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初中数学人教版七年级上册1.1 正数和负数课前预习课件ppt
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这是一份初中数学人教版七年级上册1.1 正数和负数课前预习课件ppt，共32页。
1.了解正数与负数是从实际需要中产生的。Understand psitive and negative numbers are generated frm actual needs.2.理解正数、负数及0的意义，掌握正数、负数的表示方法。Understand the meaning f psitive numbers,negative numbers and 0,and master the expressin methds f psitive numbers and negative numbers.3.会用正数、负数表示具有相反意义的量（重点、难点）。Can use psitive and negative numbers t represent quantities with ppsite meanings.
观看下面的视频，体会数的产生过程。Watch the fllwing vide t experience the generatin prcess f number.
观察下列图片，体会数的产生和发展过程.Observe the fllwing pictures experience the generatin and develpment f numbers.
由表示“没有”“空位”，产生数0The number 0 is generated by indicating "n" and "empty"
结绳计数Twine cunt由记数、排序，产生数1,2,,srting,the number is generated 1,2,3...
由分物、测量，产生分数The fractin is generated by dividing and measuring
根据实际生活的需要，人们引进了另一种数，你知道是什么数吗？结合你在实际生活中接触到的数，试举例。Accrding t the needs f real life, peple have intrduced anther number. D yu knw what it is? Cmbined with the number yu cme int cntact with in real life, try t give examples.
新闻报道：某年，我国花生产量比上年增长1.8%，油菜籽产量比上年增长-2.7%.News reprt: in a certain year,China's peanut utput increased by 1.8% and rapeseed utput increased by - 2.7% ver the previus year.
问题1：说一说上面用到的各数的含义.Questin 1: Tell me the meaning f the numbers used abve.
（1）天气预报中的3，电梯按钮中的1-10，新闻报道中的1.8%； 3 in weather frecast,1-10 in elevatr buttn and 1.8% in news reprt
（2）天气预报中的-3，电梯按钮中的-1，新闻报道中的-2.7%. - 3 in weather frecast,- 1 in elevatr buttn,- 2.7% in news reprt
问题2：上面这两类数，分别属于什么数？
有时，我们为了明确表达意义，在正数前面也加上“+”（正）号，如+3，+1.8％，+0.5，….不过一般情况下我们省略“+”不写。Smetimes, in rder t express the meaning clearly, we als add a "+" (psitive) sign befre the psitive number, such as + 3, + 1.8%, + 0.5, generally, we mit "+" and d nt write it.
例1 读出下列各数，并把它们填在相应的圈里。Example 1 Read ut the fllwing numbers and fill them in the crrespnding circles.
正数 Psitive number
负数 Negative number
(1)从定义中我们发现负数的前面必须有负号“-”.Frm the definitin,we fund that negative numbers must be preceded by a minus sign "-"
(1)负数有什么特点？What are the characteristics f negative numbers?
(2)不对.0既不是正数，也不是负数.0 is neither psitive nr negative
(2)如果一个数不是正数就是负数，对吗？If a number is nt psitive,it is negative,right?
甲汽车向东行驶3km Car A drve 3km eastward乙汽车向西行驶1km.Car B drve 1km westward
蔬菜店购进黄瓜50kg，The vegetable stre bught 50kg cucumbers蔬菜店售出黄瓜2kg.The vegetable stre sld 2kg cucumbers
它们都表示相反的意义.They all mean the ppsite
你会用正、负数来表示它们吗？Can yu use psitive and negative numbers t represent them?
这是该存折中记录的支出、存入信息，试着说说其中“支出或存入”那一栏中数字的含义是什么？This is the expenditure and depsit infrmatin recrded in the passbk. What is the meaning f the number in the clumn f "expenditure r depsit"?
例2 一物体沿东西两个相反的方向运动时，可以用正、负数表示它们的运动．Example 2 When an bject mves in tw ppsite directins frm east t west, its mtin can be expressed by psitive and negative numbers（1）如果向东运动4m记作+4m，那么向西运动5m记作_____.If the mvement f 4m t the East is recrded as + 4m, then the mvement f 5m t the west is recrded as _____（2）如果－7m表示物体向西运动7m，那么+6m表明物体____________.If - 7m indicates that the bject mves 7m t the west, then + 6m indicates the bject____________________
mves 6m t the east
例3（1）一个月内，小明体重增加2kg，小华体重减少1kg，小强体重无变化，写出他们这个月的体重增长值；Example 3 (1) Within ne mnth, Xiaming's weight increased by 2kg, Xiahua's weight decreased by 1kg, and Xiaqiang's weight did nt change. Write their weight gain value this mnth;
解：这个月小明体重增长2kg，小华体重增长-1kg，小强体重增长0kg. This mnth, Xiaming gained 2kg, Xiahua gained - 1kg and Xiaqiang gained 0kg
解：2001年商品出口总额的增长率：美国-6.4%，德国1.3%，法国-2.4%，英国-3.5%，意大利0.2%，中国7.5%.The grwth rates f ttal cmmdity exprts in 2001 were - 6.4% in the United States, 1.3% in Germany, -2.4% in France, -3.5% in Britain, 0.2% in Italy and 7.5% in China.
（2）某年下列国家的商品进出口总额比上年的变化情况是：美国减少6.4%， 德国增长1.3%，法国减少2.4%， 英国减少3.5%， 意大利增长0.2%，中国增长7.5%.写出这些国家2001年商品进出口总额的增长率.The changes in the ttal imprt and exprt vlume f the fllwing cuntries in a given year ver the previus year are as fllws:The United States decreased by 6.4%, Germany increased by 1.3%,France decreased by 2.4%, Britain decreased by 3.5%,Italy grew by 0.2% and China by 7.5%.Write the grwth rate f these cuntries' ttal cmmdity imprts and exprts in 2001.
根据相反意义合理使用正、负数对实际问题进行表示.一般情况下，把向北(东)、上升、增加、收入等规定为正，把它们的相反意义规定为负. Accrding t the ppsite meaning, use psitive and negative numbers reasnably t express practical prblems. Generally, Nrth (East), rise, increase, incme, etc. are defined as psitive, and their ppsite meaning is defined as negative
从上面的例题中看到增长 －1就是减少1，那么增长 －6.4%是什么意思呢？什么情况下增长率是0？减少 －1又是什么意思呢？Frm the example abve, we can see that grwth - 1 is t reduce 1. What des grwth - 6.4% mean? Under what circumstances is the grwth rate 0? What des reductin-1 mean?
情景：下图是吐鲁番盆地的示意图，你能用语言表述它与海平面的高度关系吗？它的含义是什么？The fllwing figure is a schematic diagram f Turpan Basin. Can yu express its relatinship with sea level in wrds? What des it mean?
海平面sea level
吐鲁番盆地 Turpan Basin
高度看作0The height is regarded as 0
记为+8844.43米 Recrded as + 8844.43m
记为－155米 Recrded as - 155 m
在地形图上表示某地的高度时，需要以海平面为基准（规定海平面的海拔高度为0 m）通常用正数表示高于海平面的某地的海拔高度，负数表示低于海平面的某地的海拔高度．该地形图上的海拔高度一般不标单位，实际采用米作单位．该地图中的正数和负数的含义是什么？When expressing the altitude f a place n the tpgraphic map, it is necessary t take the sea level as the benchmark (the altitude f the sea level is specified as 0 m). Generally, a psitive number represents the altitude f a place higher than the sea level, and a negative number represents the altitude f a place lwer than the sea level. The altitude n the tpgraphic map is generally nt in units, Actually, meters are used as units. What are the meanings f psitive and negative numbers in this map?
0只表示没有吗? 0 nly means nthing?
1.空罐中的金币数量 Number f gld cins in empty tank;2.温度中的0℃ 0℃in temperature;3.海平面的高度 Height f sea level;4.标准水位 Standard water level;5.身高比较的基准 Height cmparisn benchmark; ……
0是正负数的分界点.它不再简简单单的只表示没有，它具有丰富的意义，如0 is the dividing pint f psitive and negative numbers. It n lnger simply means nthing. It has rich meaning, such as
1.下列语句正确的是 Which f the fllwing statement is crrect ( ) A.0℃表示没有温度 0 ℃ means n temperature B.0表示什么也没有 0 means nthing C.0是非正数 0 is a nn psitive number D.0既可以看作是正数又可以看作是负数0 can be regarded as bth psitive and negative
2.你能举出实际生活中0表示的实际意义吗？请举两例Can yu cite the practical significance f 0 in real life? Please give tw examples.
答案不唯一，如：收支为0元，表示收入和支出平衡；水位变化0m，表示水位不上升也不下降.
1.下列说法，正确的是 Which f the fllwing statement is crrect （ ） A.加正号的数是正数，加负号的数是负数The number with a plus sign is psitive and the number with a minus sign is negative B.0是最小的正数 0 is the smallest psitive number C.字母a既可是正数，也可是负数，也可是0 The letter a can be either psitive r negative, r 0 D.任意一个数，不是正数就是负数 Any number is either psitive r negative
2.下列各对关系中，不具有相反意义的量的是 In the fllwing pairs f relatins, the quantity that des nt have the ppsite meaning is （ ） A.运进货物3吨与运出货物2吨 3 tns f incming gds and 2 tns f utging gds B.升温3℃与降温3℃ Temperature rise 3 ℃ and temperature drp 3 ℃ C.增加货物100吨与减少货物2000吨 Increase f 100 tns f gds and decrease f 2000 tns f gds D.胜3局与亏本400元 Win 3 games and lse 400 yuan
3.填一填 Fill in the blanks（1）如果零上5℃记作+5℃，那么零下3℃记作______ If 5 ℃ abve zer is recrded as + 5 ℃, then 3 ℃ belw zer is recrded as___________.（2）东、西为两个相反方向，如果-4米表示一个物体向西运动4米，那么+2米表示 .物体原地不动记为 . East and West are tw ppsite directins. If - 4m means an bject mves 4m t the west, then + 2m means ___________________The bject remains in place and is recrded as ________
mves 2m t the east
3.填一填 Fill in the blanks（3）某仓库运进面粉7.5吨记作+7.5吨，那么运出3.8吨应记作 _________ . 7.5 tns f flur transprted int a warehuse shall be recrded as + 7.5 tns, and 3.8 tns transprted ut shall be recrded as _________
（4）抗洪期间，如果水位超过标准水位1.5米记作+1.5 米，那么后来记录的-0.9米表示 _________ .During fld fighting, if the water level exceeds the standard water level by 1.5m, it is recrded as + 1.5m, then the later recrded -0.9m represents___________________________________
0.9m lwer than the standard water level
20，5，0.23，25%，3.14，0.62
5.某银行一天内接待了四笔大业务，存款40000元，取款25000元，存款30万元，取款7万元.若存款为正，请你用正、负数表示这四笔款项.A bank received fur majr transactins in ne day, with a depsit f 40000 yuan, a withdrawal f 25000 yuan, a depsit f 300000 yuan and a withdrawal f 70000 yuan. If the depsit is psitive, please use psitive and negative numbers t represent these fur payments
+40000元，-25000元，+300000元，-70000元.
1.正数是比零大的数，正数前面加“-”号的数叫做负数.A psitive number is a number larger than zer. A psitive number preceded by a "-" sign is called a negative number
3.具有相反意义的量应满足的条件： ①必须是同类量，而且是成对出现的； ②只要求意义相反，不要求数量一定相等.
2. 0 既不是正数也不是负数，它是正负数的分界.0 is neither psitive nr negative. It is the bundary between psitive and negative numbers
帮助家长记录一个月的生活收支帐目（收入计为正数，支出计为负数）Help parents recrd their living incme and expenditure accunts fr ne mnth (incme is psitive and expenditure is negative)
1.了解正数与负数是从实际需要中产生的。Understand psitive and negative numbers are generated frm actual needs.2.理解正数、负数及0的意义，掌握正数、负数的表示方法。Understand the meaning f psitive numbers,negative numbers and 0,and master the expressin methds f psitive numbers and negative numbers.3.会用正数、负数表示具有相反意义的量（重点、难点）。Can use psitive and negative numbers t represent quantities with ppsite meanings.
观看下面的视频，体会数的产生过程。Watch the fllwing vide t experience the generatin prcess f number.
观察下列图片，体会数的产生和发展过程.Observe the fllwing pictures experience the generatin and develpment f numbers.
由表示“没有”“空位”，产生数0The number 0 is generated by indicating "n" and "empty"
结绳计数Twine cunt由记数、排序，产生数1,2,,srting,the number is generated 1,2,3...
由分物、测量，产生分数The fractin is generated by dividing and measuring
根据实际生活的需要，人们引进了另一种数，你知道是什么数吗？结合你在实际生活中接触到的数，试举例。Accrding t the needs f real life, peple have intrduced anther number. D yu knw what it is? Cmbined with the number yu cme int cntact with in real life, try t give examples.
新闻报道：某年，我国花生产量比上年增长1.8%，油菜籽产量比上年增长-2.7%.News reprt: in a certain year,China's peanut utput increased by 1.8% and rapeseed utput increased by - 2.7% ver the previus year.
问题1：说一说上面用到的各数的含义.Questin 1: Tell me the meaning f the numbers used abve.
（1）天气预报中的3，电梯按钮中的1-10，新闻报道中的1.8%； 3 in weather frecast,1-10 in elevatr buttn and 1.8% in news reprt
（2）天气预报中的-3，电梯按钮中的-1，新闻报道中的-2.7%. - 3 in weather frecast,- 1 in elevatr buttn,- 2.7% in news reprt
问题2：上面这两类数，分别属于什么数？
有时，我们为了明确表达意义，在正数前面也加上“+”（正）号，如+3，+1.8％，+0.5，….不过一般情况下我们省略“+”不写。Smetimes, in rder t express the meaning clearly, we als add a "+" (psitive) sign befre the psitive number, such as + 3, + 1.8%, + 0.5, generally, we mit "+" and d nt write it.
例1 读出下列各数，并把它们填在相应的圈里。Example 1 Read ut the fllwing numbers and fill them in the crrespnding circles.
正数 Psitive number
负数 Negative number
(1)从定义中我们发现负数的前面必须有负号“-”.Frm the definitin,we fund that negative numbers must be preceded by a minus sign "-"
(1)负数有什么特点？What are the characteristics f negative numbers?
(2)不对.0既不是正数，也不是负数.0 is neither psitive nr negative
(2)如果一个数不是正数就是负数，对吗？If a number is nt psitive,it is negative,right?
甲汽车向东行驶3km Car A drve 3km eastward乙汽车向西行驶1km.Car B drve 1km westward
蔬菜店购进黄瓜50kg，The vegetable stre bught 50kg cucumbers蔬菜店售出黄瓜2kg.The vegetable stre sld 2kg cucumbers
它们都表示相反的意义.They all mean the ppsite
你会用正、负数来表示它们吗？Can yu use psitive and negative numbers t represent them?
这是该存折中记录的支出、存入信息，试着说说其中“支出或存入”那一栏中数字的含义是什么？This is the expenditure and depsit infrmatin recrded in the passbk. What is the meaning f the number in the clumn f "expenditure r depsit"?
例2 一物体沿东西两个相反的方向运动时，可以用正、负数表示它们的运动．Example 2 When an bject mves in tw ppsite directins frm east t west, its mtin can be expressed by psitive and negative numbers（1）如果向东运动4m记作+4m，那么向西运动5m记作_____.If the mvement f 4m t the East is recrded as + 4m, then the mvement f 5m t the west is recrded as _____（2）如果－7m表示物体向西运动7m，那么+6m表明物体____________.If - 7m indicates that the bject mves 7m t the west, then + 6m indicates the bject____________________
mves 6m t the east
例3（1）一个月内，小明体重增加2kg，小华体重减少1kg，小强体重无变化，写出他们这个月的体重增长值；Example 3 (1) Within ne mnth, Xiaming's weight increased by 2kg, Xiahua's weight decreased by 1kg, and Xiaqiang's weight did nt change. Write their weight gain value this mnth;
解：这个月小明体重增长2kg，小华体重增长-1kg，小强体重增长0kg. This mnth, Xiaming gained 2kg, Xiahua gained - 1kg and Xiaqiang gained 0kg
解：2001年商品出口总额的增长率：美国-6.4%，德国1.3%，法国-2.4%，英国-3.5%，意大利0.2%，中国7.5%.The grwth rates f ttal cmmdity exprts in 2001 were - 6.4% in the United States, 1.3% in Germany, -2.4% in France, -3.5% in Britain, 0.2% in Italy and 7.5% in China.
（2）某年下列国家的商品进出口总额比上年的变化情况是：美国减少6.4%， 德国增长1.3%，法国减少2.4%， 英国减少3.5%， 意大利增长0.2%，中国增长7.5%.写出这些国家2001年商品进出口总额的增长率.The changes in the ttal imprt and exprt vlume f the fllwing cuntries in a given year ver the previus year are as fllws:The United States decreased by 6.4%, Germany increased by 1.3%,France decreased by 2.4%, Britain decreased by 3.5%,Italy grew by 0.2% and China by 7.5%.Write the grwth rate f these cuntries' ttal cmmdity imprts and exprts in 2001.
根据相反意义合理使用正、负数对实际问题进行表示.一般情况下，把向北(东)、上升、增加、收入等规定为正，把它们的相反意义规定为负. Accrding t the ppsite meaning, use psitive and negative numbers reasnably t express practical prblems. Generally, Nrth (East), rise, increase, incme, etc. are defined as psitive, and their ppsite meaning is defined as negative
从上面的例题中看到增长 －1就是减少1，那么增长 －6.4%是什么意思呢？什么情况下增长率是0？减少 －1又是什么意思呢？Frm the example abve, we can see that grwth - 1 is t reduce 1. What des grwth - 6.4% mean? Under what circumstances is the grwth rate 0? What des reductin-1 mean?
情景：下图是吐鲁番盆地的示意图，你能用语言表述它与海平面的高度关系吗？它的含义是什么？The fllwing figure is a schematic diagram f Turpan Basin. Can yu express its relatinship with sea level in wrds? What des it mean?
海平面sea level
吐鲁番盆地 Turpan Basin
高度看作0The height is regarded as 0
记为+8844.43米 Recrded as + 8844.43m
记为－155米 Recrded as - 155 m
在地形图上表示某地的高度时，需要以海平面为基准（规定海平面的海拔高度为0 m）通常用正数表示高于海平面的某地的海拔高度，负数表示低于海平面的某地的海拔高度．该地形图上的海拔高度一般不标单位，实际采用米作单位．该地图中的正数和负数的含义是什么？When expressing the altitude f a place n the tpgraphic map, it is necessary t take the sea level as the benchmark (the altitude f the sea level is specified as 0 m). Generally, a psitive number represents the altitude f a place higher than the sea level, and a negative number represents the altitude f a place lwer than the sea level. The altitude n the tpgraphic map is generally nt in units, Actually, meters are used as units. What are the meanings f psitive and negative numbers in this map?
0只表示没有吗? 0 nly means nthing?
1.空罐中的金币数量 Number f gld cins in empty tank;2.温度中的0℃ 0℃in temperature;3.海平面的高度 Height f sea level;4.标准水位 Standard water level;5.身高比较的基准 Height cmparisn benchmark; ……
0是正负数的分界点.它不再简简单单的只表示没有，它具有丰富的意义，如0 is the dividing pint f psitive and negative numbers. It n lnger simply means nthing. It has rich meaning, such as
1.下列语句正确的是 Which f the fllwing statement is crrect ( ) A.0℃表示没有温度 0 ℃ means n temperature B.0表示什么也没有 0 means nthing C.0是非正数 0 is a nn psitive number D.0既可以看作是正数又可以看作是负数0 can be regarded as bth psitive and negative
2.你能举出实际生活中0表示的实际意义吗？请举两例Can yu cite the practical significance f 0 in real life? Please give tw examples.
答案不唯一，如：收支为0元，表示收入和支出平衡；水位变化0m，表示水位不上升也不下降.
1.下列说法，正确的是 Which f the fllwing statement is crrect （ ） A.加正号的数是正数，加负号的数是负数The number with a plus sign is psitive and the number with a minus sign is negative B.0是最小的正数 0 is the smallest psitive number C.字母a既可是正数，也可是负数，也可是0 The letter a can be either psitive r negative, r 0 D.任意一个数，不是正数就是负数 Any number is either psitive r negative
2.下列各对关系中，不具有相反意义的量的是 In the fllwing pairs f relatins, the quantity that des nt have the ppsite meaning is （ ） A.运进货物3吨与运出货物2吨 3 tns f incming gds and 2 tns f utging gds B.升温3℃与降温3℃ Temperature rise 3 ℃ and temperature drp 3 ℃ C.增加货物100吨与减少货物2000吨 Increase f 100 tns f gds and decrease f 2000 tns f gds D.胜3局与亏本400元 Win 3 games and lse 400 yuan
3.填一填 Fill in the blanks（1）如果零上5℃记作+5℃，那么零下3℃记作______ If 5 ℃ abve zer is recrded as + 5 ℃, then 3 ℃ belw zer is recrded as___________.（2）东、西为两个相反方向，如果-4米表示一个物体向西运动4米，那么+2米表示 .物体原地不动记为 . East and West are tw ppsite directins. If - 4m means an bject mves 4m t the west, then + 2m means ___________________The bject remains in place and is recrded as ________
mves 2m t the east
3.填一填 Fill in the blanks（3）某仓库运进面粉7.5吨记作+7.5吨，那么运出3.8吨应记作 _________ . 7.5 tns f flur transprted int a warehuse shall be recrded as + 7.5 tns, and 3.8 tns transprted ut shall be recrded as _________
（4）抗洪期间，如果水位超过标准水位1.5米记作+1.5 米，那么后来记录的-0.9米表示 _________ .During fld fighting, if the water level exceeds the standard water level by 1.5m, it is recrded as + 1.5m, then the later recrded -0.9m represents___________________________________
0.9m lwer than the standard water level
20，5，0.23，25%，3.14，0.62
5.某银行一天内接待了四笔大业务，存款40000元，取款25000元，存款30万元，取款7万元.若存款为正，请你用正、负数表示这四笔款项.A bank received fur majr transactins in ne day, with a depsit f 40000 yuan, a withdrawal f 25000 yuan, a depsit f 300000 yuan and a withdrawal f 70000 yuan. If the depsit is psitive, please use psitive and negative numbers t represent these fur payments
+40000元，-25000元，+300000元，-70000元.
1.正数是比零大的数，正数前面加“-”号的数叫做负数.A psitive number is a number larger than zer. A psitive number preceded by a "-" sign is called a negative number
3.具有相反意义的量应满足的条件： ①必须是同类量，而且是成对出现的； ②只要求意义相反，不要求数量一定相等.
2. 0 既不是正数也不是负数，它是正负数的分界.0 is neither psitive nr negative. It is the bundary between psitive and negative numbers
帮助家长记录一个月的生活收支帐目（收入计为正数，支出计为负数）Help parents recrd their living incme and expenditure accunts fr ne mnth (incme is psitive and expenditure is negative)
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