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一、填空题。
1.把下面的“成数”改写成百分数。
五成( )、七成( )、三成五( )、十成( )
2.把下面的百分数改写成“成数”
30,( ) 45,( ) 10,( ) 95,( )
3.利息=( )×( )×( )
4.30千克是50千克的( ,)，50千克是30千克的( ,)
5.5吨比8吨少( ,)，8吨比5吨多( ,)。
6.540米是( )米的20,。
7.( )公顷的25,是20公顷。
二、判断题。(对的画“?”，错的画“×”)
1.利息和本金的比率叫利率。 ( )
2.一块地的产量，今年比去年增长二成五，就是增长十分之二点五。 ( )
3.一种药水，水和药的比是1?20，水占药水的5,。 ( )
( )
三、选择题。(把正确答案的序号填在括号里)
1.半成改写成百分数是 ( )
A.50,
B.0.5,
C.5,
2.一块地原产小麦25吨，去年因水灾减产二成，今年又增产二成。这样今年产量和原产量比 ( )
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
A.增加了
B.减少了
C.没变
3.小英把 1000元按年利率2.45,存入银行。两年后计算她应得到的本金和利息，列式应是 ( )
A.1000×2.45,×2
B.(1000×2.45,+1000)×2
C.1000×2.45,×2+1000
四、计算题。
五、应用题。
1.一块小麦实验田，去年产小麦24.5吨，今年增产了二成。这块实验田今年产小麦多少吨,
2.一块地，去年产水稻12吨，因水灾比前年减少二成五。这块地前年产水稻多少吨,
3.李英把5000元人民币存入银行，定期1年，年利率是2.25,。到期时，李英应得利息多少元,
4.王钢把10000元人民币存入银行，定期3年，年利率是2.7,。到期时，王钢应得本金和利息一共多少元,
5.一块棉花地，去年收皮棉30吨，比前年增产了5吨。这块棉花地皮棉产量增长了几成,
6.一个养殖场，养鸭的只数比养鸡的只数少20,，养的鸡比鸭多1000只。这个养殖场养鸭多少只,
相遇。甲车每小时的速度是85千米，乙车的速度是甲车的120,。A、B两地相距多少千米,
*8.张晶在银行存了30000元人民币，定期五年，年利率是2.88,。到期时交纳利息所得税20,后，银行应付给张晶本金和利息一共多少元,(选作)
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
一、填写( )的内容。 1.
表
关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf
示两个比相等的式子叫做( )。
2.0.32?1.6化成最简单的整数比是( )，比值是( )，根据这个比值组成一个比例式另一个比是( )，比例式是( )。
10和60，这个比例是( )。
4.被减数是72，减数和差的比是4?5，减数是( )
5.因为a×b=c，当a一定时，b和c( )比例。
当b一定时，a和c( )比例。
当c一定时，a和b( )比例。
6.用20的约数组成一个比例式是( )。
一个外项是( )，这个比例式是( )。
应画( )厘米。
9.在绘画时，要把实际距离缩小500倍，使用的比例尺应该是( )。
二、分析判断。(对的画“?”，错的画“×”)
1.一般地图上用的比例尺是缩小比例尺。 ( )
2.圆的直径和它的面积成正比例。 ( )
3.y=5x，x和y成反比例。 ( )
4.数a与数b的比是5?8，数a是75，数b是120。 ( ) accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
( )
三、分析选择。将正确答案的序号填在( )里。
1.甲乙两个圆半径的比是2?1，那么甲和乙两个圆的面积的比是 ( )
(1)4?1
(2)2?1
(3)4?2
2.把一个圆柱体加工成一个与它等底等高的圆锥体，圆柱的体积与去掉部分的
) 体积的比是 (
(1)3?1
(2)3?2
(3)2?3
3.在一个比例式中，两个比的比值都等于3，这个比例式可以是 ( )
(1)3?1=1?3
(2)3?1=0.3?0.1
(3)9?3=3?1
4.修一条路，已修的是未修的80,，已修的与未修的比是 ? ( )
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
(1)80?100
(2) 4?5
(3)10?8
刘师傅现在与过去工作效率的比是 ( )
(2) 1?3
(3) 3?1
四、观察分析。
1.将下面的等式改写成比例式。
(1) 10.2×9=1.8×51
(3)51×7=17×21
(4)62a=47b
2.认真观察下面每题的解是否正确,对的画“?”，错的改正过来。
(1)15.6?2.8=2.4?x
五、说说下面各题的两种相关联的量是成正比例，还是成反比例。写出说理过
程。
1.小麦的重量一定，面粉和出粉率。
2.图上距离一定，比例尺和实际距离。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
3.先判断，再填空。
3a=b a和b成( )比例。
六、选择正确算式，并说出理由。
1.一辆汽车从甲地开往乙地，每小时行驶28千米，4.5小时到达，要4小时到达，每小时要多行几千米,
(1)28×4.5?4,28
(2)解:设每小时多行x千米。
28×4.5=(28+x)×4
(3)解:设每小时多行x千米。
28×4.5=28×4+x
(4)28,28×4.5?4
2.东风洗染厂，每天用水量比过去节约20,，原有390吨水，现在比过去多用30天，现在每天用水多少吨,
(1)390×(1,20,)?30
(2)解:设现在每天用水x吨。
390×20,=30x
(3)解:设过去用x天，则现在用(x+30)天。 accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
390?(120，30)=2.6(吨)
(4) 390×20,?30
七、解决下面的实际问题。
1.一幅地图用0.6厘米表示实际距离30千米，求这幅地图的比例尺。用线段比例尺表示出来。
2.张庄和王村相距960千米，要在两村间修筑一条笔直的马路，画在
设计
领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计
图上的距离是
这幅设计图的比例尺是多少,
这样可以提前几天完成,(用三种你认为简捷的方法解答)
4.一块平行四边形菜地，底与高的和是150米，它们的比是3?2，求这块菜地的面积是多少平方米,
*5.甲乙两地相距800千米，A、B两辆汽车分别从两地同时相向而行，已知A、B两车速度比是6?5，当两车相遇时，两车各行多少千米,(用三种方法解答)
参考答案
一、
1.比例
3.10?30=20?60
4.32
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
5.正正反
二、1.? 2.× 3.× 4.? 5.?
三、1.(1) 2.(2) 3.(2) (3) 4.(2) 5.(3)
2.(1)× (2)? (3)? (4)×
五、1.正比例 2.反比例 3.正(表略)
六、
1.(1) (2)
2.(2) (3) (4)
七、
1.
2.1?19200000
3.方法1 30,8?5=10(天)
方法3 解:设实际x天完成。(把一份稿件看为“1”)
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
一、将正确答案填在( )里。
1.从圆锥的( )到( )的距离是圆锥的高，圆锥有( )条高。
2.圆柱的体积是( )的圆锥体积的3倍，所以圆锥体积的公式是( )。
3.把4个同样大小的圆柱，熔铸成等底等高的圆锥，能熔铸( )个。
4.一个圆柱的体积是60立方厘米，和它等底等高的圆锥的体积是( )。
5.把一段圆柱形圆木，加工成等底等高的圆锥体，削去部分体积是圆柱体积的( )，是圆锥的( )。
6.用一张长是25.12厘米，宽3.14厘米的长方形厚纸板围成直圆柱，有( )种围法;其中一种围成的圆柱的高是( )厘米，直径是( )厘米;另一种围的圆柱的高是( )厘米，直径是( )厘米。
二、观察思考下面的解题过程和结果，是否正确,
1.一根圆柱形水管，内直径20厘米，水流的速度是每秒4米，这个水管1分钟可以流过多少立方米的水,
解:(1)圆柱形水管的底面积
(2)圆柱形水管的容积(4米相当圆柱的高)
314×400=125600(立方厘米)
(3)1分钟可以流过多少水
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
125600×60=7536000(立方厘米)
7536000立方厘米=7.536立方米
答:这个水管1分钟可以流过7.536立方米水。
2.有一根长20厘米，半径为2厘米的圆钢，在它的两端各钻了一个深为4厘米，底面半径为2厘米的圆锥形小孔做成一个零件，如图这个零件的体积是多少立方厘米,
解:(1)圆柱的底面积
2×2×3.14=12.56(平方厘米)
2)圆柱的体积 (
12.56×20=251.2(立方厘米)
(3)圆锥形小孔的体积
12.56×4=50.24(立方厘米)
(4)零件的体积
251.2,50.24=200.96(立方厘米)
答:这个零件的体积是200.96立方厘米。
3.一个高3分米，底面直径为20厘米的圆柱形水桶里装满水，水中放着一个底面直径为18厘米，高为15厘米的铁质圆锥体，当这个铁质圆锥体取出后，会发生怎样的变化,结果如何,
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
解:当这个铁质圆锥体取出后，桶内水面要降低，因为这个物体原来占据了一些空间，结果怎样，就要先求圆锥体的体积，再求变化的结果。
(1)圆锥的底面积
(2)圆柱的底面积
(3)圆锥的体积
(4)水面降低的米数
1271.7?314=4.05(厘米)
三、综合运用知识解决实际问题。
1.有A、B两个容器，如图，先把A容器装满水，然后将水倒入B容器，B容器中水的深度是多少厘米,
*2.如右图，是一个棱长为4分米的正方体零件，它的上、下、左、右面上各有一个半径为2厘米的圆孔，孔深为1分米，这个零件的表面积是多少,体积是多少,
*3.把一个直径是2分米的圆柱的底面分成许多相等的扇形，然后沿直径把圆切开，拼成一个和它体积相等的长方体，这个长方体表面积比原来圆柱的表面积增加8平方分米，这个长方体的体积是多少,
*4.如图，这顶帽子，帽顶部分是圆柱形，用花布做的，帽沿部分是一个圆环，也是用同样花布做，已知帽顶的半径，高和帽沿宽都是1分米，那么做这顶帽子至少要用多少平方分米的花布,
*5.把一个长7厘米，宽6厘米，高4.5厘米的长方体铁块和一个棱长5厘米的正方体的铁块，熔铸成一个大圆柱体，这个圆柱体的底面积是78.5平方厘米，那圆柱的高应是多少厘米,
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
参考答案
一、
1.顶点 底面圆心 1。
3.12
4.20立方厘米
6.2，25.12厘米，1厘米，3.14厘米，8厘米
二、1.正确 2.错误 3.正确
2.提示:正方体零件的表面积增加了4个小圆柱的侧面积。正方体零件的体积减少了4个小圆柱的体积。
表面积:4×4×6×100，3.14×2×2×10×4=10102.4(平方厘米)
体积:4×4×4×1000,2×2×3.14×10×4=63497.6(立方厘米)
3.提示:表面积增加8平方分米，实际是两个以半径为宽，高为长的长方形。
8?2?(2?2)=4(分米)高
3.14×(2?2)2×4=12.56(立方厘米)或
8?2×3.14×2?2=12.56(立方厘米)
4.18.84平方分米
5.4厘米
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
小升初数学总复习(五)
——比例的意义和基本性质
主要内容
比例的意义和基本性质
学习目标
1、使学生初步理解图形的放大和缩小，能利用方格纸按一定比例将简单图形放大或缩小，初步体会图形的相似，进一步发展空间观念。
2、使学生联系图形的放大和缩小理解比例的意义和作用，认识比例的“项”、“内项”和“外项”;理解并掌握比例的基本性质，会应用比例的基本性质解比例。
3、使学生在认识比例、应用比例的过程中，进一步体会不同领域数学内容的内在联系，增强用数和图形描述现实问题的意义和能力，丰富解决问题的策略，发展对数学的积极情感。
考点分析
1、把一个图形按一定比放大或缩小，就是把它的每条边按一定的比放大或缩小。
2、表示两个比相等的式子叫做比例。
3、组成比例的四个数，叫做比例的项。两端的两项叫做比例的外项，中间的两项叫做比例的内项。
4、在比例里，两个外项的积等于两个内项的积。这叫做比例的基本性质。 accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
5、根据比例的基本性质，如果已知比例中的任意三项，就可以求出这个比例中的另一个未知项。求比例的未知项，叫做解比例。
典型例题
例1、(把图形按某个比相应放大或缩小，形状没有改变，只是大小变了)
(1)长方形A的长是1.5厘米，宽是1厘米;长方形B的长是3厘米，宽是2厘米。这两个长方形的长有什么关系?宽呢?
(2)如果要把长方形A按 1:2的比缩小，长和宽应是原来的几分之几?各是多少?
分析与解:
(1)长方形B的长是长方形A的2倍，宽也是长方形A的2倍。或者说长方形B和长方形A长的比是2:1，宽的比也是2:1。
把长方形的每条边放大到原来的2倍，放大后的长方形的长和宽与原来长方形的比是2:1，就是把长方形A的长和宽按2:1的比进行放大。
由此可见，放大或缩小前后图形形状没有改变，还是长方形，只是大小变了。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
例2、(根据指定的比，将图形按要求放大或缩小)
先按3:2的比画出长方形A放大后的图形B，再按1:2的比画出长方形A缩小后的图形C。(1)图B的长、宽各是几格? (2)图C呢? (3)观察这三幅图形，你有什么发现?
点评:按比例放大图形或缩小图形，关键是要先根据比确定是放大还是缩小，然后确定好每条边的长度，画出图形就行了。
例3、(将两个相等比写成一个等式)
图B是由图A放大后得到的，你能分别写出这两幅图中各自的长与宽的比吗?比较写出的两个比，你有什么发现?
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
点评:像这样的比例一共可以写8个。但它们不变的是2和7要么同时为
内项，要么同时为外项，而1.4和10这一组数也一样。写的时候可以一组一组地写
了。
例7、(按比例放大的含义)
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
王叔叔在电脑上将下面的图片按比例放大，放大后的图片的长是12.5厘米，你有什么发现?
分析与解:按比例放大就是把原图形中的各部分线段都按相同的比放大，放大前后的相关线段的厘米数是可以组成比例的。两张图片长的比与宽的比可以组成比例，两张图片中各自长、宽的比也可以组成比例。
例8、(解比例)上图中宽是多少厘米?
分析与解:在解比例时，根据比例的基本性质把比例转化为积相等的式子，然后再根据等式的性质来解答。
解:设宽是?厘米。
答:放大后图片的宽是10厘米。
点评:像上面这样求比例中的未知项，叫做解比例。
小学数学总复习专题讲解及训练(六)
主要内容
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
比例尺、面积变化、确定位置
学习目标
1、使学生在具体情境中理解比例尺的意义，能看懂线段比例尺。会求一幅图的比例尺，能按给定的比例尺求相应的实际距离或图上距离，会把数值比例尺与线段比例尺进行转化。
2、使学生在经历“猜想-验证”的过程中，自主发现平面图形按比例放大后面积的变化规律。
3、在解决问题的过程中，进一步体会比例以及比例尺的应用价值，感知不同领域数学内容的内在联系，增强用数和图形描述现实问题的意识和能力，丰富解决问题的策略。
4、使学生在具体情境中初步理解北偏东(西)、南偏东(西)的含义，初步掌握用方向和距离确定物体位置的方法，能根据给定方向和距离在平面图上确定物体的位置或描述简单的行走路线。
5、使学生在用方向和距离确定物体位置的过程中，进一步培养观察能力、识图能力和有条理的进行表达的能力。发展空间观念。
6、使学生积极参与观察、测量、画图、交流等活动，获得成功的体验，体会数学知识与生活实际的联系，拓展知识视野，激发学习兴趣。
考点分析
1、图上距离和实际距离的比，叫做这幅图的比例尺。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
4、知道 了物体的方向和距离，就能确定物体的位置。
5、根据物体的位置，结合比例尺的相关知识，可以在平面图上画出物体的位置。画的时候先按方向画一条射线，在根据图上距离找出点所在的位置。
6、描述行走路线要依次逐段地说，每一段都应说出行走的方向与路程。
典型例题:
例1、(认识比例尺)
王伯伯家有一块长方形的菜地，长40米，宽30米。把这块菜地按一定的比例缩小，画在平面图上长4厘米，宽3厘米。你能分别写出菜地长、宽的图上距离和实际距离的比吗?
分析与解:图上距离和实际距离的单位不同，先要统一成相同的单位，写出比后再化简。
点评:求一幅地图的比例尺是一种比较简单的题目。做的时候唯一要注意的就是末尾0的问题:一是米、千米化成厘米的时候要在米、千米那个数的末尾加上2、5个0;二是在求比例尺的结果时要注意0的个数。多数一数、想一想，是不会有错的。
例2、(对比例尺的理解及比例尺的两种表示方法)
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
比例尺1:1000表示图上距离是实际距离的几分之几?实际距离是图上距离的多少倍?图上1厘米表示实际距离多少米?
例3、一个手表零件长2毫米，画在一幅图上长4厘米，这幅图的比例尺是多少?
错误解法:4厘米 = 40毫米 2 : 40 = 1 : 20
思路分析:无论什么样的图纸，比例尺始终是图上距离与实际距离的比，根据比例尺的定义，用“图上距离 : 实际距离 = 比例尺”去求。
正确解答:4厘米 = 40毫米 40 : 2 = 20 : 1
点评:比例尺通常情况下都应该写成前项是1的比。但比例尺的作用除了把实际距离缩小，还可以把实际距离扩大，这样比例尺的前项就比后项大，这时后项通常化成1。在解答时，只要坚持好“图上距离 : 实际距离 = 比例尺”，图上距离在前就可以了。
例4、(根据比例尺求图上距离或实际距离)
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
例5、(平面图形按照一定的比放大后，面积扩大了比的平方倍)
下面的大长方形是由一个小长方形按比例放大后得到的图形。分别量出它
们的长和宽，算算大长方形与小长方形面积的比是几比几。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
例6、(认识北偏东(西)若干度、南偏东(西)若干度等方向)
如图，一辆汽车向正北方向行驶，你能说出商场和书店分别在汽车的什么方向吗?
分析与解:从图上可以看出，以汽车为中心，书店在汽车的东北方向，商场在汽车的西北方向。
怎样才能更准确地表示它们的位置呢?
东北方向也叫做北偏东方向，书店在汽车的北偏东60º方向。
西北方向也叫做北偏西方向，商场在汽车的北偏西45º方向。
答:书店在汽车的北偏东60º方向，商场在汽车的北偏西45º方向。
例7、(知道了物体的方向和距离，才能确定物体的具体位置)
量出上图中书店到汽车的图上距离，根据比例尺算一算，书店在汽车北偏东60º方向的多少千米处?商场呢?
分析与解:从图中量得书店和商场到汽车的图上距离分别是1.2厘米和2.3厘米，根据比例尺，图上距离1厘米代表实际距离3千米，分别算出实际距离。
1.2 × 3 = 3.6(千米)???书店
2.3 × 3 = 6.9(千米)???商场
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
答:书店在汽车北偏东60º方向的3.6千米处，商场在汽车北偏西45º方向的6.9千米处。
点评:只有在方向词的后面添上角的度数，才能准确描述物体所在的位置。确定方向时，一定要先确定好南或北，再看是偏东还是偏西，如果图中没有画线，要先连线。算实际距离就根据前面比例尺的相关知识去求。
例8、(辨析)书店在汽车的北偏东60º方向，表示汽车也在书店的北偏东60º方向。
分析与解:书店在汽车的北偏东60º方向，是以汽车为中心，由北向东旋转60º;而以书店为中心，汽车在书店的西南方向，即南偏西60º方向。
书店在汽车的北偏东60º方向，表示汽车在书店的南偏西60º方向。
例9、(根据给定的方向和距离，有序地确定物体的具体位置)
海面上有一座灯塔，灯塔北偏西30º方向30千米处是凤凰岛。
你能在图上指出凤凰岛大约在什么位置吗?
分析与解:
(1)先确定北偏西30º的方向，画一条射线。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
(2)再算出灯塔到凤凰岛的图上距离是多少厘米。
30 ? 10 = 3(厘米)
点评:在表示凤凰岛的具体位置时，先要画出表示方向的射线，再确定灯塔到凤凰岛的图上距离。且在画表示方向的射线时，应从表示灯塔的点开始画起，并注意正确摆好量角器。
例10、(用方向和距离描述简单的行走路线)
下图是某市旅游1号车行驶的线路图，请根据线路图填空。
(1)旅游1号车从起点站出发，向( )行驶到达青水公园，再向( )偏( )( )的方向行( )千米到达抗战纪念碑。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
(2)由绿博园向南偏( )( )的方向行( )千米到达购物中心，再向北偏( )( )的方向行( )千米到达人民公园。
分析与解:先找准方向，再说出具体的路程。(1)旅游1号车从起点站出发，向( 东 )行驶到达青水公园，再向( 北 )偏(东)(40º)的方向行(1.8 )千米到达抗战纪念碑。
(2)由绿博园向南偏(东)(60º)的方向行(1.7)千米到达购物中心，再向北偏( 东 )
(70º)的方向行(1.5)千米到达人民公园。
点评:在进行描述的时候，一定要先说清楚方向再说路程。说方向的时候为了说清楚，通常情况下不用东北、西北、东南、西南等说法，而用南偏东、南偏西、北偏东、北偏西多少度的说法更为准确。
小学数学总复习专题讲解及训练(七)
主要内容
正比例和反比例
学习目标
1、使学生结合实际情境认识成正比例和反比例的量，能根据正、反比例的意义判断两种相关联的量是否成正比例或反比例。
2、使学生初步认识正比例的图像是一条直线，能利用给出的具有正比例关系的数据在方格纸上画出相应的直线，能根据具有正比例关系的一个量的数值看图估计另一个量的数值。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
3、使学生在认识成正比例、反比例的量的过程中，初步体会数量之间相依互变的关系，感受有效表示数量关系及其变化规律的不同数学模型，进一步提升思维水平。
4、使学生进一步体会数学与日常生活的密切联系，增强探索数学知识和规律的意识，养成积极主动地参与学习活动的习惯，提高学好数学的信心。
考点分析
1、两种相关联的量，一种量变化，另一种量也随着变化。如果这两种量中相对应的两个数的比的比值(也就是商)一定，这两种量就叫做成正比例的量，它们之间的关系叫做正比例关系。
如果用字母x和y分别表示两种相关联的量，用k表示它们的比值，正比例关系可以用这样的式子来表示:= K(一定)。
2、用“描点法”可以得到正比例的图像，正比例的图像是一条直线。对照图像，能根据一种量的值，估计另一种量相对应的值。
3、两种相关联的量，一种量变化，另一种量也随着变化。如果这两种量中相对应的两个数的乘积一定，这两种量就叫做成反比例的量，它们之间的关系叫做反比例关系。
如果用字母x和y分别表示两种相关联的量，用k表示它们的积，反比例关系可以用这样的式子来表示:xy = K(一定)。
4、两个变量的比值一定，这两个变量成正比例;两个变量的积一定，这两个变量成反比例;没有上述两种关系，这两个变量不成比例。
典型例题
例1、(正比例的意义)一列火车行驶的时间和路程如下表。这两种量有什么关系?
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
分析与解:
(1)从上表可以看出，表中有时间和路程两种量。
(2)从左往右看，时间扩大，路程也扩大;从右往左看，时间缩小，路程也缩小。所以它们是两种相关联的量。
(3)路程和时间的比值始终不变，„„这个比值就是火车的行驶速度。
通过观察和计算，我们对路程和时间的关系有两点发现:第一点路程和时间是两种相关联的量，也就是时间变化，路程也随着变化;第二点路程和对应的时间的比的比值(也就是速度)是一定的，有这样的关系:
具备了这两个条件，我们就可以得到结论:行驶的路程和时间成正比例关系;行驶的路程和时间成正比例的量。
点评:判断两种量是不是成正比例，分三步:一看它们是不是相关联的两种量;二是看一种量变化，另一种量是不是也随着变化;满足了前面两个条件，再看它们的比值是否一定。不要省去任何一步。如果用字母x和y分别表示两种相关联的量，用k表示它们的比值，正比例关系可以用这样的式子来表示:
例2、(判断是否成正比例)
练习本的单价一定，买练习本的数量和总价是不是成正比例?为什么? accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
分析与解:根据正比例的意义，看两个变量的比值是否一定，如果两个变量的比值一定，那么这两个变量就成正比例，反之，则不成正比例。
买练习本的数量和总价是两种相关联的量，它们与练习本的单价有下面的关系:
所以练习本的数量和总价成正比例。
例3、(正比例的图像)磁悬浮列车匀速行驶时，路程与时间的关系如下。
(1)图中的点A表示时间为1分钟时，磁悬浮列车驶过的路程为7千米。请你试着描出其他各点。
(2)连接各点，它们在一条直线上吗?
(3)根据图像判断，列车运行2分半钟时，行驶的路程是多少千米?行驶30千米大约需要几分钟?
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
分析与解:根据提供的各组数据描出图像的许多个点，再依次连成直线。路程和时间相对应的数的比值都是7，即速度一定，路程和时间成正比例，图像是一条直线。对照图像，可以根据时间的值估计出路程的值，也可以根据路程的值估计出时间的值，估计时允许有一定的出入。
(1)描点、连线如图。
(2)在一条直线上，因为路程和时间成正比例，正比例的图像是一条直线。
(3)根据图像，列车运行2分半钟时，行驶的路程是17.5千米;行驶30千米大约需要4.3分钟。
例4、(辨析)圆的周长和直径成正比例，圆的面积和半径成正比例?
分析与解:圆的周长和直径成正比例，而圆的面积和半径却不成正比例。
可列表判断。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
圆的周长和直径的相对应的数的比值都是3.14，所以圆的周长和直径成正比例。而圆的面积和半径的相对应的数的比值是变化的，所以圆的面积和半径不成正比例。
圆的周长和直径成正比例，圆的面积和半径却不成正比例。
例5、(反比例的意义)
下表是王师傅加工一批零件时，每小时加工零件个数随时间变化的情况。这两种量有什么关系?
分析与解:
(1)从上表可以看出，表中有每小时加工零件的个数和加工的时间两种量。
(2)从左往右看，每小时加工零件的个数扩大，加工的时间反而缩小;从右往左看，每小时加工零件的个数缩小，加工的时间反而扩大。所以它们是两种相关联的量。
(3)每小时加工零件的个数和相对应的加工的时间的积都始终不变，如20 × 12 = 240，30 × 8 = 240，40 × 6 = 240„„而这个积就是这批零件的总个数。
通过观察和计算，我们发现:每小时加工零件的个数和加工的时间是两种相关联的量，每小时加工零件的个数随着加工的时间变化而变化，但无论它们怎么变化，相对应的积是一定的，有这样的关系:每小时加工零件的个数 × 加工的时间 = 零件的总个数(一定)。
所以每小时加工零件的个数和加工的时间成反比例的量，它们之间的关系叫做反比例关系。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
点评:判断两种量是不是成反比例，和正比例一样，分三步:一看它们是
不是相关联的两种量;二是看一种量变化，另一种量是不是也随着变化;满足了前面
两个条件，再看它们的乘积是否一定，进行判断。不要省去任何一步。如果用字母
x和y分别表示两种相关联的量，用k表示它们的比值，正比例关系可以用这样的
式子来表示:xy = K(一定)。
accountable for the violation, Had a negative impact on society. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, the initiative to accept social supervision. Give full play to the role of the news media, widely publicized safety production areas to carry out the "four winds" special significance, focus, work measures, dynamic work, the report published telephone. Launched the employees and the whole social supervision and reporting production safety and harm the interests of the masses, the formation of a strong prevention and treatment of the special rectification work atmosphere. 2, enhance political concentration. To strengthen the ideological and political construction, always adhere to the correct political line, politics Governance position, political orientation, political road, continuously enhance political acumen and political discernment, firm road confidence, theory system of self-confidence and self-confidence. To further strengthen the theory of armed Marx doctrine of Chinese consciously use the latest achievements of the armed mind, guide practice and promote the work. With a high degree of political consciousness, the Bureau take the lead in-depth study to implement the spirit of general secretary Xi Jinping's important speech series, and timely to the cadres and workers to study and implement of special supervision and inspection. 3, focus on remediation Yung lazy, scattered. "Cadres and carry out" mediocre, lazy, scattered "special rectification action, strengthen dedication, strong quality", The tree image, team spirit and the socialist core values education, vigorously to create a pioneering spirit, unity and struggle, serious and lively atmosphere. Take a thorough investigation, and severely punish free, absenteeism, tardiness, AWOL behavior, and resolutely put an end to work time on the Internet stocks, playing games, watching entertainment phenomenon. (five) are failing to buck passing the problem of lack of awareness of the overall situation. The individual members of the team too much emphasis on personal interests and the interests of small groups, prior conditions, the first hit "small abacus". The lack of big talk about the principle of small speaking style, have something to say, not behind talking about, no more Tricks of consciousness and self-discipline, relegates, passing each other, not unite to form a good atmosphere, and sometimes even against each other. A few members of the team that is the power sector in the safety supervision department, safety supervision department is working to better cope with personal interests, perfunctory in the daily supervision process, the illegal behavior of enterprise there do not want to offend people speak hard, to relax the stringent requirements of the enterprise. The rectification measures: (LED Le
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