2026秋小学数学三升四年级奥数拓展应用题12天暑假专项提升训练

2026秋小学数学三升四年级奥数拓展应用题12天暑假专项提升训练第1天植树问题专项（基础入门：两端都栽）10题核心公式：棵数=间隔数+1、间隔数=棵数-1、总长=间隔数×间距1.一条笔直的小路长80米，在小路一侧从头到尾种树，每隔5米种一棵，一共需要种多少棵树？________________________________________________________________________________________________________________________________2.学校走廊长63米，计划在走廊一侧摆放绿植，两端都放，每隔7米放一盆，一共需要多少盆绿植？________________________________________________________________________________________________________________________________3.在一条长100米的公路一侧植树，两端都栽，一共种了21棵树，请问每两棵树之间的间距是多少米？________________________________________________________________________________________________________________________________4.公园步道长48米，一侧从头到尾安装路灯，每隔6米装一盏，一共要安装多少盏路灯？________________________________________________________________________________________________________________________________5.一条道路一侧种树，两端都栽，每隔4米种一棵，一共种了30棵，这条道路总长多少米？________________________________________________________________________________________________________________________________6.校园围墙边的小路长72米，一侧从头到尾栽桂花树，每隔8米栽一棵，一共栽多少棵？________________________________________________________________________________________________________________________________7.笔直的河道一侧全长90米，两端都栽柳树，一共栽了19棵，相邻两棵柳树间距多少米？________________________________________________________________________________________________________________________________8.小区健身路长55米，一侧从头到尾摆放休闲椅，每隔5米放一把，一共放多少把椅子？________________________________________________________________________________________________________________________________9.一条公路一侧两端都栽树，间距3米，一共栽了41棵树，这条公路长多少米？________________________________________________________________________________________________________________________________10.广场长廊长84米，一侧从头到尾挂灯笼，每隔12米挂一个，一共需要挂多少个灯笼？________________________________________________________________________________________________________________________________第2天植树问题专项（基础入门：一端栽一端不栽）10题核心公式：棵数=间隔数、总长=间隔数×间距、间距=总长÷间隔数1.一条小路紧靠围墙，全长60米，在小路一侧种树，围墙一端不栽，另一端栽树，每隔6米种一棵，一共种多少棵？________________________________________________________________________________________________________________________________2.圆形花坛外围的直道长45米，一端挨着花坛不栽花，另一端栽花，每隔5米栽一盆月季，一共栽多少盆？________________________________________________________________________________________________________________________________3.河边步道长88米，靠河一端不栽树，另一端栽树，一共栽了11棵杨树，相邻两棵树间距多少米？________________________________________________________________________________________________________________________________4.小区小路长36米，一端是楼房不摆放花盆，另一端摆放，每隔4米摆一盆，一共摆多少盆？________________________________________________________________________________________________________________________________5.一段公路长77米，一端有桥墩不栽树，另一端栽树，每隔7米栽一棵，一共栽多少棵？________________________________________________________________________________________________________________________________6.校园跑道侧边长96米，一端是看台不装灯，另一端装灯，一共装了12盏灯，灯的间距是多少米？________________________________________________________________________________________________________________________________7.一条直路一端靠墙，全长54米，每隔9米种一棵梧桐树，一共能种多少棵？________________________________________________________________________________________________________________________________8.湖边直道全长42米，靠湖水一端不栽树，栽树一端共种7棵柳树，树间距多少米？________________________________________________________________________________________________________________________________9.步行街一侧长66米，一端是商铺不挂招牌灯，每隔11米挂一盏，一共挂多少盏？________________________________________________________________________________________________________________________________10.一段绿化带直道长81米，一端是道路交叉口不栽灌木，一共栽了9丛灌木，间距是多少米？________________________________________________________________________________________________________________________________第3天植树问题专项（基础入门：两端都不栽）10题核心公式：棵数=间隔数-1、间隔数=棵数+1、总长=间隔数×间距1.两条楼房之间的小路长40米，在小路两侧种树，两端都是楼房不栽树，每隔5米种一棵，一侧种多少棵？________________________________________________________________________________________________________________________________2.两座教学楼之间距离63米，中间栽树，两端不栽，每隔7米栽一棵，一共栽多少棵？________________________________________________________________________________________________________________________________3.两段围墙之间的通道长32米，两端围墙不摆放花盆，中间每隔4米摆一盆花，一共摆多少盆？________________________________________________________________________________________________________________________________4.两栋居民楼相距72米，中间栽桂花树，两端不栽，一共栽了8棵，相邻两棵树间距多少米？________________________________________________________________________________________________________________________________5.公园两处假山之间距离56米，中间栽花，两端不栽，每隔8米栽一盆，一共栽多少盆？________________________________________________________________________________________________________________________________6.街道两处路口之间长90米，中间安装路灯，两端路口不装，每隔10米装一盏，一共装多少盏？________________________________________________________________________________________________________________________________7.两个公交站台相距48米，中间种树，两端不栽，一共种了11棵树，树间距多少米？________________________________________________________________________________________________________________________________8.图书馆和食堂之间距离35米，中间摆绿植，两端不摆，每隔5米摆一盆，一共摆多少盆？________________________________________________________________________________________________________________________________9.两段护栏之间通道长66米，两端不栽树，中间每隔6米栽一棵，一共栽多少棵？________________________________________________________________________________________________________________________________10.两个花坛之间相距80米，中间栽冬青，两端不栽，一共栽了19丛，间距是多少米？________________________________________________________________________________________________________________________________第4天植树问题三类模型混合变式10题1.一条长90米的公路，一侧植树，两端都栽，每隔6米一棵，一共多少棵？________________________________________________________________________________________________________________________________2.两栋房子之间相距50米，中间种树，两端不栽，每隔5米一棵，一共多少棵？________________________________________________________________________________________________________________________________3.靠墙小路长70米，一端靠墙不栽树，一端栽树，每隔7米一棵，一共多少棵？________________________________________________________________________________________________________________________________4.笔直大道一侧两端都栽树，间距4米，共26棵，大道全长多少米？________________________________________________________________________________________________________________________________5.河边直道长64米，靠河一端不栽树，共栽8棵树，树间距多少米？________________________________________________________________________________________________________________________________6.两个亭子之间相距77米，中间摆石凳，两端不摆，每隔11米摆一张，一共摆几张？________________________________________________________________________________________________________________________________7.校园主干道长100米，一侧从头到尾插彩旗，每隔10米一面，一共多少面？________________________________________________________________________________________________________________________________8.围墙边通道长49米，一端围墙不栽花，共栽7盆花，花盆间距多少米？________________________________________________________________________________________________________________________________9.两堵墙之间距离84米，中间栽树，两端不栽，每隔7米一棵，一共多少棵？________________________________________________________________________________________________________________________________10.一条小路两端都栽树，共31棵，间距5米，小路总长多少米？________________________________________________________________________________________________________________________________第5天间隔问题专项（锯木头基础）10题核心规律：锯的次数=段数-1、总时间=单次时间×锯的次数1.一根木头锯成4段需要12分钟，照这样计算，锯成1段需要几分钟？锯成7段需要几分钟？________________________________________________________________________________________________________________________________2.一根木材锯成3段需要6分钟，锯成8段需要多少分钟？________________________________________________________________________________________________________________________________3.一根木棍锯成5段用了20分钟，单次锯木头需要几分钟？锯成6段需要多久？________________________________________________________________________________________________________________________________4.锯一根钢管，每锯一次需要3分钟，锯成9段需要多少分钟？________________________________________________________________________________________________________________________________5.一根木头锯成6段需要25分钟，锯成3段需要多少分钟？________________________________________________________________________________________________________________________________6.工人锯木料，锯一次需要4分钟，用28分钟可以把木料锯成几段？________________________________________________________________________________________________________________________________7.一根竹子锯成2段需要2分钟，锯成10段需要多少分钟？________________________________________________________________________________________________________________________________8.锯一根长木条，锯成4段用时15分钟，锯成5段需要多少分钟？________________________________________________________________________________________________________________________________9.师傅锯木头，30分钟把木头锯成7段，每锯一次需要几分钟？________________________________________________________________________________________________________________________________10.一根木材，锯一次需要5分钟，锯完一共用了35分钟，这根木材被锯成了几段？________________________________________________________________________________________________________________________________第6天间隔问题专项（爬楼梯基础）10题核心规律：爬的层数=终点楼层-起点楼层、总时间=单层时间×层数1.小明从1楼爬到4楼需要9分钟，照这样计算，从1楼爬到6楼需要几分钟？________________________________________________________________________________________________________________________________2.小红从1楼爬到3楼用了4分钟，她从1楼爬到8楼需要多少分钟？________________________________________________________________________________________________________________________________3.小刚爬楼梯，从2楼爬到5楼用了6分钟，从5楼爬到9楼需要几分钟？________________________________________________________________________________________________________________________________4.一栋楼房每层楼梯攀爬时间相同，从1楼爬到5楼需要12分钟，爬一层需要几分钟？________________________________________________________________________________________________________________________________5.小丽从1楼爬楼梯，每层用时2分钟，她爬到7楼一共需要多少分钟？________________________________________________________________________________________________________________________________6.小强从3楼爬到6楼用了9分钟，他从4楼爬到10楼需要多少分钟？________________________________________________________________________________________________________________________________7.小亮爬楼梯，从1楼到4楼用时8分钟，照这样速度，16分钟能从1楼爬到几楼？________________________________________________________________________________________________________________________________8.每层楼梯有18级台阶，小明从1楼爬到5楼，一共走了多少级台阶？________________________________________________________________________________________________________________________________9.小红从2楼爬到7楼，每层有20级台阶，她一共走了多少级台阶？________________________________________________________________________________________________________________________________10.小刚爬一层楼梯需要3分钟，他从1楼爬到9楼，一共需要多少分钟？________________________________________________________________________________________________________________________________第7天间隔问题专项（敲钟基础）10题核心规律：敲钟间隔数=敲钟次数-1、总时长=单次间隔时间×间隔数1.一座时钟3点敲3下，用时6秒，那么5点敲5下需要多少秒？________________________________________________________________________________________________________________________________2.钟表2点敲2下，3秒敲完，7点敲7下需要多少秒？________________________________________________________________________________________________________________________________3.广场大钟4点敲4下，9秒敲完，12点敲12下需要多少秒？________________________________________________________________________________________________________________________________4.闹钟5点敲5下，用时8秒，敲一下的间隔时间是多少秒？________________________________________________________________________________________________________________________________5.教学楼大钟6点敲6下，10秒敲完，9点敲9下需要多少秒？________________________________________________________________________________________________________________________________6.时钟敲4下用了12秒，按照这个速度，敲8下需要多少秒？________________________________________________________________________________________________________________________________7.寺庙大钟3点敲3下，4秒敲完，10点敲10下需要多少秒？________________________________________________________________________________________________________________________________8.钟表敲5下用时12秒，敲几下用时18秒？________________________________________________________________________________________________________________________________9.街头时钟7点敲7下，18秒敲完，4点敲4下需要多少秒？________________________________________________________________________________________________________________________________10.闹钟敲6下用15秒，间隔时间不变，敲10下需要多少秒？________________________________________________________________________________________________________________________________第8天间隔问题三大模型混合变式10题1.一根木头锯成5段需要16分钟，锯成9段需要多少分钟？________________________________________________________________________________________________________________________________2.小明从1楼爬到6楼用时10分钟，从1楼爬到10楼需要多少分钟？________________________________________________________________________________________________________________________________3.时钟4点敲4下，6秒敲完，8点敲8下需要多少秒？________________________________________________________________________________________________________________________________4.工人锯木料，锯一次需要6分钟，锯完共用42分钟，木料被锯成几段？________________________________________________________________________________________________________________________________5.小红从3楼爬到7楼走了80级台阶，每层台阶数相同，她从1楼爬到5楼走多少级台阶？________________________________________________________________________________________________________________________________6.大钟5点敲5下，12秒敲完，敲9下需要多少秒？________________________________________________________________________________________________________________________________7.一根木材锯成3段用时8分钟，锯成7段需要多少分钟？________________________________________________________________________________________________________________________________8.小亮爬楼梯，每层用时4分钟，从2楼爬到8楼需要多少分钟？________________________________________________________________________________________________________________________________9.时钟敲3下用5秒，敲12下需要多少秒？________________________________________________________________________________________________________________________________10.锯一根钢管，锯成6段需要20分钟，锯成4段需要多少分钟？________________________________________________________________________________________________________________________________第9天简化版鸡兔同笼专项（画图法入门）10题解题要求：全程使用画图法，先画头，再画腿，补全差额，禁止用方程1.笼子里有鸡和兔共8只，一共有22条腿，鸡和兔各有多少只？（答题空白+画图区）________________________________________________________________________________________________________________________________2.鸡兔同笼，共6个头，20条腿，鸡、兔各几只？（答题空白+画图区）________________________________________________________________________________________________________________________________3.笼子里鸡和兔一共10只，腿一共有28条，鸡和兔分别有多少只？（答题空白+画图区）________________________________________________________________________________________________________________________________4.鸡兔同笼，共9个头，26条腿，鸡、兔各有几只？（答题空白+画图区）________________________________________________________________________________________________________________________________5.笼子里有鸡和兔共7只，总腿数24条，鸡和兔各多少只？（答题空白+画图区）________________________________________________________________________________________________________________________________6.鸡兔同笼，共12个头，34条腿，鸡、兔各几只？（答题空白+画图区）________________________________________________________________________________________________________________________________7.笼子里鸡兔共5只，腿有16条，鸡和兔各有多少只？（答题空白+画图区）________________________________________________________________________________________________________________________________8.鸡兔同笼，共11个头，30条腿，鸡、兔各几只？（答题空白+画图区）________________________________________________________________________________________________________________________________9.笼子里鸡兔共13只，腿一共有36条，鸡和兔各多少只？（答题空白+画图区）________________________________________________________________________________________________________________________________10.鸡兔同笼，共4个头，14条腿，鸡、兔各几只？（答题空白+画图区）________________________________________________________________________________________________________________________________第10天简化版鸡兔同笼专项（列表法入门）10题解题要求：全程使用列表法，有序列举鸡和兔的数量，验证腿数，禁止用方程1.鸡兔同笼，共10个头，32条腿，鸡和兔各有多少只？（答题空白+列表区）________________________________________________________________________________________________________________________________2.笼子里鸡兔共14只，总腿数40条，鸡、兔各几只？（答题空白+列表区）________________________________________________________________________________________________________________________________3.鸡兔同笼，共8个头，26条腿，鸡和兔分别有多少只？（答题空白+列表区）________________________________________________________________________________________________________________________________4.笼子里鸡兔共15只，腿一共有42条，鸡、兔各几只？（答题空白+列表区）________________________________________________________________________________________________________________________________5.鸡兔同笼，共12个头，38条腿，鸡和兔各多少只？（答题空白+列表区）________________________________________________________________________________________________________________________________6.笼子里鸡兔共7只，腿22条，鸡、兔各几只？（答题空白+列表区）________________________________________________________________________________________________________________________________7.鸡兔同笼，共16个头，44条腿，鸡和兔各有多少只？（答题空白+列表区）________________________________________________________________________________________________________________________________8.笼子里鸡兔共9只，腿28条，鸡、兔各几只？（答题空白+列表区）________________________________________________________________________________________________________________________________9.鸡兔同笼，共18个头，50条腿，鸡和兔各多少只？（答题空白+列表区）________________________________________________________________________________________________________________________________10.笼子里鸡兔共6只，腿18条，鸡、兔各几只？（答题空白+列表区）________________________________________________________________________________________________________________________________第11天鸡兔同笼变式（生活拓展题）10题解题要求：沿用画图法、列表法，适配生活场景变式，无方程解题1.停车场有三轮车和小轿车共9辆，一共有32个轮子，三轮车和小轿车各有几辆？________________________________________________________________________________________________________________________________2.池塘里有鸭子和乌龟共11只，一共有34条腿，鸭子和乌龟各多少只？________________________________________________________________________________________________________________________________3.文具店有钢笔和圆珠笔共12支，钢笔5元一支，圆珠笔3元一支，总价46元，两种笔各有多少支？________________________________________________________________________________________________________________________________4.小区车位停电动车和汽车共10辆，总轮子数34个，电动车和汽车各几辆？________________________________________________________________________________________________________________________________5.农场有小鸡和小兔共13只，腿一共有38条，小鸡和小兔各多少只？________________________________________________________________________________________________________________________________6.玩具车有两轮摩托和四轮汽车共8辆，轮子共26个，两种玩具车各几辆？________________________________________________________________________________________________________________________________7.果园里有鸡和鹅共14只，总腿数36条，鸡和鹅各多少只？________________________________________________________________________________________________________________________________8.货架上有笔记本和练习本共15本，笔记本4元，练