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×３位数のかけ算

Posted2024年11月24日
Updated2024年11月24日
By水道方式教育図書 管理人

×３位数のかけ算は、百位の乗数を、部分積を百位から記述する手続きが理解できれば、これまでと同様のアルゴリズムで計算することができます。
部分積の和では、３段のたて書きの加法を行います。くり上がった場合は４段の加法となり、ここで誤答が生じることも多くなります。
生徒が誤った答えを出したときには、計算のどの段階で間違えたのかを発見させ、まちがい傾向の分析を促すような指導も必要です。

３位数×３位数の型分け（★は積が４位数の問題を含む）

［１］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array} \begin{array}{rr} & 231 \\ \times & 223 \\ \hline \end{array} \begin{array}{rr} & 112 \\ \times & 431 \\ \hline \end{array} \begin{array}{rr} & 324 \\ \times & 212 \\ \hline \end{array}
［２］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array} \begin{array}{rr} & 321 \\ \times & 114 \\ \hline \end{array} \begin{array}{rr} & 429 \\ \times & 215 \\ \hline \end{array} \begin{array}{rr} & 714 \\ \times & 118 \\ \hline \end{array}
［３］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square \\ & \square\square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array} \begin{array}{rr} & 321 \\ \times & 243 \\ \hline \end{array} \begin{array}{rr} & 602 \\ \times & 171 \\ \hline \end{array} \begin{array}{rr} & 342 \\ \times & 182 \\ \hline \end{array}
［４］
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square\square \\ \end{array} \begin{array}{rr} & 213 \\ \times & 634 \\ \hline \end{array} \begin{array}{rr} & 422 \\ \times & 721 \\ \hline \end{array} \begin{array}{rr} & 423 \\ \times & 922 \\ \hline \end{array}
［５］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ & \square\square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array} \begin{array}{rr} & 932 \\ \times & 123 \\ \hline \end{array} \begin{array}{rr} & 486 \\ \times & 254 \\ \hline \end{array} \begin{array}{rr} & 276 \\ \times & 385 \\ \hline \end{array}
［６］
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square \\ & \square\square\square\square\hspace*{0.8em} \\ & \square\square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square\square \\ \end{array} \begin{array}{rr} & 411 \\ \times & 352 \\ \hline \end{array} \begin{array}{rr} & 986 \\ \times & 231 \\ \hline \end{array} \begin{array}{rr} & 763 \\ \times & 821 \\ \hline \end{array}
［７］
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square\square \\ \end{array} \begin{array}{rr} & 463 \\ \times & 324 \\ \hline \end{array} \begin{array}{rr} & 564 \\ \times & 213 \\ \hline \end{array} \begin{array}{rr} & 513 \\ \times & 314 \\ \hline \end{array}
［８］
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ & \square\square\square\square\hspace*{0.8em} \\ & \square\square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square\square \\ \end{array} \begin{array}{rr} & 911 \\ \times & 423 \\ \hline \end{array} \begin{array}{rr} & 624 \\ \times & 536 \\ \hline \end{array} \begin{array}{rr} & 367 \\ \times & 498 \\ \hline \end{array}
［９］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\hspace*{0.13em}0\hspace*{0.13em} \\ \hline & \hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em} \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\hspace*{0.14em}0\hspace*{0.15em} \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\square\hspace*{0.13em}0\hspace*{0.13em} \\ \hline & \square\square\square\hspace*{0.14em}0\hspace*{0.15em} \\ & \square\square\square\hspace*{0.8em} \\ \hline & \square\square\square\square\hspace*{0.14em}0\hspace*{0.15em} \\ \end{array}		 \begin{array}{rr} & 236 \\ \times & 410 \\ \hline \end{array} \begin{array}{rr} & 183 \\ \times & 240 \\ \hline \end{array} \begin{array}{rr} & 223 \\ \times & 420 \\ \hline \end{array}
［１０］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\hspace*{0.13em}0\hspace*{0.13em}\square \\ \hline & \square\square\square \\ & \hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\hspace*{0.13em}0\hspace*{0.13em}\square \\ \hline & \square\square\square \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array}		 \begin{array}{rr} & 234 \\ \times & 301 \\ \hline \end{array} \begin{array}{rr} & 316 \\ \times & 402 \\ \hline \end{array} \begin{array}{rr} & 648 \\ \times & 302 \\ \hline \end{array}
［１１］★
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em} \\ & \hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em} \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square\square\square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \square\square\square\hspace*{0.14em}0\hspace*{0.15em}\hspace*{0.14em}0\hspace*{0.15em} \\ \end{array}		 \begin{array}{rr} & 241 \\ \times & 300 \\ \hline \end{array} \begin{array}{rr} & 612 \\ \times & 400 \\ \hline \end{array} \begin{array}{rr} & 977 \\ \times & 600 \\ \hline \end{array}


２位数×３位数の型分け

［１２］
\setstretch{0.7} \begin{array}{rr} & \square\square \\ \times & \square\square\square \\ \hline & \square\square \\ & \square\square\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\square \\ \end{array} \begin{array}{rr} & 47 \\ \times & 222 \\ \hline \end{array} \begin{array}{rr} & 41 \\ \times & 232 \\ \hline \end{array} \begin{array}{rr} & 99 \\ \times & 111 \\ \hline \end{array}
［１３］
\setstretch{0.7} \begin{array}{rr} & \square\square \\ \times & \square\square\square \\ \hline & \square\square\square \\ & \square\square\square\hspace*{0.8em} \\ & \square\square\square\hspace*{1.6em} \\ \hline & \square\square\square\square\square \\ \end{array} \begin{array}{rr} & 86 \\ \times & 347 \\ \hline \end{array} \begin{array}{rr} & 63 \\ \times & 867 \\ \hline \end{array} \begin{array}{rr} & 73 \\ \times & 234 \\ \hline \end{array}
［１４］
\setstretch{0.7} \begin{array}{rr} & \square\square \\ \times & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \hspace*{1.5em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ & \square\square\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\hspace*{0.17em}0\hspace*{0.15em} \\ \end{array} \begin{array}{rr} & 24 \\ \times & 340 \\ \hline \end{array} \begin{array}{rr} & 92 \\ \times & 570 \\ \hline \end{array} \begin{array}{rr} & 36 \\ \times & 220 \\ \hline \end{array}
［１５］
\setstretch{0.7} \begin{array}{rr} & \square\square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\square \\ & \hspace*{1.5em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\square \\ \end{array} \begin{array}{rr} & 24 \\ \times & 302 \\ \hline \end{array} \begin{array}{rr} & 75 \\ \times & 801 \\ \hline \end{array} \begin{array}{rr} & 36 \\ \times & 409 \\ \hline \end{array}
［１６］
\setstretch{0.7} \begin{array}{rr} & \square\square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ & \hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.15em}0\hspace*{0.15em} \\ \end{array} \begin{array}{rr} & 76 \\ \times & 800 \\ \hline \end{array} \begin{array}{rr} & 94 \\ \times & 500 \\ \hline \end{array} \begin{array}{rr} & 84 \\ \times & 100 \\ \hline \end{array}
［１７］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\square \\ \hline & \square\square \\ & \square\square\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ \end{array}		 \begin{array}{rr} & 8 \\ \times & 324 \\ \hline \end{array} \begin{array}{rr} & 6 \\ \times & 278 \\ \hline \end{array} \begin{array}{rr} & 84 \\ \times & 100 \\ \hline \end{array}
［１８］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\square \\ \hline & \square \\ & \square\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\square \\ \hline & \square\square\square\square \\ \end{array}		 \begin{array}{rr} & 7 \\ \times & 311 \\ \hline \end{array} \begin{array}{rr} & 6 \\ \times & 811 \\ \hline \end{array} \begin{array}{rr} & 4 \\ \times & 422 \\ \hline \end{array}
［１９］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\square \\ \hline & \square \\ & \square\hspace*{0.8em} \\ & \square\hspace*{1.6em} \\ \hline & \square\square\square \\ \end{array} \begin{array}{rr} & 2 \\ \times & 213 \\ \hline \end{array} \begin{array}{rr} & 4 \\ \times & 211 \\ \hline \end{array} \begin{array}{rr} & 3 \\ \times & 321 \\ \hline \end{array}
［２０］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \hspace*{0.15em}0\hspace*{0.15em} \\ & \square\square\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \end{array}		 \begin{array}{rr} & 8 \\ \times & 760 \\ \hline \end{array} \begin{array}{rr} & 9 \\ \times & 240 \\ \hline \end{array} \begin{array}{rr} & 4 \\ \times & 670 \\ \hline \end{array}
［２１］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \hspace*{0.15em}0\hspace*{0.15em} \\ & \square\hspace*{0.8em} \\ & \square\hspace*{1.6em} \\ \hline & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \hline & \square\square\hspace*{0.15em}0\hspace*{0.15em} \\ \end{array}		 \begin{array}{rr} & 3 \\ \times & 320 \\ \hline \end{array} \begin{array}{rr} & 9 \\ \times & 110 \\ \hline \end{array} \begin{array}{rr} & 4 \\ \times & 210 \\ \hline \end{array}
［２２］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\square \\ & \hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\square\hspace*{1.6em} \\ \hline & \square\square\square\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\square\square\square \\ \end{array}		 \begin{array}{rr} & 7 \\ \times & 806 \\ \hline \end{array} \begin{array}{rr} & 6 \\ \times & 903 \\ \hline \end{array} \begin{array}{rr} & 9 \\ \times & 305 \\ \hline \end{array}
［２３］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\square \\ & \hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\hspace*{1.6em} \\ \hline & \square\square\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\square\square \\ \end{array}		 \begin{array}{rr} & 2 \\ \times & 306 \\ \hline \end{array} \begin{array}{rr} & 8 \\ \times & 109 \\ \hline \end{array} \begin{array}{rr} & 4 \\ \times & 104 \\ \hline \end{array}
［２４］
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square \\ & \hspace*{0.15em}0\hspace*{0.15em}\hspace*{0.8em} \\ & \square\hspace*{1.6em} \\ \hline & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \end{array}
↓
\setstretch{0.7} \begin{array}{rr} & \square \\ \times & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \hline & \square\hspace*{0.15em}0\hspace*{0.15em}\square \\ \end{array}		 \begin{array}{rr} & 2 \\ \times & 403 \\ \hline \end{array} \begin{array}{rr} & 8 \\ \times & 101 \\ \hline \end{array} \begin{array}{rr} & 3 \\ \times & 201 \\ \hline \end{array}
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