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\hspace{0.2em}0 \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square\hspace{0.2em}0 \\ \ &\ &\hspace{-1.75em}\square\square \\ \cline{2-3} \ &\ &\hspace{0.6em}\hspace{0.2em}0 \\ \end{array}  \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em3& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 150 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em4& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 360 \\ \end{array}

 \setstretch{0.8} \begin{array}{rcc} \cline{2-3} \kern1em9& \kern-0.6em {\big)} \kern0.1em & \hspace{-0.8em} 810 \\ \end{array}


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