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位数のたし算(型分け)

小学生の計算練習の最初の天王山が3位数の加減算です。
全部の型を与える必要はありません。例えば上下が入れ替わったような型は、子どもによっては飛ばすこともできます。
未定着な箇所や理解が難しい場合は、スモールステップで集中的に取り組めば良いと思います。

2-9分類法による指導順序

[水源地]
\begin{array}{rr} & 222 \\ + &   222 \\ \hline \end{array}
\begin{array}{rr} & 222 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   22 \\ \hline \end{array}

\begin{array}{rr} & 22 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   22 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   22 \\ \hline \end{array}

\begin{array}{rr} & 22 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 22 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   20 \\ \hline \end{array}

\begin{array}{rr} & 20 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   20 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   20 \\ \hline \end{array}

\begin{array}{rr} & 22 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   22 \\ \hline \end{array}

\begin{array}{rr} & 20 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 20 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   20 \\ \hline \end{array}

\begin{array}{rr} & 20 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   2 \\ \hline \end{array}

\begin{array}{rr} & 2 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   2 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   2 \\ \hline \end{array}

\begin{array}{rr} & 2 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 2 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   2 \\ \hline \end{array}

\begin{array}{rr} & 2 \\ + &   200 \\ \hline \end{array}

\begin{array}{rr} & 222 \\ + &   0 \\ \hline \end{array}

\begin{array}{rr} & 0 \\ + &   222 \\ \hline \end{array}

\begin{array}{rr} & 220 \\ + &   0 \\ \hline \end{array}

\begin{array}{rr} & 0 \\ + &   220 \\ \hline \end{array}

\begin{array}{rr} & 202 \\ + &   0 \\ \hline \end{array}

\begin{array}{rr} & 0 \\ + &   202 \\ \hline \end{array}

\begin{array}{rr} & 200 \\ + &   0 \\ \hline \end{array}

\begin{array}{rr} & 0 \\ + &   220 \\ \hline \end{array}
[繰り上がり1回/一位⇒十位]
\begin{array}{rr} & 229 \\ + &   229 \\ \hline \end{array}
\begin{array}{rr} & 229 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   229 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   221 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   201 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   221 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   201 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   29 \\ \hline \end{array}

\begin{array}{rr} & 29 \\ + &   229 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   21 \\ \hline \end{array}

\begin{array}{rr} & 29 \\ + &   221 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   29 \\ \hline \end{array}

\begin{array}{rr} & 29 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   21 \\ \hline \end{array}

\begin{array}{rr} & 29 \\ + &   201 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   9 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   229 \\ \hline \end{array}

\begin{array}{rr} & 229 \\ + &   1 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   221 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   9 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   1 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   201 \\ \hline \end{array}
[繰り上がり1回/十位⇒百位]
\begin{array}{rr} & 292 \\ + &   292 \\ \hline \end{array}

百位が欠位している3次退化型へ発展可能
\begin{array}{rr} & 292 \\ + &   290 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   292 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   290 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   212 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   210 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   212 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   210 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   92 \\ \hline \end{array}

\begin{array}{rr} & 92 \\ + &   292 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   12 \\ \hline \end{array}

\begin{array}{rr} & 92 \\ + &   212 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   92 \\ \hline \end{array}

\begin{array}{rr} & 92 \\ + &   290 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   12 \\ \hline \end{array}

\begin{array}{rr} & 92 \\ + &   210 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   90 \\ \hline \end{array}

\begin{array}{rr} & 90 \\ + &   292 \\ \hline \end{array}

\begin{array}{rr} & 292 \\ + &   10 \\ \hline \end{array}

\begin{array}{rr} & 90 \\ + &   212 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   90 \\ \hline \end{array}

\begin{array}{rr} & 90 \\ + &   290 \\ \hline \end{array}

\begin{array}{rr} & 290 \\ + &   10 \\ \hline \end{array}

\begin{array}{rr} & 90 \\ + &   210 \\ \hline \end{array}
[繰り上がり2回]
\begin{array}{rr} & 299 \\ + &   299 \\ \hline \end{array}

百位が欠位している3次退化型へ発展可能
\begin{array}{rr} & 299 \\ + &   219 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &  291 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   211 \\ \hline \end{array}

\begin{array}{rr} & 289 \\ + &   219 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   299 \\ \hline \end{array}

\begin{array}{rr} & 289 \\ + &   211 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   201 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   291 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   99 \\ \hline \end{array}

\begin{array}{rr} & 99 \\ + &   299 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   19 \\ \hline \end{array}

\begin{array}{rr} & 19 \\ + &   299 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   91 \\ \hline \end{array}

\begin{array}{rr} & 99 \\ + &   291 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   19 \\ \hline \end{array}

\begin{array}{rr} & 99 \\ + &   211 \\ \hline \end{array}

\begin{array}{rr} & 289 \\ + &   19 \\ \hline \end{array}

\begin{array}{rr} & 89 \\ + &   219 \\ \hline \end{array}

\begin{array}{rr} & 99 \\ + &   209 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   99 \\ \hline \end{array}

\begin{array}{rr} & 289 \\ + &   11 \\ \hline \end{array}

\begin{array}{rr} & 89 \\ + &   211 \\ \hline \end{array}

\begin{array}{rr} & 99 \\ + &   201 \\ \hline \end{array}

\begin{array}{rr} & 209 \\ + &   91 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   9 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   299 \\ \hline \end{array}

\begin{array}{rr} & 9 \\ + &   291 \\ \hline \end{array}

\begin{array}{rr} & 299 \\ + &   1 \\ \hline \end{array}

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