请教數學題

jilin1960

Thirty-two feet of fencing materials is used to enclose a garden that is a rectangluar region .if the numble of square feet in the region is f ,what is the largest possible value of f?

laorenjia

回覆 laorenjia 的帖子

Eviepa
我諗你打漏咗個「認」字。

laorenjia

eviepa 發表於 15-2-25 22:23
laorenjia,

和你有點相似，我比較容易變成child mode，十年前對著年幼的女兒，可以聊天聊得大家都很高興， ...

我哋確實有好多地方似，有時睇你啲嘢，分分鐘以為喺自己寫嘅。

eviepa

今次版主又做得好快手喎，我正想正式警告大家聰明仔爸又番黎，都未出手，聰明仔爸呢個新網名lamyeelok已經俾版主封左戶。

laorenjia

friendlyguy 發表於 15-2-26 23:03
回覆 laorenjia 的帖子

Dear Laorenjia, The following is how we solve the chicken and rabbit problem  ...

Then you must be younger than me. I was taught your arithmetic method as well at p5. Actually I used the same method In my old post but I just used cutting rabbits' feet to make it more interesting for kids to remember.

friendlyguy

回覆 laorenjia 的帖子

Dear Laorenjia,

The following is how we solve the chicken and rabbit problem in primary:

• Assuming all animals has 2 legs. There will only be 12X2=24legs

• But,there are 32 legs. Therefore, there is 32-24=8legs in surplus

• These 8 legs are all come from rabbit. Each rabbit contributes 2 legs. Therefore, there is 8/2=4 rabbits

• Putting all together: (32-12X2)/2=4 rabbits. There is 12-4=8 chickens

  
  

In my primary school days, X should not appear in the equation. No algebra of any form was taught.

friendlyguy

laorenjia

friendlyguy 發表於 15-2-26 01:25
There are different branches of mathematics. The method Uncleedward used in solving the chicken and  ...

Dear Friendlyguy
Thank you for coming to my rescue and your endorsement, again. It's interesting to note from your reply that you could be even older than me as I was not taught simultaneous equationso to solve chickens and rabbits questions in my primary school days. We just used simple equations. By letting the number of chickens be x, the number of rabbits is then 12(total number of chickens and rabbits) - x,  we can then formulate the equation to account for the number of feet : x*2 + (12-x)*4=32. It's true though most secondary school students, once they have learned simultaneous equations, they tend to forget simple equations. However these questions seldom appear in primary schools today, with a few exceptions like the primary section of spcc.

Thanks again for your explanation.

eviepa

我肯定讀小五時我做到正確答案。如果小學五年班有多D呢類咁有挑戰性嘅題目，我就唔會覺得數學係一科悶蛋科目。

friendlyguy

回覆 kenwong888 的帖子

I don't think it is necessary if the student already know fraction and decimal. If the data provided in the original problem is 30 ft. A student can still use guess and check method to deduce the answer should be 7.5ft.

6X9=54

7X8=56

8X7=56

9X6=54

Therefore:

7.5X7.5=56.25

However, if the student has not been taught with fraction, your condition will be necessary.

I believe the thread owner's son is a P5 student in SIS. I think fraction has already been taught.

Guess and check method is a very good exercise for primary student since require the student to manipulate a series of simple arithmetic equation before an answer come out. It can develop their mathematical sense for higher level maths., such as mathematical induction. In this case, a reasonably intelligent student can deduced that for a given perimeter, the area of a square is larger than a rectangle.

kenwong888

friendlyguy 發表於 15-2-26 01:25
There are different branches of mathematics. The method Uncleedward used in solving the chicken and  ...

Maybe the question should be revised as the fence is one-meter long each right???
Otherwise I only see the question ill-formed for primary student standard...

friendlyguy

There are different branches of mathematics. The method Uncleedward used in solving the chicken and rabbit problem is arithmetic which may be the most basic and fundamental category of mathematics. Simultaneous Equations is an algebraic method which, in my opinion can only be understood by student who has learned the basic arithmetic. That’s why, in my date, we learn to solve this problem arithmetically in P5 or P6. Once we learn algebra in secondary school, everybody will tackle this type of problem with simultaneous equations which is an easier and faster method. I don’t think any of these methods lacking proper mathematical treatment or insight into mathematical problems.

Knowledge has to be built up bit by bit.

Come back to the maths problem in this thread. The table made by laorenjia is using the `guess and check’ method which is considered a very proper way of tackling maths problem in primary school. A junior secondary student will solve it by completing the square (algebra) while a senior student will use differentiation (calculus). These are all proper maths methods.

I can’t image a student, even for the maths genius, can learn calculus without learning algebra and arithmetic first.

eviepa

laorenjia,

wunma的消失，也令我有點悵然。BK再不是從前地踎茶餐廳，而是一間有規模的連鎖飲食集團，甚麼都變了。

女兒長大了，現在其中一個身份是補習老師，大學同學們也多有一份或以上補習的，有時也會傾談一下怎樣補習。談及補習英文，同學們都著重補文法；她則主力鼓勵閱讀。

很有趣，在第一代閱讀派開風氣之先，再經過第二代自創或跟隨者的分享後，現在《小學雜談》內，閱讀功效最大已近乎共識，文法練習已淪為輔助工具。

更加有趣的是，過去十年內，傾談過英語學習的老師中，用很大力氣去誘導子女英語閱讀的，比例十分高，尤其是英文老師。

第一代及第二閱讀派取得的成果有目共睹，經常上EK小學、中學論壇的，都知道甚麼是最好，但離開EK的，文法才是正宗。

英語老師用很大的力度讓自己的孩子閱讀，但自己的學生、別人的孩子，絕大部分卻仍懵然不知................。

我很有興趣繼續看下去，這格局幾時會變。

四十年前，狠狠地打仔被認為是教仔良方。現在絕少人抱這種態度。不打少罵肯定是香港教仔要走的路向，這格局幾時會變？

巨輪始終會轉向，我卻很喜歡用自己的螳臂，企圖加速巨輪的轉變。

laorenjia

eviepa 發表於 15-2-25 22:23
laorenjia,

和你有點相似，我比較容易變成child mode，十年前對著年幼的女兒，可以聊天聊得大家都很高興， ...

I actually feel pity for myself as if I am repeating part of my life, even possibly with the same people. And I saw the disappearance of some old friends like Wunma indicated by deleted entries in the old post and possibly judy. I feel agitated n sad suddenly. I never used punctuation marks like I just did, not even with wisekiddad n it  was with an unworthy opponent(I'm a snob after all as Wicked described in the old post). I pity myself.

laorenjia

kenwong888 發表於 15-2-25 22:32
Both Module 1 & 2 include Calculus!!!
Still sleeping & dreaming right???

Dear dreaming friend

IT'S EXACTLY RIGHT!!!
M1 n M2 are called extended modules n are separate from so called Maths, RIGHT???

kenwong888

laorenjia 發表於 15-2-25 22:07
My dear friend
The guy dreaming definitely is not me. Pls read carefully. I was referring a post e ...

Both Module 1 & 2 include Calculus!!!
Still sleeping & dreaming right???

eviepa

laorenjia 發表於 15-2-25 17:33
琴日—家去睇戲，賀歲片中除港產片外，就只剩慌失失企鵝未睇，因家人受我影響，都喜歡睇戲。其它戲都睇過， ...

laorenjia,

和你有點相似，我比較容易變成child mode，十年前對著年幼的女兒，可以聊天聊得大家都很高興，所以有時讓太太說我大唔透。不過，我正經起來，講家事國事天下事，太太卻搭不上咀來。自我陶醉一下，這可能叫做未失赤子之心。

我比較懶，懂得一種甚麼都能解的方法就不去理會低層次的方法。見你這幾個回合，我還很清楚記得當年你也是這樣，正想說你當年又是這樣，還未說出口，你自己就將當年的討論的論題列了出來。

講到長方形，相同邊界，長和闊甚麼比例面積會最大這問題，我在大概小五時，自己就想出了答案，肯定是正方形是面積最大。後來，六年級末段時學習座標的曲線，當中有例子介紹這問題，才知道長和闊不同比例可的形成一條曲線，亦證實了我的想法。

對高中孩子來說，明白正方形是面積最大，相信不難。

laorenjia

kenwong888 發表於 15-2-25 20:52
Are you still dreaming???
HKCE???
Now is HKDSE!!!

My dear friend
The guy dreaming definitely is not me. Pls read carefully. I was referringa to a post entry I wrote in 2007 when hkdse was nowhere close. And the last time I checked, core maths in hkdse still doesn't cover differentiation. RIGHT??? Finally pay attention to the main message other people are trying to convey, will you? RIGHT???

kenwong888

laorenjia 發表於 15-2-25 17:33
琴日—家去睇戲，賀歲片中除港產片外，就只剩慌失失企鵝未睇，因家人受我影響，都喜歡睇戲。其它戲都睇過， ...

Are you still dreaming???
HKCE???
Now is HKDSE!!!
Need to learn differentiation right???

laorenjia

琴日—家去睇戲，賀歲片中除港產片外，就只剩慌失失企鵝未睇，因家人受我影響，都喜歡睇戲。其它戲都睇過，張就時間就連粵語版都殺啦。全場我哋係唯一成人組別，好多細路，妻子隔離嗰個得兩歲左右。企鵝彈吓彈吓佢就笑，企鵝跌出飛機佢就喊，但我都唔係好得幾多，老婆係咁叫我咪笑得咁大聲。我個人就係咁，掂吓啲細路仔嘢就會turn into the child mode. 為咗教女兒數學，我確費了一番苦心，硏究用算術方法而非代數方法教女兒高小算術。但不知為什麼，有些家長總覺得我的方法不正統，非要用代數方法甚至微積分不可。這些家長要嗎是沒有孩子，要嗎孩子都不用教。可惜我接觸的孩子小學時都沒有好奇心學—元二次方程或者微積分。我只能嘆一句，這些家長都離開小學日子太遠了，都已經忘了自己小學數學的日子是怎樣走過來的。說來奇怪，我幾年前對Judy的雞兔同籠問題提出非代數的將兔仔腳斬去的血腥算術解法也有些家長與這裏的家長差不多，在提不出他們所謂正確的算術解法的同時，老是用'right?','understand?'等empty-worded questions and condescending tone 同人講嘢。幾年過去，如出—轍。

http://www.edu-kingdom.com/forum ... 75529&extra=&page=2

由post no. 29 開始。

As I said then,  

Non-algebraic methods tend to more tedious than using equations but they tend to be more interesting as well.

It is always nice for a kid to master more advanced mathematical tools than those currently taught at school, but in no way this should be the requirement for all the students.

For example, in Mathematics at HKCE level, we are not supposed to use differentiation to find the minimum or maximum value of a quadratic function. The more tedious "completing the square" method is expected. Even in Additional Mathematics, to find the area of a triangle in coordinate geometry, one is not expected to use the more general, and much simpler "determinant" method learned in more advanced maths.