汉宫洗浴首席搓澡师
范文一：鸡兔同笼问题方程解决
1.张大妈养鸡兔共200只，鸡兔足数共560只，求鸡兔各有多少只？
解：设___________________
2. 刘老师带了41名同学去北海公园划船，共租了10条船．每条大船坐6人，每条小船坐4人，问大船、小船各租几条？
解：设___________________
3. 自行车越野赛全程 220千米，全程被分为 20个路段，其中一部分路段长14千米，其余的长9千米．问：长9千米的路段有多少个？ 解：设___________________
4. 12张乒乓球台上共有34人在打球，问：正在进行单打和双打的台子各有几张？
解：设___________________
5.五年级（2）班50名同学栽树，男生一人栽3棵，女生一人栽2棵，总共栽树115棵，问几名男生，几名女生？
解：设___________________
6. 鸡、兔共笼，鸡比兔多26只，足数共274只，问鸡、兔各几只？
解：设___________________
7.鸡与兔共有110个头，但鸡的脚比兔的脚少20只，求鸡兔各有多少头？ 解：设___________________
8.某次数学竞赛共20道题，评分标准是：每做对一题得5分，每做错或不做一题扣1分．小华参加了这次竞赛，得了64分．问：小华做对几道题？
解：设___________________
9. 六年二班全体同学，植树节那
天共栽树180棵．平均每个男生栽5棵、每个女生栽3棵；又知女生比男
生多4人，该班男生和女生各多少人？
解：设___________________
10.乐乐百货商店委托搬运站运送500只花瓶，双方商定每只运费0．24元，但如果发生损坏，那么每打破一只不仅不给运费，而且还要赔偿1．26元，结果搬运站共得运费115．5元。问：搬运过程中共打破了几只花瓶? 解：设___________________
范文二：三步列表法解决鸡兔同笼问题
三步列表法? 解决鸡兔同?笼问题
陕西省西乡?县城北小学? 罗太银 邮编:72350?0 电话:15891?06702?6
在教学鸡兔?同笼时，我发现许多?学生对书上?的三种列表?方法掌握不?是很理想，不能正确利?用列表的方?法解决鸡兔?同笼问题，于是就有不?少教师给学?生讲解假设?法、列方程法、画图法等方?法，帮助学生来?解决鸡兔同?笼问题。我通过反复?思索，对书上的列?表法进行改?变，总结出了一?套三步列表?法，利用它来帮?助学生解决?鸡兔同笼问?题，收到了很好?的成效，现对三步列?表法解决鸡?兔同笼问题?与大家探讨?如下:
例:鸡兔同笼共?12个头，32条腿，鸡兔各有几?只,
鸡/只 1 2
兔/只 11 10
腿/条 46 44 32
1、先用逐一列?表的方式，计算出一只?鸡11只兔?的腿数，和2只鸡1?0只兔的腿?数，为第三步做?准备。通过第一、二步的计算?，我们发现了?兔子只数减?少一只时，腿数减少2?。
2、思考兔子要?减少多少只?，腿才能减少?到32条:44-32=12(条) 12?2=6 (只) ，这是我们可?以先把第三?步的腿数3?2填在表中?，这样上面计?算时的所有?数据，从表中就能?清楚找到:12?是与4432的差?，我们把它叫?做后差，2是46与?44的差，我们把它叫?做前差，6是后差与?前差的商。说明兔子要?减少6只，那么鸡就增?加6只，因此在第
三?步的表中，鸡数就是2?，6=8，兔子数就是?10,6=4，将6和4分?别填在第三?步的表中。如下表
鸡/只 1 2 8
兔/只 11 10 4
腿/条 46 44 32
我把上面这?种经过三步?的列表，求出鸡兔只?数的列表方?法称做“三步列表法?”。
三步列表的?口诀是:
一二计算找?规律，二差相除求?答案。
一二计算指?第一、第二步的计?算，通过计算找?出兔子减少?或增加1只?时，腿数的变化?规律。为了能准确?求出鸡兔只?数，在第一第二?步的表中鸡?兔只数最好?只增减1只?。
二差相除指?后差除以前?差，并用第二步?表中的鸡兔?数与商进行?相加减，求出答案。
在使用三步?列表法时，我建议最好?使用从1开?始的列表方?式，如果对表熟?练时，也可使用取?中列表法。
希望我的三?步列表法能?对大家解决?鸡兔同笼问?题有所帮助?。
范文三：解决鸡兔同笼问题的不同策略
用不同的策略解答“鸡兔同笼”的问题
解决“鸡兔同笼”问题的4种方法:
鸡兔同笼，有20个头，54条腿，鸡兔各多少只,
解题策略与答案的连接:
1.列表法................................................................................................................................................ 1 2.画图法................................................................................................................................................ 2 3.算术法................................................................................................................................................ 3
解法1: ......................................................................................................................................... 3
解法2: ......................................................................................................................................... 4 4.列方程................................................................................................................................................ 4
解法1: ......................................................................................................................................... 4
解法2: ......................................................................................................................................... 5
1.列表法
中分方式(各占一半)
头 / 个 鸡 / 只 兔 / 只 腿 / 条
20 10 10 60
20 11 9 58
20 12 8 56
20 13 7 54
答:鸡13只、兔7只。
备注:还有其他的方式解答，这里省略不写。
indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
2.画图法
(1)画出20个头 (2)每个头都有2条腿
(3)每个头再画2条腿，使得共有54条腿。
(4)数一数，鸡兔各有几只。(鸡:2条腿，兔:4条腿)
答:鸡13只、兔7只。
鸡兔同笼，有17个头，42条腿，鸡、兔各有几只,
画图的详细过程与答案:
第一步:用“?”表示头～共画出17个。
第二步:假设全都是“鸡”～即每个头都画2条腿。
,共有34条腿～少了8条腿,
indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
第三步:每个头再画2条腿～画了4个刚好42条腿。
第四步:数一数～鸡、兔各有几只。,鸡13只、兔4只,
第五步:写出答句。,略,
3.算术法
解法1:
假设全是鸡，先求出兔有几只。(即鸡20只，兔0只:腿数少了，增加兔的数量。)
(1)分步列式解答:
20只鸡共有几条腿:2×20 = 40(条)
比实际少了几条腿:54,40 = 14(条)
每只鸡比每只兔少几条腿:4,2 = 2(条)
共有兔几只:14?2 = 7(只) 鸡:20,7 = 13(只)
(2)综合算式解答:
兔:(54,2×20)?(4,2) 鸡:20,7 = 13(只)
= 14?2
indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
= 7(只)
答:鸡13只、兔7只。
解法2:
假设全是兔，先求出鸡有几只。(即鸡0只，兔20只:腿数多了，
减少兔的数量。)
(1)分步列式解答:(略)
(2)综合算式解答:
鸡:(4×20,54)?(4,2) 兔:20,13 = 7(只)
= 26?2,
= 13(只)
答:鸡13只、兔7只。
4.列方程
解法1:
解:设鸡有x只，兔有(20-x)只。 2x + (20 - x)×4 = 54
2x + 80 – 4 x = 54
80 – 2x = 54
2x = 26
x = 26?2
x = 13 20-x = 20 – 13 = 7
indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
答:鸡13只、兔7只。
解法2:
解:设兔有x只，鸡有(20-x)只。
4x + (20 - x)×2 = 54
4x + 40 – 2 x = 54
40 + 2x = 54
2x = 14
x = 14?2
x = 7
20-x = 20 – 7 = 13
答:鸡13只、兔7只。
类似的“鸡兔同笼”问题
请利用表格解答下列各题
第1题(鸡兔同笼)
1.鸡兔同笼，有17个头，42条腿，鸡、兔各有几只,
头 / 个 鸡 / 只 兔 / 只 腿 / 条
? ? ? ?
第2题(类似“鸡兔同笼”)
2.小明的储蓄罐里有1角和5角的硬币共27枚，价值5.1元，indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
1角和5角的硬币各有多少枚,
硬币总数 / 1角 / 枚 5角 / 枚 总价值 / 元
枚
? ? ? ?
第3题(类似“鸡兔同笼”)
3.用大小卡车往城市运29吨蔬菜，大卡车每辆每次运5吨，小卡车每辆每次运3吨，大小卡车各用几辆能一次运完,
大卡车 / 辆 小卡车 / 辆 总质量 / 吨
? ? ?
1.鸡兔同笼～有17个头～42条腿～鸡、兔各有几只,
2.小明的储蓄罐里有1角和5角的硬币共27枚～价值5.1元～1角和5角的硬币各有多少枚,
3.用大小卡车往城市运29吨蔬菜～大卡车每indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
辆每次运5吨～小卡车每辆每次运3吨～大小卡车
各用几辆能一次运完,
indicate the direction of the arrow mark; a variety of emergency lights, emergency response time of not less than 45min. 5. protective grounding (1) electrical equipment for metal housings, metal frame, metal wiring pipes and accessories, cable protection tubes, metal sheath of the cable, such as charged bare metal parts shall be grounded or neutral. (2) electrical equipment and fittings of dedicated ground wire should be singled out and grounding line or the zero connection protection line (network) connected to electrical wiring work in the zero line should not be used as protective earthing wire. (3) electrical equipment and earthing connection, use multiple soft stranded wire, their copper wire minimum area shall not be less than 4mm2, vulnerable to mechanical damage of parts should be installed in protection tubes. (4) electrical device for armored cable and ground or neutral wire should be connected to the equipment grounding bolts inside, steel and metal casing should be connected to the equipment grounding bolt. (5) grounding bolts should have a locking device or petty, before fastening the grounding line, on its ground terminal and ... Project organization. Project organization is composed of three layers: the core layer, management and operational level. 1. core layer: formed by the project manager, Assistant Project Manager, responsible for construction work, materials and equipment, management and coordination. 2. Management: engineering, technology, finance and budget
范文四：三步列表法 解决鸡兔同笼问题
三步列表法 解决鸡兔同笼问题
陕西省西乡县城北小学 罗太银 邮编：723500 电话：15891067026
在教学鸡兔同笼时，我发现许多学生对书上的三种列表方法掌握不是很理想，不能正确利用列表的方法解决鸡兔同笼问题，于是就有不少教师给学生讲解假设法、列方程法、画图法等方法，帮助学生来解决鸡兔同笼问题。我通过反复思索，对书上的列表法进行改变，总结出了一套三步列表法，利用它来帮助学生解决鸡兔同笼问题，收到了很好的成效，现对三步列表法解决鸡兔同笼问题与大家探讨如下：
例：鸡兔同笼共12个头，32条腿，鸡兔各有几只？
1、先用逐一列表的方式，计算出一只鸡11只兔的腿数，和2只鸡10只兔的腿数，为第三步做准备。通过第一、二步的计算，我们发现了兔子只数减少一只时，腿数减少2。
2、思考兔子要减少多少只，腿才能减少到32条：44-32=12（条） 12÷2=6 （只） ，这是我们可以先把第三步的腿数32填在表中，这样上面计算时的所有数据，从表中就能清楚找到：12是44与32的差，我们把它叫做后差，2是46与44的差，我们把它叫做前差，6是后差与前差的商。说明兔子要减少6只，那么鸡就增加6只，因此
在第三步的表中，鸡数就是2＋6=8，兔子数就是10－6=4，将6和4分别填在第三步的表中。如下表
我把上面这种经过三步的列表，求出鸡兔只数的列表方法称做“三步列表法”。
三步列表的口诀是：
一二计算找规律，二差相除求答案。
一二计算指第一、第二步的计算，通过计算找出兔子减少或增加1只时，腿数的变化规律。为了能准确求出鸡兔只数，在第一第二步的表中鸡兔只数最好只增减1只。
二差相除指后差除以前差，并用第二步表中的鸡兔数与商进行相加减，求出答案。
在使用三步列表法时，我建议最好使用从1开始的列表方式，如果对表熟练时，也可使用取中列表法。
希望我的三步列表法能对大家解决鸡兔同笼问题有所帮助。
范文五：假设法解决鸡兔同笼问题
鸡兔同笼——假设法解题
140例1鸡兔同笼
一只笼子里关着8只鸡和5只兔，它们一共有几个头和几条腿？
跟我来!
动手画图数一数，算一算。
5个5个的数头：5，10，13，共计13个头。
2条2条的数鸡腿数：2，4，6，8，10，12，14，16，共计16条腿；
4条4条的数兔腿数：4，8，12，16，20，共计20条腿。
鸡兔共有：16?+?20?=?36(条)腿。
名师点拔:?让孩子了解一只健全的鸡兔各有几条腿；
学会2倍数、4倍数和5倍数快速数数。
画图解题精习：
画图解题精习1：
1.?草地上有10只小鸟和6只松鼠，它们一共有几个头和几条腿？
2.小明和妈妈看到马路上一共开过4辆轿车，6辆摩托车和5辆三轮车，一共有多少只轮子？
3.?笑笑喜欢画画，他在纸上画了6个三角形，5个长方形，3个正五边形。你知道知笑笑一共画了多少个多边形吗？这些多边形共有多少个角？
例题2?鸡兔同笼
例题：鸡、兔关在同一笼子里，共有12个头，32条腿，笼里有几只鸡？几只兔？
跟我来！
画图第一步：
将12只全看成鸡，数鸡腿:2,4,6,8,10,12,14,16,18,20,22,24，共计24条腿。
比题中32条腿少算：32?-?24?=?8条腿。
画图第一步：
将少算的8条腿，2条2条的分别加在鸡身上：2+2+2+2=8条，共加得4只兔。
鸡的只数：12?-?4?=?8只。
名师点拔：
假设法是解决一些思考题的一种重要方法。
低年级孩子做此类题，不限于严格的写具体算式。在写写画画中弄明白道就行，目的是培养孩子的动手动脑探究问题的良好习惯。
画图精习四：
1.?小红家共养鸡和狗共9只，共有26条腿，鸡有几只？狗有几只？
画图第一步：
假设___只全是鸡，数鸡腿：_________________________________，共计___条腿。
比题中___条腿少算：_________________条腿。
画图第二步:
将少算的___条腿，2条2条的分别加在鸡身上：_________________条，共加得___只兔。
鸡的只数：_________________。
2.?鸡、兔关在一个笼子里，共有11个头，28条腿，有几只鸡？?几只兔？
画图第一步：
假设___只全是鸡，数鸡腿：_________________________________，共计___条腿。
比题中___条腿少算：_________________条腿。
画图第二步:
将少算的___条腿，2条2条的分别加在鸡身上：_________________条，共加得___只兔。
鸡的只数：_________________。
3.?鸡兔同笼，共有12个头，34条腿，有几只鸡？?几只兔？（参1，2题画图解题）
例题3?鸡兔同笼。
一只蛐蛐6条腿，一只蜘蛛8条腿。有蛐蛐和蜘蛛共10只，共68条腿，蛐蛐和蜘蛛各有多少只？
跟我来！
方式一：列数分析。
将10只昆虫全看成蛐蛐：6，12，18，24，36，42，48，54，60，共计有60条腿。
少算：68?-?60?=?8(条）腿。
将少算的8条腿，2条2条加到蛐蛐身上：2+2+2+2?=?8（条）
有4只蛐蛐变成蜘蛛。
蛐蛐的只数：10?-?4?=?6（只）
名师点拔：些类题看起来较复杂，如果动手动脑边阅题边写写画画，列数呀，画图呀，解决问题的?思路就清晰可见。
画图精习三：
1.?一辆小轿车有4个轮子，一辆小卡车有6个轮子，车棚里放着小轿车和小卡车共9辆，共56个轮子。小轿车、小卡车各有多少辆？
画图第一步:
假设全是小轿车,数轮子:________________________________共计___个轮子。
少算：________________个轮子。
画图第二步：
将少算的___个轮子,两个两个添加到小轿车上:____________个，共加得___辆小卡车。
小轿车：________________(辆)
2.一只蛐蛐6条腿，一只蜘蛛8条腿，蛐蛐和蜘蛛共8只，54条腿，蛐蛐和蜘蛛各几只？
画图第一步:
假设全是蛐蛐，数蛐蛐腿:________________________________共计___条腿。
少算：________________（条）腿。
画图第二步：
将少算的6条腿加在蛐蛐的身上：________________（条），蜘蛛有___只。
蛐蛐：_______________(只)
例4?鸡兔同笼
小明在桌了摆了12个白棋子，每2个白棋子插入3个黑棋子，共可插入多少个黑棋子?
跟我来!
画图第一步：
小明在桌了摆了____个白棋子。
___个白棋子，2个2个的组合，有___个组合，_______________个）间隔。
画图第二步:
每2个白棋子插入3个黑棋子。
___个间隔，能摆放下5组3个黑棋子：_______________________共计___个黑棋子。
画图精习四：
1.?小强在地上一字排开摆了12块方积木，如果他每隔3个方积木插入4块三角积木，共可插多少块三角积木?
画图第一步：
小强在地上一字排开摆了12块方积木。
___块方积木，3块3块组合，有___个组合，________________（个）间隔。
画图第二步：
每隔___个方积木插入___块三角积木。
____个间隔，能摆放下3组4块三角形方积木：______________，共计____块。
2.?在学校花坛的四周摆了12盆兰花，每三盆兰花之间摆4盆仙人球。问一共要摆多少仙人球？
画图第一步:___盆兰花3分盆一摆放在花坛边，共有___个组合，___个间隔。
画图解题二：___个间隔，可摆仙人球：________________，共计___盆。
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