算数・数学の図を書くことについて
今回は算数・数学の図の話です。生徒の問題を解いている姿を見ると、複雑な文章題にも関わらず頭の中で考えて問題を解いている生徒がいらっしゃいます。せっかく紙とペンがあるなら、そのツールを上手に使って、重要な部分に頭のリソースを使えるようにしていきましょう。
なぜ図を書くことが重要なのか
例えば算数の速さの問題、太郎くんが湖を右回りに、次郎くんが左回りにと言った問題(そんなことするかい!みたいなツッコミはまた今度)において、太郎くんの走った距離、速さ、時間が重要となりますが、実際に図を書いた方が、イメージとその走った距離がわかりやすい場合があります。
10分後に太郎くんと次郎くんは出会い、さらにもう一周走って出会いました。
これを言葉で考えると大変ですが、

このように図に書くと、どのような距離を走ったかが明確になります。
数学でも、座標平面上に点を打つことで、実際にどのような図形が描けるのかがわかると、非常に問題を解くのに有効となります。また、実際に出した答えが、例えば2π/3(120°)なのに、図では鋭角で、π/6(30°)であった時には、どうもおかしいな、見直しをした方がいいかな、といったことにつながります。
図を書く練習
最初は何を書いていかわからないかもしれません。
むしろ無駄な図を書くことで時間がかかってしまい、問題を解く時間がない!といったことも起こるかもしれません。ただ、最初は時間がかかっても、継続して図を書くことを心がけることで、”このパターンの問題はこう書く”、"あ、ちょっと方針が違うみたいだから別のあのやり方で書いてみよう”といった形で、複数のパターンで図を書くことも重要です。
問題文の理解
問題文を一読して全て理解する人はそういません。そんな子はもしかしたら勉強の必要がないかもしれません。問題文を理解する手助けとして図を書いていきましょう。
全体感の把握
設問が複数ある場合にも図はもちろん重要です。問題の全体感を把握するために、設問の前の提示文を読んで、図を書き、この問題は何に関して言っているのかと言ったことを考えて問題を解いていきましょう。
各分野における図を書くことの重要性
割合
割合の問題で、20%引きなどは、棒グラフで視覚的に書くことで、よりどういった売買が行われているかがわかります。
速さ
速さの問題は、まずは登場人物がどのような行動をとっているのかを書きましょう。
図書館まで走っているのか、AB地点を折り返しているのか、など文章に書かれていることを図にすることで非常に理解が進みます。
結論
要は図を書けということです。書いてみてダメでも、特にデメリットはありませんから、図を書く練習をたくさんしながら、問題を解いていきましょう。
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