Prime Factorisation Homework

Textbook p9 #2:

The Prime factorisation of a number is 2^4 X 3^5 X 7^2 X 11.

Write down 3 factors of the number that are greater than 100.

(Hint: 16 X 11 = 176, which is a factor.)

My Answer: 2673, 539 and 23814

2^4 X 3^5 X 7^2 X 11= 2X2X2X2X3X3X3X3X3X7X7X11

2X2X2X2=16

3X3X3X3X3=243

7X7=49

Since the hint given is taking 16 times 11 to get the factor, then I guessed other factors could be calculated using 243 and 49 times 11 respectively.

So we have, 243 X 11=2673 and 49 X 11=539

Then I used the calculator to calculate the answer for 2X2X2X2X3X3X3X3X3X7X7X11 which is 2095632 and then I used the calculator to double check that both 2673 and 539 are factors for 2095632, which means my guess was correct.

Now, I have to find one more factor for this question. I used 2X2X2 (Please note that I used 2X2X2X2 to times 11 the previous time but now I am using 2X2X2 to times 11)times 11 and the answer is 88. So from here I know 88 is a factor of 2095632, but since it is not more than 100, I used 2095632 to divide it and got the result 23814. 

After doing the homework, I realise that using the prime factorization, we are able to get the original number given and to find the factors and the highest common factors. :)

Textbook p9 #26:

The Prime factorisation of two numbers are 2 X 3^2 X 7^3 X 13 and3 X 7^2 X 13^3 X 17 .

Write down 3 common factors of the numbers.

My Answer: 3, 7 and 13

Prime number 3, 7 and 13 are present in the two prime factorisations and so these three numbers are the 3 common factors. :)

Lai Ziying

Maths Homework 19.1.2010

Textbook: Brainworks (p8)
Q24(b) A mathematician proposed that "Every even number greater than 2 can be expressed as a sum of two prime numbers." Do you agree? Why?

Yes, I do agree because I was able to express the even numbers (which I anyhow pick for myself to try out) as a sum of two prime numbers. Then I went online and found the information below.

Why Does Every Even Number Greater Than 2 Can Be Expressed As A Sum Of 2 Prime Numbers?

Even numbers have several ways to be the sum of two prime numbers. For example, the number 36 can be shown as '5+31', '7+29', or '17+19'. By looking at these examples, it appears that the higher the even number, the more pair of prime numbers there are that add up to it.

There is an assumption that says that every even number can be expressed as the sum of two prime numbers at least in one way. This assumption is called as Goldbach's conjecture, after Christian Goldbach, a Prussian mathematician who propounded it. it remains to be one of the most ancient problems that is yet not completely solved in the field of mathematics. The conjecture basically states that every even integer that is greater than the number 2 can be expressed as the sum of two primes.

Cited from: http://www.blurtit.com/q710414.html

Lai Ziying

12 January: Numbers as a Language

After doing research on the Internet, I have learnt the history of the development of numeration systems. I choose the Roman numeration system to present 2010 is because the Roman numeration system is more pragmatic with respect to mathematics than the other numeration systems. Being pragmatic is how I feel about my learning is going to be in SST in 2010.


Lai Ziying

Communication Homework

1 Why is communication important?

We need so socialise with the others through communication and it also enables us to get connected with one another. Also, through communication, we will be able to understand the people around us as well as the world. Without communication, we are able to achieve nothing but become a loner.

2 What is/are your favourite form/s of communication? Why?

My favourite way of communicating with others is talking. I feel that I am able to express and receive messages more freely and clearly through talking. When we communicate by talking over the phone, we are able to ensure that the person gets the message on time as sometimes people check their online social networks and handphone messages only at a certain time and this may delay the person from getting the message right away.

3 How do you decide which form of communication to use in a situation?

I will look at the form of the message and the audience that I want to pass the message to and choose the form of communication that will ensure that the people get the message in time.

4 What difficulties do you face in communicating with others?

I don’t think I face any difficulties in communicating with others as long as I know what I want to say and how to go about expressing it in a way that people understand.

Lai Ziying

随笔 100percent 我的copyright :D

时间过得很快，时间能证明爱的价值和存在，除此之外，时间还能做些什么呢？

时间VS离别

时间代表着相聚和离别。有时候的离别是短暂的痛苦，但是，我们也要珍惜和我们相聚的人，因为他们和我们在一起的时间也许没有我们想象中的那般长久。离别前，我们或许经常这么告诉自己：“这是倒数第X天，我要好好珍惜。”


我们就这么说着，直到最后一天，看着挚爱的人要离开自己时，直到他们坐的车门紧紧地关上，直到车子启动离去后，我们才恍然大悟，无论离别再怎么难舍难分，也不过是一霎那间的事。霎那过后，车里的人带着我们的思念离去，我们便继续我们的旅程，谁也不必在原地踏步，因为时间不等人，也因为地球不会因为我们的情绪而停止自转。


离别让我们学会经历感慨和难过，也让我们学会克服自己的担忧和调整自己的情绪。离别让我们的思绪纷飞，更加地让我们明白自己的内心，更了解自己的需要。

时间VS交错

有人说，跨年时是个喜庆的日子，人们那么说着是因为大家都和自己的家人在一起。那些在外漂流的游子便说了这么一句话：“跨年对我而言并没什么大不了，因为我觉得时间不仅仅是在跨年时才交错着，它在一秒一秒之间便已经在交错，哪怕是现在，跟下一秒，我们都在经历着得到和失去，我们都在跨越时间。”

小时候VS长大后

小时候我看着大人部落格里的文章写道：“最近真累！”时，我觉得大人很爱抱怨；小时候读到大人的感受：“为什么上天这么不公？！”时，我觉得大人无理取闹。现在的我偶尔在生活中感到疲惫时，我便上网写写自己的感受，忽然才发现，原来大人口中的“累”不仅仅是身体的，更多的是心灵的，我明白因为我感同身受。但我不停止在“抱怨”这一阶段，而是用最适合自己的方式为自己调解疲惫，让自己放松，休息是为了走更长远的路。虽然“最近真累”我和大人们有同感，但后者--“为什么上天这么不公”，我却有不同的感想。


若你在生活中真的遭受到会让你发出如此感慨的话时，为何不让自己停止钻牛角尖，停止浪费时间发无谓的牢骚，然后开始自我检讨，开始积极向上往前走呢？当人们成功时，我们会自信满满地告诉别人：“命运掌握在自己手里。”，但当我们经历消极时，又为何要把自己的坎坷归咎于“上天”呢？


刚刚听到一首歌：“穿上一件蓝色旗袍... ...”
小时候听到的是：“穿上一件蓝色旗袍... ...”
现在的我听到的是：“女孩喜欢蓝色旗袍，那给她自信，让她觉得很有安全感。”


CD里播着：“很爱很爱你，所以愿意让你飞到更幸福的地方去。”
小时候的我听到的是懵懵懂懂的：“很爱很爱你，所以愿意让你飞到更幸福的地方去。”
但现在的我听到的是：“因为爱你所以放弃你，但假装放下让你飞，自己却独自面对孤独的悲伤。”


时间会让人成长，但有些人在时间的推移下，继续一成不变。


小女孩时期的我们会因为鼻子旁边长了颗青春痘而闹得全世界都知道，那时我们在找共鸣，在找人与我们分享青春期时的“乐”和“悲”。但时间走了，我们也该像个大女孩了。痘痘还是会长出来，但是我们不能再把这些鸡毛蒜皮的事一件件地在网络上交代了。有人会觉得你肤浅，但我个人认为，把写这些鸡毛蒜皮的事的时间花在更有意义的事情上，会让人更有一番成就。


这就是长大，需要分清轻重，需要明白自己需要什么，需要学会舍取和适应。


更多时候，我从自己身边的例子深深感觉和总结道，我们应该为自己定时设定一个目标，然后带着自己的冲劲和无限的热忱去实现理想。理想不必多宏大，但那是对自己的一个肯定以及确保自己不怠慢人生的一个必须点。

成长VS失去了保护层

小时候舅舅到家里做客，看着坐在客厅的我手中拿着画笔一丝不苟地上颜色时，作为室内设计师的他便教他眼中的那个小女孩--我，如何涂颜色。那时的我忘了说声谢谢，那时的我沉浸在自己的杰作中自得其乐。


长大了，没有人再可以那样细心、耐心、手把手地教你如何上颜色，如何均匀颜色了，一切都得依赖自己，去探寻，去发现。偶尔当我们觉得迷失时，总会有个叫做“家”的地方让我们振作。当我们回到自己熟悉和熟悉自己的人的身边时，家的味道回来了，哪怕在外面迷失了一天，疲惫了一天，失去方向了一天，但当我们回到自己熟悉的地方、熟悉的人的身旁时，原本的自信和淡定又会回来的！


长大失去了大人给予我们的保护层，并不是因为他们不愿意给予，只是他们无法给予，也不该继续给予。因为我们的环境在改变，要适应环境的人是我们，不是他们。停止给予我们保护层会让我们独立，会让他们放心，这也是我们双方都该做的。

成长VS欣赏和思考

对我自己而言，对于成长最深的体会就是学会思考。

灵感源自于潜意识的思考，沉思让人学会彷徨和独立。

对我个人而言，学会思考是一切的基石。

以下是一些我喜欢的语句，它们曾经让我一度思考和斟酌:

忙碌的蜜蜂没有悲伤的闲暇

多建一所学校就可以少建一座监狱

越学越觉得自己无知

以后到了社会工作，是比实力，而不是比考试谁能得100分

时间VS青春

或许时间可以代表着我们人生的路。下面这段话是摘抄自《在青春的岁月》里，无论你的人生历程有多少，我觉得，你都能如我一样，从下面这段话里找到共鸣。只是随着时间的推移，共鸣的程度会越加的深，与人分享的感慨也会越加地多：（括号里的字是我自己写的内容）

我们浪费掉了太多青春，

那是一段如此自以为是又如此狼狈不堪的青春岁月。

有欢笑，也有泪水；

有朝气，也有颓废；

有甜蜜，也有荒唐；

有自信，也有迷茫；

我们敏感，我们偏执；

我们顽固到底的故作坚强；

我们轻易的伤害别人，也轻易的被别人所伤害；

我们追逐于颓废的快乐，陶醉于寂寞的美丽；

我们坚信自己与众不同，坚信世界会因为我而改变；

我们觉醒其实我们已不再年轻，我们的前途或者也不再是无限的，其实它又可曾是无限的。

（赖同学我本人不认同这句话的后两个部分，我觉得那是情绪低谷时人们才会说的话）

曾经在某一瞬间，我们都以为自己长大了，有一天，我们终于发现，长大的含义除了欲望，还有勇气责任和坚强，以及某种必须的牺牲。

（的确，依照我自己的生活经历而言，我曾经无数次地在博客中写道自己成长了，但随着这样的字眼出现的次数增加，我发现，我们只是在某一瞬间，在一个阶段后发觉自己长大了，但其实，我们也会觉醒，自己还在继续成长。路还很长，成长的脚步不间断。）

在生活面前我们都还是孩子，其实我们从未长大，还不懂得爱和被爱......

（有时候摸索，有时候迷惘，有时候绝望中带着坚强。有句话说，最坚强的人不是没有眼泪的人，而是含着泪奔跑的人。曾经有那么一个时刻，不，是许多那样的时刻，我害怕自己落队，害怕自己跟不上生活的脚步，而对于未来的“隐隐约约”，我有着强烈的担忧。但那些都是过程罢了，有担忧才有思考，有思考才有实践。不要忧愁，因为生活本身就让我们对它有信心，对我们自己有信心。时间到了，我们会依照自己的需要活出最好的自己。失望，但不绝望！）

时间VS很多很多

It's just the beginning, we still have a long way to go... Enjoy! It may be tough, but beautiful :)

*(Life is tough but beautiful is my primary school teacher's motto)



赖紫莹
101


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My Personal Reflection On the Amazing Race

 
I think our school value "Expanding Our Learning Networks" means that our learning should not be just limited from the books or the school compound but anywhere. Such as we went around the Clementi Neighbourhood today and through out the whole activity, we observed, led, thought and so on. Through the whole process, we built up our bond within the class and learnt new things outside the school compound.This school value teaches me that we are able  to learn new things from anywhere.
 
This value is important because it will teach us to be more observant of the things around us and we will be more creative and innovative in thinking. This value alslo suggests that we should not limit our learning network.
 
Lai Ziying

My Reflection On the Team Building Challenge

I think "Forging Excellence" means as a school, we should play our indivisual part and when all our parts are being played well, we are forging excellence. So the excellence is not for each indivusual, but to the whole school as a team. Since this "excellence" needs to be "forged", each one of us matters and is important. We should aim for our goal and live up to excellence and then when our dreams come true, that's when we are an excellent and united team as a school.
 
 
I think my interest and enthusiasm in learning will help me to success. Plus, I know what I want and I am willing to work towards my goal! No matter how tough it is going to be. Because I know I will pull through it all!
 
 
I think I should try to understand my friends around me and find an effective way to communicate with them. I have to make them feel that I respect them so that they may respect me in the same way and pay attention to my opinions.
 
 
I can contribute to the success of our class by sharing my thoughts with my classmates and help them if I am able to. Besides sharing point of views and helping one another, I will do whatever I can to make our class an united team so that we will be stronger!
 
 
Lai Ziying