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北京版四年级上册数学全册知识小结一大数的认识一、计数单位与数位顺序表 1.一(个)、十、百、千、万、十万、百万……都是计数单位。
2.数位顺序表。
3.在数位顺序表中,从个位起向左数,每四位为一级,分别是个级、万级、亿级……4.每相邻两个计数单位之间的进率都是10。
这就是十进制计数法。
二、大数的读法、写法 1.大数的读法: (1)读数时,要从高位读起,按照数位顺序表划分数级,先读亿级,再读万级,最后读个级。
(2)读亿级上的数时,先要按照个级上的数的读法来读,再在后面加一个“亿”字;读万级上的数时,先要按照个级上的数的读法来读,再在后面加一个“万”字;读个级上的数时,直接读即可。
(3)每级末尾不管有几个0,都不读,其他数位上有一个或者连续几个0,都只读一个零。
2.大数的写法: (1)写数时,从高位起一级一级往下写,即先写亿级,再写万级,最后写个级。
(2)哪一个数位上一个计数单位也没有,就在那个数位上写0占位。
三、数的大小比较 1.比较大数的大小时,首先要看数的位数,位数多的那个数就大。
2.如果位数相同,就比较最高位,最高位上的数大的那个数就大。
3.如果最高位上的数相同,就比较下一位上的数,下一位上的数大的那个数就大。
4.如果最高位的下一位上的数也相同,就按照上述方法依次比较下去,直到比较出大小为止。
四、数的改写 1.改写整亿、整万的数。
(1)改写整万的数时,先分级,然后去掉万级后面的4个0,并在末尾写上“万”字。
(2)改写整亿的数时,先分级,然后去掉亿级后面的8个0,并在末尾写上“亿”字。
2.用“四舍五入”法求近似数用“四舍五入”法求一个数的近似数,精确到哪一位就看它的下一位是大于5,等于5,还是小于5。
(1)如果精确位的下一位大于或等于5,就把精确位后面的数全部舍去,并向前一位进1。
(2)如果精确位的下一位小于5,就直接把精确位后面的数全部舍去。
10个十万是一百万,10个一百万是一千万,10个一千万是一亿。
北师大版四年级上册各单元知识点梳理四年级上册单元知识梳理考点分析 A B C D了理掌运内知识点知识点包含的要素分析突出知识点教学策略数学思想检测形式解解握用容1、认识数级、数位、计数单位，并了解它们之间的对“十进制”突出“相邻两个单位”，数应关系。
数位突出“个级”、“万级”和1、填空与万以内数的数位顺序联系，加以比一2、十进制计数法。
“亿级”;第五位是万位，第九1、类比 2、判断 1 2 3 较和类推。
数 3、数数。
能一万一万地数，位是亿位。
3、选择十万十万地数，一百万一百万地数……1、先分级，在读数。
从高位起，一级一级地往下读。
读亿级或万级的数时，要按照个级的读法来读，再1、以万以内数读法的旧知识为基础，在后面加个万字或亿字。
每级末尾加以联系和区别。
1、填空人的0都不读，其他数位不管有一个或2、复习万以内数的写法，进行知识1、亿以内数的读、写数方1、迁移 2、连线口连续几个0都只读一个“零”。
迁移类推。
在掌握读数的基础上，再法。
3、给数字按 1、2 普2、从高位写起，一级一级地往下写。
讨论写法。
2、比较数大小的方法。
2、类推大小顺序排查哪一位上一个单位也没有，就在那3、复习万以内数的大小比较方法，列一位上写0。
进行知识迁移类推。
3、先数位数，分两种情况比较。
一种是位数多的数就比较大;另一种是位数相同，从高位开始比较。
development of freezing plans and emergency precautions. 3, night-time setting the full-time attendant to ensure someone on duty and on duty day and night recording, while setting the Weatherman, responsible listens to and published on the weather conditions. 4, should complete the construction of the winter rainy season Shi ... Has not finished filling the pit covered with a poncho, should be drained before the next fill clean water content meet the requirements before construction began. 5, higher in the winter rain, prior to construction, priority project areas, and built a simple waste water facilities, in order to ensure normal construction. The 12th chapter, resources planning and advancement, introduction of new technology, new technology, new equipment, new material measures in order to ensure the survival of seedlings planted, in the planting process except in strict accordance with the tender specified planting methods and technical measures, the application of new technology to ensure quality: 1, the use of some new scientific achievements and improve survival. (1) ABT-3 rooting powder. This kind of rooting powder for Evergreen coniferous trees take root and valuable species of fast rooting, improve the survival rate is obvious.(2) KD-1 Super absorbent polymers. Insurance agent can enhance soilwater storage, water retention and improve survival. (3) the use of puffing chicken manure. High temperature expansion1、能将整万、整亿的数改以“万”作单位的改写方法是把个写成以“万”或“亿”为单级的4个0去掉，在后面加上“万”位的数。
北京版英语四年级上册单元要点整理Unit 1: Greetings- Practice responding to greetings appropriately.- Understand the importance of greetings in different social settings.Unit 2: Classroom Rules- Learn and follow classroom rules such as raising hand, listeningto the teacher, and being respectful to classmates.- Understand the importance of following rules for a conducive learning environment.- Discuss the consequences of not following classroom rules.Unit 3: Numbers- Learn to count from 1 to 100.- Practice writing and recognizing numbers.- Learn to use numbers in various contexts, such as telling time and giving phone numbers.Unit 4: Family- Learn vocabulary related to family members: father, mother, brother, sister, etc.- Describe family members using basic sentences.- Understand the roles and importance of family in our lives.Unit 5: School Subjects- Learn vocabulary related to school subjects, such as English, math, science, etc.- Identify and talk about different school subjects.- Discuss personal preferences and interests in various subjects.Unit 6: Food- Learn vocabulary related to food items, such as fruits, vegetables, snacks, etc.- Describe different food items using basic sentences.- Understand the importance of a balanced diet and making healthy food choices.Unit 7: Animals- Learn vocabulary related to animals, such as pets, farm animals, and wild animals.- Identify and talk about different animals.- Understand basic characteristics and habitat of various animals.Unit 8: Colors- Learn vocabulary related to colors.- Identify and talk about different colors.- Describe objects and things using colors.Unit 9: My Body- Learn vocabulary related to body parts, such as head, shoulders, knees, toes, etc.- Identify and talk about different body parts.- Understand the importance of taking care of our bodies.Unit 10: Clothes- Learn vocabulary related to different clothing items, such as shirts, pants, shoes, etc.- Describe clothing items and preferences using basic sentences.- Discuss appropriate clothing choices for different occasions.以上是北京版英语四年级上册单元要点的整理。
北京版四年级上册数学《乘法》知识点归纳第一课：购物知识点：1、探究并把握两、三位数乘一位数（不进位）的运算方法，并能正确的进行运算。
2、师引导学生在看明白图意的基础上，提取数学信息，提出问题，并能运用不同的方法解决问题。
3、让学生经历独立摸索、合作交流的过程，探究两、三位数乘一位数（不进位）的运算方法。
教师要有意识的引导学生列竖式运算乘法。
在运算中明确算理，学会竖式的书写。
用乘数从个位起依次去乘另一个乘数的每一位，把得数写在对应的数位上。
第二课：去游乐场知识点：1、探究并把握两、三位数乘一位数（进位）的运算方法，并能正确的进行运算。
结合具体情境，逐步培养提出问题，解决问题的意识和能力。
3、明白得满十进一的算理，进而类推出满几十进几的算法，初步把握进位法则：两（三）位数乘一位数，从个位乘起，哪一位乘积满几十，就向前一位进几。
培养学生对知识的类推能力和主动猎取新知识的学习适应。
第三课：乘火车知识点：1、探究并把握两、三位数乘一位数（连续进位）的运算方法，并能正确的进行运算。
2、结合具体情境，逐步培养提出问题，解决问题的意识和能力。
3、在已有两位数乘一位数进位乘法的基础上，放手让学生自主探究连续进位乘法的运算方法，并能正确运算。
4、体验算法的多样化第四课：05=？知识点：1、探究并把握0和任何数相乘都等于0那个规律。
2、一个因数中间或末尾有0的乘法是本节课的教学重点。
3、借助乘法的意义找规律等方法探究并把握0和任何数相乘都等于0那个规律。
4、因数末尾有0的乘法，当因数末尾有0时，运算时0能够先不参加运算，运算终止后因数末尾有几个0就在乘积后加几个0。
因数中间有0的乘法，能够通过对比进行教学，如：4023=1206，3078=2456，同样是因数中间有0，什么缘故一个乘积中间有0，而另一个却没有。
通过讨论4023积中间是0的那位，因为没有进位，积当中就保留了0，而3078，因为发生了进位，因此积当中的0就不见了。
北京课改版四年级上册数学期末复习全册单元知识点总结首先确定数的位数，然后根据数位顺序表确定数级。
将数从高位起每四位分一段，用逗号隔开，最后加上对应的计数单位。
例如：xxxxxxxx可以改写为3,4567,890.2.改写小数。
将小数点后的数按照数位顺序表从左往右依次编号，然后将小数点向右移动相应的位数，最后在末尾补上零。
例如：0.025可以改写为25/1000或0.0250.3.改写分数。
将分子和分母同时除以它们的最大公约数，得到最简分数。
例如：20/25可以改写为4/5.4.改写百分数。
将百分数转化为小数，然后按照小数的规则进行改写。
例如：75%可以改写为0.75.改写整万的数时，先将数分级，然后去掉万级后面的四个0，最后在末尾加上“万”字。
同理，改写整亿的数时，先分级，去掉亿级后面的八个0，再在末尾加上“亿”字。
使用“四舍五入”法求一个数的近似值，精确到哪一位取决于它的下一位是大于5、等于5还是小于5.如果精确位的下一位大于或等于5，就把精确位后面的数全部舍去，并向前一位进1.如果精确位的下一位小于5，就直接舍去精确位后面的数。
约等号“≈”表示约等于。
需要注意的是，只有整亿的数改写成以“亿”为单位的数时可以使用“=”连接，而非整亿的数改写后是一个近似数，需要用“≈”连接。
在进行三位数乘两位数的计算时，首先将较大的数写在上面，相同数位对齐。
然后用两位数的个位与另一个因数的每一位依次相乘，所得积的末位与个位对齐。
接着用两位数的十位与另一个因数的每一位依次相乘，所得积的末位与十位对齐。
最后将两次乘得的积相加即可。
如果一个因数中间有0，则需要将下面的两位数的个位或十位与相乘后，加上进位数，写在相应位置。
如果因数的末尾有0，则先将前面的数相乘，再在积的末尾添上相应数量的0.在进行三位数乘两位数的估算时，可以根据“四舍五入”法将三位数看成整百或整十数，将两位数看成整十数来进行估算。
在乘法算式中，一个因数不变，另一个因数乘（或除以）几（除外），积也乘（或除以）相同的数。
北京版四年级上册英语单元重要知识点总结Unit 1: Meet My Family- Learn to introduce family members: father, mother, older brother, older sister, younger brother, younger sister, etc.- Practice simple dialogues to talk about family members using phrases like "This is my..." and "These are my..."Unit 2: At School- Learn and practice school-related vocabulary such as classroom, teacher, student, pencil, book, etc.- Introduce school subjects and interests using sentences like "I like..." and "I don't like..."Unit 3: My Day- Learn and use time-related words and phrases, such as morning, afternoon, evening, etc.- Practice describing daily routines using present tense sentences like "I get up at..." and "I go to bed at..."- Understand and use words related to the activities performed during different times of the day.Unit 4: My Toys- Learn and identify different toy names with words like doll, ball, robot, car, etc.- Describe toys using adjectives and simple sentences like "It'sbig/small/light/heavy/fun."Unit 5: My Body- Learn and recognize body parts vocabulary like head, shoulders, knees, toes, etc.- Practice asking and answering questions related to body parts using sentences like "What's this?" and "These are my..."Unit 6: At the Park- Learn and understand words and phrases related to park activities, such as swing, slide, seesaw, etc.- Describe park activities and express preferences using phrases like "I like to..." and "I don't like to..."Unit 7: In the Kitchen- Learn and practice kitchen-related vocabulary, including words like table, chair, fridge, stove, etc.- Understand and use simple imperative sentences like "Sit down" and "Stand up" in a kitchen context.Unit 8: At the Zoo- Learn and recognize animal names, such as lion, elephant, giraffe, monkey, etc.- Practice asking and answering questions about animals using sentences like "What's this?" and "Is it a...?"- Understand and use adjectives to describe animals.以上就是北京版四年级上册英语单元的重要知识点总结。
英语四年级上册单元知识点梳理（北京版）zoo look so sadspeak, Ms, Mrs, there,bring,school, bad, cold,drinkcall, hold onhave some books, call herback bring to school,stay in bed phone numberword, computer, easy, light,合作与交流（请求与提供帮助）ruler, bat, openturn off the light, close thewindow, pass me the water,open the door,borrow your markersReview of unit 1-3词汇功能句型/交际用语语法知识get, pen, kind, brown, think, shoe, buy, shop, shape, flavor, colour, that, this, those, these, pair, sneakers, sandals, overcoat looks nice, that pair of shoes these sandals, those sneakers -Which kind would you like? first,: teacher, winter, slipper,Which 开头疑问句例：Which kind would you like?eat, healthy, cook, duck, soup, sorry, chicken, vegetables, meatballs, jiaozi, salad, pizza, sandwich, ship, mushroom take order, order the food on your menu, for breakfast -What would you like to eat?-I’d like some vegetables.-May I take your order now?-Yes. I’d like/I’ll have asalad, fish, and mushroomsoup.-How much is it?-It’s sixty yuan.-Here is the money.[ai]: find, nice, kite, ice[æ]: cat, that, m a n, flag,hat, blackMay I 开头的疑问句。
一、单词、短语1.颜色（colour）：red红色blue蓝色yellow黄green绿色brown棕色black黑色white白色pink粉色purple紫色orange 橙色gray灰色2.鞋（shoes）：sneakers运动鞋sandals凉鞋boots靴子slippers拖鞋3.服饰（clothes）：jacket夹克衫trousers/ pants裤子shorts短裤coat外套overcoat大衣shirt衬衫T-shirt T恤skirt短裙dress连衣裙gloves手套uniform制服socks袜子cap帽子hat礼帽4.食物（food）：meatball肉丸Peking Duck烤鸭chicken鸡肉fish鱼肉salad沙拉soup汤hamburger汉堡sandwich三明治chips薯条ice cream冰激凌pie 派pizza披萨cake蛋糕potato土豆cabbage卷心菜mushroom蘑菇5.饮品（drinks）：water水milk牛奶tea茶soy milk豆浆juice 果汁6.数字（number）：onetwothreefour fivesixseveneightnineteneleventwelvethirteenfourteenfifteensixteenseventeeneighteennineteentwenty20thirty30forty40fifty50sixty60seventy70eighty80ninety90one hundred100 7.自然(nature): snow雪，下雪rain雨，下雨wind风ice冰air空气8.天气（weather）snowy下雪的rainy多雨的windy刮风的cloudy多云的sunny阳光充足的fine晴朗的hot热的cold 冷的warm温暖的cool凉爽的9.地点（place）park school farm zoo forest lake grassland mountain10.季节（season）spring春天summer夏天autumn/fall秋天winter冬天动词短语：want to想要look nice看起来好look at看try .on试穿get cold 变冷take your order点餐become water变成水go to parks去公园take long walks去散步close to nature 亲近自然visit my uncle看望我的叔叔find out找到其他短语、短句：Excuse me打扰下here you are给您how much多少钱 a pair of一双how about怎么样Of course 当然for me 给我in summer在夏天In Sydney在悉尼on weekends在周末on a farm在农场in the forest在森林on the grassland在草原by the lake 在湖边in the mountains在山上on the internet 在网上二、句子：购物 1.Can I help you?/What can I do for you? 我能帮你吗？Yes. I want to get a pen. 是的。
北京版小学英语四上知识梳理Unit 1 Why are you so happy?feeling（情绪）：sad悲伤的, surprised感到惊讶的, angry生气的, tired劳累的, excited兴奋的, upset苦恼的, worried担心的,glad高兴的, happy，again又，再次, why为什么, book书, look for 寻找, get well 康复, messy脏乱的，missing丢失，hope希望，square正方形，worry担心back at school回校, played too hard玩得太累, come back回来, go to the zoo去动物园, eat up fish 吃光鱼, read books读书, get well康复1. Why are you (so) happy? 你为什么(这么)高兴？Because we are back at school. 因为我们都回到了学校。
2. Why do you look so sad? 为什么你看起来这么伤心？Because my dog is missing. 因为我的狗丢了。
3. Nice to see you all again.很高兴再次见到你。
4. So do I.我也是。
5. Don’t be sad/upset. 别伤心/心烦。
6. I hope so. 我希望如此。
7. It’s square in shape and blue in colour. 它是方形，蓝色的。
8. Let’s look for it together. 我们一起寻找吧。
9. Don’t worry. 别担心。
10. She will get well soon. 她将很快康复的。
注意：句子的表达及人称和动词搭配 I am, you/we/they are, he/she/ it is.I/you/we do, he/she/it doesUnit 2 May I speak to Mike?话题：打电话speak说话, robot机器人, housework家务劳动, Ms女士, Mrs太太, there在那里, really真的, bring带来, school学校, bad严重的, cold感冒, drink喝have a look看一看, do housework做家务, hold on稍等, call back回电话, bad cold重感冒, go to school去上学, stay in bed卧床休息, drink a lot of water大量喝水, play football踢足球, come to my birthday party参加我的生日聚会，bring… to school带到学校来，call back回电话，1. May I speak to Mike? This is Yangyang. 我能找一下麦克吗？我是洋洋。
Speaking. / Please hold on. …, it’s for you. 请说。
/ 请稍等。
…找你的电话。
2. Is Guoguo there? 果果在吗？Sorry, she is not home / here. 抱歉，她不在家/在这里。
3. Is Miss Wang home / there? 王老师在吗？This is Wang Ping. / Speaking. Who’s calling, please? 我是王萍。
/请说。
请问你是谁？4. Do you want to have a look? 你想看看吗？5. I’m doing housework with my mum. 我正和妈妈一起做家务。
6. Please tell her to call back. 请告诉她给我回电话。
7. Will you bring them to school tomorrow? 你明天能把他们带到学校来吗？Yes, I will.是的，我会的。
8. What’s your phone number? It’s …. 你电话号码是多少？是…。
9. What can I do for you? 我能为你做些什么？10. I have a bad cold. I can’t go to school tomorrow.我得了重感冒。
我明天不能去上学。
11．Please stay in bed and drink a lot of water. 请卧床休息，多喝水。
Unit 3 Will you do me a favour?功能：帮助他人及寻求帮助学习用品：computer电脑，door门，window窗户，glass玻璃杯，ping-pong bat乒乓球拍，markers记号笔，ruler尺子，scissors剪刀，crayons蜡笔，pencilsharpener转笔刀，学习用品词汇补充：pen钢笔pencil铅笔pencil-case铅笔盒ruler尺子an eraser橡皮schoolbag 书包pencil sharpener削铅笔刀crayon蜡笔bag包book书magazine杂志story-book故事书newspaper报纸English/ math/Chinese/music/art/. book教科书动词：borrow借入, take拿到，形容词：easy容易的，kind体贴的hold books拿书, close the window关窗户, turn off the light关灯, pass me the water递水, open the door开门, turn off the radio关收音机, turn on the light开灯, play word game玩字谜游戏, a glass of water一杯水, do sb. a favour帮忙1. Would you please hold these books for me? 你能帮我拿这些书吗？No problem.没问题。
2. Would you mind opening the door, please? 请问，你介意打开门吗？（mind + doing）Sure. No problem. 当然不介意，没问题。
3. Can I borrow your ping-pong bat? 我可以借你的乒乓球拍吗？Yes, of course. 是的，当然可以。
4. Would you show me how to play this word game on the computer? 你能告诉我在电脑上怎样玩这个游戏吗？5. It’s kind of you. 你真是太好了。
6. Would you like a glass of hot water? 你想要一杯热水吗？Yes, please. / No, thanks. 是的，麻烦了。
/ 不用了，谢谢。
7. Will you do me a favour, please? 你能帮一个忙吗？Sure. 当然。
8. Can I take the red one? 我可以拿这个红色的吗？Fine. 好的。
Unit 5 Which kind would you like?话题：购物衣服类：trousers裤子, T-shirt T恤衫, shorts短裤, overcoat大衣, cap鸭舌帽, school uniform 校服, jacket夹克衫，pants长裤skirt短裙子dress连衣裙socks袜子jeans牛仔裤shirt衬衫shoes鞋子sweater毛衣coat上衣raincoat雨衣shorts短裤hat(有沿的)帽子sunglasses太阳镜tie领带scarf围巾gloves手套sneakers网球鞋slippers拖鞋sandals凉鞋boots靴子小类别：shoe鞋子：slippers拖鞋, sandals凉鞋, boots靴子, sneakers运动鞋,总称：kind种类, shape形状, colour颜色,动词：buy买, sell出售, get获得, think想、认为,指示代词：this 这个，that 那个，these这些，those那些,形容词：brown棕色的, comfortable舒适的,其他：pen钢笔, pair一双, how much多少钱，shop商店, dollar美元,try on 试穿，go with与…相配1. Which kind would you like? 你想要哪种？This one looks nice. 这种看起来不错。
2. Excuse me. May I look at that pair of shoes, please? 我能看看那双鞋吗？Sure. Here you are. 当然可以，给你。
3. The red one will look nice on you. 红色的你穿会很漂亮。
It will go with my trousers.它与我的裤子很搭。
4. Can I help you? 要我帮忙吗？（需要买什么？）Yes. I want to get a pen. 是的，我想买支钢笔。
5. What colours do you have? 你有什么颜色的？We have black, blue, green, and brown. 我们有黑色，蓝色，绿色和棕色的。
6. I will take a brown one. 我要买支棕色的。
7. I think so. 我也这么认为的。
8. May I try them / it on? 我能试穿吗？Certainly. / Sure you can. 当然可以。
9. How much are they? 他们多少钱？Thirty dollars. 三十美金。
10. It’s getting cold. 天变冷了。
11. It’s won’t go with my trousers. 它和我的裤子不配。
