5年级“撕卡片”的排列组合题

大胖上周一张数学课堂练习卷子上的一个题目引起了胖爸的兴趣。

下图是一张6个数字相连的数字卡片,如果想撕下相连的4张,共有多少种不同的撕法?(如1456就是其中的一种撕法)

这个题目格子少,因此数字并不多,顺着去画穷举出来也花不了多少时间,这也是题目所要求的。不过如果从计算的角度来看,需要动动脑子。

先从6个卡片中任选4张卡片:C(6,4),然后我们需要从中减去存在不相连的卡片情形,这个比较好数,一共有以下4种情况:

细心一点会发现它对应着4个斜线:24、26、35、15。

那么最终符合题意的撕法:

C(6,4)-4=11

扩展一下:
在m×n的方格数字卡片中,如果想撕下相连的k张,一共有多少种不同的撕法?

A heavy rain, a strong wind这里的不定冠词a用得到底对不对?

最近在大胖五年级下的英语知识点讲义上看到了一个句子:

We will have heavy rain and a strong wind tomorrow.

这里令人疑惑的是,前面的heavy rain没有a,但是后面的strong wind则有a,那么到底用不用a呢?

事实上,这里用不用不定冠词a都可以,也都可以找到许多“权威”的例子。rain和wind本身确实是不可数名词,但是有一些不可数名词前加上形容词后,却“成为”可数的了,就像a quick breakfast一样。总体而言,正如大胖知识点上所列的那样,heavy rain前倾向于不用a,而strong wind前则倾向于用a。而且查阅一些国家气象局网站,他们大多使用:

a heavy rain event
strong winds gusts

下面是一些例子:

The flood mitigation projects on Rice University’s campus are tested every time there is a heavy rain. (fema.gov)

Heavy rain would be a concern for much of Arkansas and surrounding areas. (美国气象局weather.gov)

As well as strong winds, there will be heavy rain across many parts of the UK. (英国气象局 metoffice.gov.uk)

There is a strong wind or other hazard making the water unsafe for them. (arun.gov.uk)

5 tips for staying safe in strong wind. (英国气象局 metoffice.gov.uk)

2024年华二初中校园开放日(4月13日),我看到的优势与不足

出发

2024年嘉定区华二初中的校园开放日于4月13日(周六)举行。

胖爸早早地就扫码预约好了,周六上午前两个多小时就带着大胖出发,辗转公交、地铁11号线,然后步行到达华二初中正门,结果还是迟到了大约3分钟,按照通知的时间应该是中午12:30。

在校门口经老师核验过手机短信之后,我们便顺利进入校园。在六年级学生红领巾志愿者的指引下,家长和学生分开行动。(因为小志愿者们都佩戴了红领巾,所以胖爸判断他们是六年级。)

下面先讲家长部分的安排。

学校介绍

在红领巾和老师的指引下,家长们进入了左侧的阶梯讲堂。而小朋友们则径直往前进入雨操室。

“小同学,所以我们现在是要分开活动对吗?”胖爸问一个红领巾(女生)。

“是的。”

“那我们一会儿在那儿碰头呢?”

“结束以后会有老师带队的。”

“好的,谢谢。”

胖爸走进阶梯讲堂,华二初中的学校介绍已经开始了,这时大约是12:35左右。胖爸赶紧直奔最后一排,找了个靠边的位置坐下,开始仔细聆听,也不时地拍照、录影。

大约5分钟之后,场内就座无虚席了。(下面这个图是散场以后拍的)

在总共大约80分钟的介绍里,三位老师和一位校长详细介绍了学校的办学历史、学校特色、华二优势、课程研究与设置、校园活动、食堂伙食等等,基本上涵盖了家长想了解的各个方面。下面挑几个胖爸觉得比较重要的。

1. 师资年龄结构很好

2. 教师的学历结构

3. 教师的职称结构

4. 丰富多彩的校园活动(体育节、科技节、艺术节)

5. “幸福花儿”课程体系

斯诺克大胖肯定会非常感兴趣。另外右下方的“科学创智”中不知道为何没有列出VR/AR、3d打印、Python编程等。

6. 课后服务课程

另外还有几个关键词值得一说:AI分层教学与走班跨学科

“人工智能”(AI)是整场“介绍会”中胖爸听到最多的关键词:

分层次“走班”教学解决学生基础不一的问题:

跨学科教学:

介绍会结束前,老师透露,孩子们都被带到教室里面“上课”去了,这次有语文、数学、英语、美术等等各个学科的老师,孩子们会被随机安排到其中两个科目中去。结束之后家长们就可以去操场和孩子们碰头了。

学生课堂

下面的课堂情景都是大胖口述的。

大胖一进雨操室,就站到其中一个队伍中去,每组25人。没想到这一组竟然碰到了大胖小学的同班同学。一行人在红领巾的带领下先后去了两个教室。第一个教室是美术老师(女),于是老师让每个小朋友画一幅“你心目中的学校”,结束之后可以交给老师,也可以自己带回家。大胖就自己带回来了。

接着大胖一组来到了数学教室。数学老师(男)比较年轻,将孩子们分成了5个小组,然后玩24点速算,先小组比赛,然后每个组的第一名再上台“总决赛”。

好像没有出现(3÷7+3)×7这样的“难题”。

“大胖,你们上课上得怎么样?”

“你怎么知道我们去上课了?”

“刚刚快结束的时候校长和家长说的。你们每人两堂课。你上的是哪两个科目?”

“先是美术,然后是数学。”

“哇,美术是你的强项啊。画小兔子吗?”

“不是,老师让我们画心目中理想的学校。”

“哦!那数学呢?有没有走神?”

“数学是算24点。”

“算得怎么样?”

“我们先分成5组,每组的第一名再最后上台比赛。我们组有一个可厉害了,几乎老师一出题他就算出来了。”

“那你怎么样?”

“我是我们小组第二。”

“课堂上有没有走神?还是十分的聚精会神?”

“嗯。没有走神!”

“比你们小学的课堂呢?”

“完全没有。”

“那还不错!”

参观

这一波家长基本都走完了,学校操场基本已经空了,胖爸觉得还意犹未尽,就和大胖一起继续参观校园。

华二初中并不大,而且建筑格局和大胖的小学几乎一致。

我们从操场出发,来到了校园中央的小花园、食堂、顺着铁梯来到二楼的“空中花园”,然后爬到三楼教学楼,逛了一圈,还发现了一个“隐藏”于角落的“咖吧”。在三楼的楼梯口,胖爸还遇到一位老师,胖爸和她攀谈了一会儿。主要聊了聊学校的分层次走班教学、跨学科的教学。

走班教学大体上就是每个班级的学生根据各科成绩划分几个组,比如A、B、C。那么上课的时候就是各个班级A组的在一起上课,B组在一起上课……也就是说你在语文、数学、英语课堂上很可能是和许多其他班级的小朋友一起听课。胖爸简单地总结为“编制上在一个班,课堂上可能是不同班。”现在华二初中的走班教学已经非常成熟了。

这位老师还介绍说华二初中正在研究让非常好的学生不限于在本年级上课,甚至可以到下一个年级去上课。这听上去有点类似于“保留编制的特定学科的跳级”。这个创新非常好,也非常符合胖爸的“让真正爱学习的孩子的学习无限好”的教学理念。不过学校的这个思路目前还在研究阶段,尚未实施。但是华二初中能够有这样的想法,胖爸还是必须点个赞!

最后胖爸聊到了跨学科教学,主要是传统教学中语文是语文、数学归数学、英语就英语的问题,从教师、考试层面就给孩子们的学习在学科之间划出了明确的壁垒,这样对于孩子未来的学习是不好的。淡化(而不是消除)学科间的壁垒,让各科知识在学习中能够融会贯通,统一解决问题,这样的学习会更加有效。该老师举例说学校有一定的跨学科教学,比如文言文中的数学(如《九章算术》)。但这样的“跨学科”还算不上真正意义上的跨学科,就好像做一道英文版的数学题(Please calculate the area of a square with sides of 4 cm.)。和这位老师简短沟通下来,胖爸觉得华二初中的“跨学科”教学推进得不够,深度和广度可能都不够。

不足

可能由于报名的家长人数众多,时间有限,学校的特色无法给家长逐一呈现。胖爸十分理解。华二初中确实有不少教学理念与胖爸的想法殊途同归,有些理念甚至超过了胖爸的预期(如跨年级走班)。

开放日结束后,胖爸就不断地在思考这样一个问题:

一个学校面向家长的开放日,到底应该给家长呈现最好的,还是最真实的,还是既最好又真实的?

胖爸总结一下,这次华二初中开放日事实上在家长宣传会上呈现的就是“最好的”,可谓处处挠你心扉,当然做不做得到,做不做得好,得以后才知道。宣传会结束之后胖爸自己又走访了一下,下面胖爸把自己感受到的不足之处罗列一下:

1. “教育为先”和“利益为先”

校长这番话听了很难不让人联想到是在影射嘉定世外,而且嘉定世外的开放日就在次日(4月14日,周日)。

2. 细节太少

宣传会较着重于宏观的学校介绍,缺少学科的细节描绘。这次宣传会没有安排科任老师介绍具体学科教学的特色或优势,尤其是“走班”形式下不同层次的教学特征(针对语文、数学、英语)。胖爸也没有机会能够和华二初中的科任老师沟通,很是遗憾。科任老师对具体学科的教学理念和学习理念(因为老师也应该在自己的学科上持续学习)对教学亦至关重要。

3. 关键问题

下面的一些问题,胖爸好像没有听到:

1)华二初中还有机会直升华师大二附中吗?若有,名额如何?

2)2020、2021、2022、2023连续四年报名/录取人数比。因为录取人数在官网是公开的,所以如果能够提供四年报名的人数供参考就好了。胖爸后来在3楼和老师聊天得知,2020年接近2:1,2023年约4.5:1,大致是呈上升趋势(报名/录取)。

4. 不确定性

这个问题不应该丢给华二初中。

当大胖恋恋不舍离开华二初中时,胖爸突然反应过来:“就算你报名了也未必摇号摇得到!”

几乎每一个老师都在强调,如果对口公办学校录不满,不妨一摇。可见摇号这种不确定性也影响着学校。

总结

胖爸带着“挑刺儿”的态度去参加华二初中的开放日活动,刺儿没挑到,还仿佛遇见了教育上志同道合的“同志”。跨年级“走班”的创意确实令胖爸眼前一亮。大胖在四年级的时候,我就曾把六年级的英语卷子给他做,还故意把“六”给扣掉了。结果大胖还做对了。

现在小学英语背单词,默中文,写作让小朋友背“范文”,完全看不到学好英语的希望,纯粹是把英语作为考试的工具。

希望华二初中能够迅速推进跨年级“走班”的教学策略,让爱学习的孩子的学习无限好!

由于华育、兰生复旦的开放日都安排在了同一天,因此鱼与熊掌无法兼得了,胖爸亦无法做出比较。另外关于上宝中学,胖爸没有找到他们的官方网站。

最后,胖爸也不忘给大胖打好预防针:“未来你很可能不会来到华二初中读书。但是你要知道,真正的炭火,无论是在沙漠,还是在冰天雪地,它都能发光发热。所以学校不是最重要的,关键还是要看你自己!”

最后的确认:在不到20%摇号“中奖”的概率下,我们最终商议还是不报华二初中了!

2024.4.7英语阅读理解练习

How Things Move

We can watch things around us move. When something is in motion, it changes its position. Objects can move from one place to another. They can move in many directions. If you roll a ball, it might move in a straight line. It might also move in a curve. A swing can move back and forth. A light switch can move up and down. Fans have blades that move in a circle.

If you want to know if something is moving, you can compare it to other things around it that are not moving. If the things behind the object are changing, the object is probably moving. If they are not changing, the object is probably not moving.

You can measure the distance an object moves. Just measure the distance between where it was when it started to move and where it was when it stopped. Distance can be measured in inches, feet, yards or miles. Those measurements are in the customary system. It can also be measured in millimeters, centimeters, meters and kilometers. Those measurements are in the metric system.

1. What happens when a ball is rolled?
A. It can move in a straight line or a curve. B. It can move up and down.
C. It can move in a circle. D. It can move back and forth.

2. You are around 145 _________ tall.
A. millimeters B. centimeters C. meters D. kilometers

3. What’s the Chinese for “probably”?
A. 很可能 B. 不可能 C. 慢慢地 D. 快速地.

4. When something is in motion, what does it change?
________________________________________________________________

5. How does a light switch move?
________________________________________________________________

6. How can you test if something is moving or not?
________________________________________________________________

2024.4.6英语阅读理解练习

Color Shows Mood

Artists use color to create patterns. Color can also show different moods. Bright colors make us feel happy and energetic. Dark colors make us feel calm or sad.

The primary colors are red, yellow, and blue. They are the colors that can be mixed together to make different colors. Mixing two primary colors makes a secondary color. The secondary colors are orange, green, and violet (purple). Orange is made by mixing yellow and red. Green is made by mixing yellow and blue. Violet is made by mixing red and blue. Intermediate colors can be made by mixing a primary and a secondary color together. Some intermediate colors are blue violet and red orange. Black, white, and gray are special colors. They are called neutral colors.

Colors have been organized into a color wheel. It shows the three primary colors, the three secondary colors, and the six intermediate colors. Artists use the color wheel. It helps them know which colors they want to use together.

1. How may an artist use colors to influence(影响) the viewer’s mood?
A. By using only primary colors.
B. By using bright colors to evoke feelings of sadness.
C. By using dark colors to make the viewer feel energetic.
D. By using bright colors to make the viewer feel happy and energetic.

2. What can be created by mixing a primary color and a secondary color together?
A. A neutral color. B. A primary color. C. An intermediate color. D. A secondary color.

3. What is the purpose of the color wheel for artists?
A. It helps them mix primary colors to create secondary colors.
B. It helps them decide which colors to use together.
C. It helps them create neutral colors like black, white, and gray.
D. It helps them create patterns with colors.

4. What are the primary and secondary colors?
________________________________________________________________

5. Tell four neutral colors according to(根据) the text:
________________________________________________________________

6. What’s the Chinese for “intermediate colors”?
A. 过渡色 B. 中间色 C. 三原色 D. 混合色

2024.3.29英语阅读理解练习

The New Girl

There was a new family in the neighborhood. They had a little girl about Fiona’s age, and Fiona really wanted to meet her. The first time Fiona saw the new girl in school, she smiled and said hello. When she saw her on the bus home from school, Fiona asked if they could sit together, and she told the new girl all about their neighborhood. One afternoon a few days later, when Fiona was outside playing with some of her friends, the new girl came outside. She stood in her front yard, looking uncomfortable. Fiona smiled, and waved, and called to her, and invited her to come and play, which her new friend was happy to do!

What’s the new girl’s name?
A. Fiona B. Neighborhood C. Not sure.

She stood in her front yard. Who is she?
A. Finoa B. The new girl C. Not sure.

She stood in her front yard, looking uncomfortable. “looking uncomfortable” means ________________________.
B. looking for something B. not feeling good C. thinking about something. D. Interesting in something.

What is the main idea?
A. Fiona takes the bus to school.
B. There is a new family in the neighborhood.
C. Fiona is a very friendly girl.

Which of the following is a supporting idea?
A. Fiona smiles and says hello.
B. The family has a girl about Fiona’s age.
C. There is a new family in the neighborhood.

2024.3.28英语阅读理解练习

Our elementary school chorus had the largest participation in its history this year. They did eight performances – three in school, and five around town – and received an award for Most Improved School Vocal Group from the state. There was a lot of great talent, and ten students make All County Chorus.

1. What’s the Chinese for “chorus”?
A. 合唱团 B. 诗社 C. 跳踢队 D. 球队

2. What does the text tell?
A. Our elementary school chorus is very popular.
B. Our elementary school chorus had a very successful year.
C. There are a lot of students in our elementary school chorus.

Helen held the new baby carefully in her lap, while her anxious parents hovered nearby. Helen could hardly believe how tiny she was. Helen’s heart swelled with pride, and a new sense of responsibility.

1. Helen’s heart swelled with pride means ______________.
A. Her heart is beating with pride.
B. Her heart is full of pride.
C. Her heart stops with pride.
D. Her heart has nothing to do with pride.

2. What does the text tell?
A. Helen is going to take care of the baby.
B. Helen is a nurse.
C. Helen has a new baby sister.

2024.3.27英语阅读理解练习

Food is our fuel

Everything that is alive needs energy. All animals get the energy they need from food. People are animals. Think about the human body as an amazing machine. It can do all kinds of things for us. Food is the fuel that helps keep the amazing machine running.

Plants use sunlight to make their own food. Animals are not able to do that. Some animals eat plants. Some animals eat other animals as meat. Some animals, like people, eat both plants and animals.

Since plants make their own food using sunlight, the Sun’s energy is found in plants. The Sun’s energy is very strong. It loses a lot of its strength by the time it goes into a plant.

When we eat plants, we get more of the sun’s energy than when we eat animals. That’s why it is good to eat fruits and vegetables. When an animal eats a plant, the energy is less strong. The animal also used its energy to find the plant to eat. When a second animal eats the first animal, it gets even less energy than the first animal got. The second animal used a lot of energy to chase its prey.

Like a car that has to be filled with gasoline, living things have to eat again and again. Instead of gasoline, living things use food as fuel.

1. What’s the Chinese for energy?
A. 精神 B. 食物 C. 能量 D. 动物

2. Where do all animals get their energy?

3. Where do plants get their energy?

4. If our bodies are amazing machines, then food is our _____________________.

5. Why do we get more energy from eating vegetables than we get from eating meat?

6. If a third animal eats the second animal, will it get more or less energy?

It’s time for Chinese class前面到底要不要冠词a?

在大胖的知识点上出现两个“奇怪”的句子:

It’s time for Chinese class. = It’s time to have a Chinese class.

前一句没有冠词a,后一句却有a。那么到底要不要“a”呢?

事实上有没有冠词a都可以,两个句子都是正确的,不过二者表达的意思稍有不同。

表达一般意义上的“该上语文课了”,习惯上不用冠词a:

It’s time for Chinese class.

下面的例子则说明了为什么用冠词a:

We just had 3 English classes. It’s time for a Chinese class.