[{"data":1,"prerenderedAt":143},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-a\u002Fmathematics-and-human-activities\u002Fmeasurement-surveying-and-geometry":3},{"topic":4,"category":116,"seo":120,"breadcrumbs":125,"prerequisites":132,"nextTopics":133,"relatedTopics":142},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":22,"learningGoal":26,"blocks":27},"high-school-mathematics-a-mathematics-and-human-activities-measurement-surveying-and-geometry","measurement-surveying-and-geometry","測る活動と測量","測れる基準と縮尺を使い、図上の長さから実際の距離を求め、単位と距離感で検算する測量の考えを学びます。","\u002Fhigh-school\u002Fmathematics-a\u002Fmathematics-and-human-activities\u002Fmeasurement-surveying-and-geometry","\u002Fhigh-school\u002Fmathematics-a\u002Fmathematics-and-human-activities","beginner","student_high",5,"2026-07-27","ai_generated",[17,18,19,20,21],"数学A","数学と人間の活動","測量","縮尺","間接測定",[23,24,25],"比","長さの単位換算","平面図形","縮尺と基準線を使い、図上の量と現地の量を対応させる測量の基本方針を説明できる。",[28,34,43,49,58,68,74,80,96,106],{"id":29,"type":30,"title":31,"subtitle":32,"shortDefinition":33},"hero","HeroBlock","測れるものから測れない距離へ","基準と図形が測量を支える","川幅や広い土地のように直接ものさしを当てにくい長さも、測れる基準線と図形の関係へ置き換えれば求められます。縮尺は現地と図を一定の比で結ぶ約束です。数値だけでなく単位と測り方の条件も記録します。",{"id":35,"type":36,"term":37,"definition":38,"plainExplanation":39,"keywords":40},"definition","DefinitionBlock","測量と縮尺","測量は位置・距離・角度などを測って土地や構造を表す活動で、縮尺は図上の長さと実際の長さの一定の比です。","縮尺1:25000は、図上の1という長さが現地の25000という同じ単位の長さに対応するという意味です。図上から現地へは25000倍、現地から図上へは25000で割ります。どちらの向きでも、計算前にcm、m、kmを同じ単位へそろえることが欠かせません。",[41,21,42],"測れる基準","単位をそろえる",{"id":44,"type":45,"src":46,"alt":47,"caption":48},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fmathematics-a\u002Fmathematics-and-human-activities\u002Fmeasurement-surveying-and-geometry\u002Fmeasurement-surveying-and-geometry.svg","縮尺1対25000の地図上4センチメートルと現地1キロメートルの対応図","図上4cmを25000倍すると100000cmです。単位をm、kmへ直すと1000m=1kmになります。「掛ける」と「単位換算」を二段に分けて検算する図です。",{"id":50,"type":51,"steps":52,"title":57},"steps","StepBlock",[53,54,55,56],"図上と実際のどちらを求めるか、矢印で向きを決める","縮尺を同じ単位どうしの比として読み直す","現地へは掛け、図上へは割るという倍率を選ぶ","最後に求める単位へ換算し、距離感も確かめる","縮尺問題の4手順",{"id":59,"type":60,"title":61,"points":62,"body":67},"key-points","KeyPointBlock","直接測定と間接測定",[63,64,65,66],"測れる基準線を正確に決める","位置や向きを図へ記録する","図形の対応関係を保つ","結果の大きさと単位を現地で検算する","測りたい対象へ直接届かなくても、測れる長さと同じ形・同じ比を作れば推定できます。測った基準と推定した量を分けて記録することが大切です。",{"id":69,"type":70,"scenario":71,"explanation":72,"result":73},"example","ExampleBlock","縮尺1:25000の地図で、学校から駅までが4cmだった。実際の距離を求める。","実際の長さは図上の25000倍なので、4×25000=100000cmです。100cm=1mより1000m、1000m=1kmより1kmです。いきなり4÷25000とせず、現地の方が地図より大きいという見積もりで方向も確かめます。4cmの地図表示が1kmの現地距離になるのは自然な桁かも確認します。","実際の距離は1kmです。倍率を使う段階と単位を変える段階を分けると、どこで桁が変わったか説明できます。",{"id":75,"type":76,"warningTitle":77,"message":78,"severity":75,"action":79},"warning","WarningBlock","倍率の向きと単位を混ぜない","1:25000を使って実距離を求めるときは図上の長さを25000倍します。ただし答えをcmのままにすると距離感を読み誤ります。","現地は図より長いかを見積もり、計算式に単位を書きます。最後に指定単位へ直して常識的な距離か確かめましょう。",{"id":81,"type":82,"title":83,"questions":84},"quiz","QuizBlock","確認テスト",[85],{"question":86,"choices":87,"answerIndex":91,"choiceExplanations":92},"縮尺1:50000の地図で2cmの距離は、実際には何kmですか。",[88,89,90],"1km","0.1km","100km",0,[93,94,95],"正解です。図上から現地なので2×50000=100000cm、さらに1000m=1kmです。","0.1kmは100mです。100000cmをmへ直すと1000mになるため、換算で桁を一つ小さくしすぎています。","縮尺の倍率を使った後の単位換算ができていません。100000cmは1000mであり、100kmではありません。",{"id":97,"type":98,"title":99,"points":100},"summary","SummaryBlock","まとめ",[101,102,103,104,105],"測量は測れる基準から間接的に量を求める","縮尺は図上と現地の同じ単位での比を表す","倍率の向きは大きさの見積もりで確かめる","図上から現地か、現地から図上かを先に決める","計算後は求める単位と距離感で検算する",{"id":107,"type":108,"title":109,"nextTopics":110,"relatedKeywords":112},"next-action","NextActionBlock","次は歴史的な測るパズルへ",[111],"high-school-mathematics-a-mathematics-and-human-activities-wasan-oil-measuring-state-puzzle",[113,114,115],"**和算**","状態","不変量",{"path":10,"title":18,"description":117,"parentPath":118,"accentToken":119},"数量や図形と人間の活動、整数の約数・倍数、ユークリッドの互除法、二進法、座標、数学史、ゲームやパズルを整理していくカテゴリです。","\u002Fhigh-school\u002Fmathematics-a","signal-blue",{"title":121,"description":122,"canonicalUrl":123,"ogImage":124},"測る活動と測量 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