Interactive Heuristic Problem Solving Guide 1 (part 2 of 2)

Practice Time!

1. A florist had to send vases to her customer. Customer will be charged $14 for every vase delivered without broken, she will not charge the customer and will compensate customer $5 for every broken vase. That day, she delivered a total of 2880 vases, and collected $33480. What was the total amount of vases that she delivered without broken? (2520)
2. Henry and Ramu played a dart game. When Henry won, Ramu gave him $4. When Ramu won, Henry gave him $3. In a day, they played 20 games. How many games did Henry win if he won $66. (18)
3. The company delivers some flower vase. For every vase delivered on time, the company charge $20. For every vase delivered late, the company compensate $5. If the total company collected was $5000 after delivering 320 vases, how many of them were delivered late? How many were delivered on time? (56, 264)
4. The company delivers some flower vase. For every vase delivered on time, the company charge $20. For every vase delivered late, the company will not charge a single cent (vases are free of charge). If the total company collected was $5000 after delivering 320 vases, how many were delivered late? How many of them were delivered on time?
5. The company delivers some flower vase. For every vase delivered on time, the company charge $20. For every vase delivered late, the company charge $18. If the total company collected was $9100 after delivering 505 vases, how many were delivered late? How many of them were delivered on time?
6. The company delivers some flower vase. For every vase delivered on time, the company charge $20. For every vase delivered late, the company give customer 25% discount. If the total company collected was $3100 after delivering 205 vases, how many were delivered late? How many of them were delivered on time?
7. The company delivers some flower vase. For every vase delivered on time, the company charge $20. For every vase delivered late, the company will discount $3 for every vase. If the total company collected was $3500 after delivering 205 vases, how many were delivered late? How many of them were delivered on time?  

Challenging Advanced Learners:

X Delivery Company charges $6 for parcels delivered on time and free of charge for parcels delivered late. In the month of May, X Delivery Company collected $2592. For every 20 parcels delivered, 2 were delivered late. 

(a) What was the total number of parcels that were delivered on time? (432)

(b) How much less money did X Delivery Company collect in May due to the late delivery of the parcels?  ($288)

Miss Liew: How is this question different from those mentioned above? 

Words to the readers:

Are you able to solve these questions? 

What pattern/rule do you observe? 

Are you able to generalise the rule to other questions? 

Interactive Heuristic Problem Solving Guide 1 (part 1 of 2)

More often than not, students do not lack practice questions, but the techniques on HOW to analyse and sieve out the "gems" behind each clue given in the problem sums. While it is important to guide the students the correct way to solve a question, they need to know why certain methods are wrong and not applicable too. For example, to learn why a particular solid is called a pyramid, one has to know why the other solids are not called a pyramid. This is what we call the non-examples.

In my blog, other than showing the different ways to solve a question, I will also include the common misconceptions that tend to arise or careless mistakes that students tend to make. 

Are you ready? Here we go... :) 

Example 1:

There are 50 questions in a quiz. 5 points are rewarded for each question answered correctly and 2 points are deducted for each question answered incorrectly. Jowe answered all the questions and scored a total of 194 points. How many questions did he answer correctly?

50 x 5 = 250

250 - 194 = 56

5 + 2 = 7

56 ÷ 7 = 8

50 - 8 = 42

He answered 42 questions correctly.

Common error(s):

50 x 5 = 250

250 - 194 = 56

56 ÷ 2 = 28

50 - 28 = 22

Discussion between the student and Miss Liew:

Student: Why not dividing 56 by 2? The question said 2 points are deducted, which means Jowe lost 2 points if he answered wrongly. Right?

Miss Liew: No.. He lost 7 points if he answered wrongly.

Student: What.....?

Miss Liew: First of all, he lost 5 points that he could have earned if the answer was correct. Then, he got deducted another 2 points for the wrong answer. So, he lost a total of 7 points for each question!

(More help: If students still cannot get this, ask them if they get the 5 points if they answer the question wrongly. After they agree that they did not get 5 points and still lose another 2 points, students will sense the loss as 7 points.)

Student: Is the 5 points what we call the.............?

Miss Liew: Yes, that 5 points is what we call the opportunity cost.

Student: Ah, now I understand!

Let's extend the problem:

Scenario 1: Instead of 2 points, what if 3 points are deducted for every wrong answer? How will this affect your working? 

Scenario 2: What if, instead of deducting points, no points were given for wrong answers? How will this affect your working?

Scenario 3: What if only 1 point was given for each wrong answer? How will this affect your working?

(This scenario is rare but well... for practice purpose.)

Be an innovator:

Student: Miss Liew, is it true that this 'opportunity cost' concept is only applicable to questions involving correct and wrong answers?

Miss Liew: Of course not. Do you want to try setting a question that is related to delivering vases and involves the 'opportunity cost' concept?

Student: What? I can set a question by myself?

Miss Liew: Of course you can. Everyone is an innovator.

Student: Ok! Let me try!

Words to the readers:

Thanks for reading. 

Have you encountered this type of questions before? 

What other difficulties do you face when coaching your child/student this type of question?

Let's share, exchange ideas and support one another.

(to be continued...)

合抱之木，生于毫末；九层之台，起于累木；千里之行，始于足下。

P2 Chinese: Common Misconceptions (11/9/2018)

1）月亮，读成月光。--> 亮 and 光 to them，seem to have the same connotation。
2）故事的故，写成攵+古。
3）借，写成错。
4）讲，写成进。
5）灾，读成 zhai。
6）灭和灾，混淆了。
7）从，读成chong。
8）着急，读成zhao1ji2 （大人们，我们也无意间犯了同样的错误吧！）
9) 了解了“着”也念zhao2，同学们今后笼统地把所有“着”都读成zhao（例：坐着zuozhao)
10)邻，读成ling，以为“林”和“淋"也是ling，“铃”。

乱了吧？
您的孩子/学生也曾经犯过同样的 boo-boo 吗？ 欢迎留言。

人是从哪里来的? 猴子进化来的吗？

关于人的来源，自古以来不外乎两种: (1） 人是自然而然就有的。2）人是出于一个智慧的设计，智慧的创造。 进化论认为：人是从猴子进化，演化来的。这种说法认为人是自然而然就有的。为什么这样说呢？ 持这种说法的人说：“人是从猴子进化来的。” 那么，猿猴是怎么来的？ “猿猴是从哺乳类进化来的” 那么，哺乳类是怎么来的？ “哺乳类是从爬虫类来的” 那么，爬虫类是怎么来的？ “爬虫类是从两栖类进化来的” 那么，两栖类是怎么来的？ “两栖类是从鱼类进化来的” 那么，鱼类是怎么进化来的？ “鱼类是从更低级的，从蛋白质，核酸，之类物质进化来的” 那么，无机物怎么来的？ “无机物是从原子分子来得” 那么，原子分子怎么来的？ “自然而然就有的” 所以他们最后就是说，人是自然而然就有的。 这是对人来源的一种解释，这种解释实际上是一种没有解释的解释。 “人是自然而然就有的",这样的解释给我们一个结论：人生是没有意义的，人活着是没有目的的。 因为根据这个理论，有些东西经过演化，经过碰碰撞撞就变成了无机物，有些通过进一步的演化进化，就变成了有机物，有些碰来碰去就变成了石头，有些碰来碰去就变成了狗，猫，另有些碰来碰去就变成了猴子，变成了人。那么，人生存的意义，跟这些猴子，狗，鱼，猫，甚至跟这些土，石，基本上没有什么本质的差别，全部都是物质的东西，人生存是没有意义，也是没有目的的。这种解释事实上否定了人生存的意义，价值和目的。 （人为什么活着？） 但是从经历来看，从深处的感觉来看，人生是有目的的。 在每一个人内心的深处都有一个“有目的”及“要有目的”的感觉。其实，这种感觉乃是神放在人里面，使人寻求神这位永远者。圣经传道书３：１１说：“神造万物，各按其时成为美好，又将永远安置在人心里。”这里的“永远”乃是指神所栽种，历代以来就在运行的一种要有目的的感觉；日光之下，除神以外，别无什么可以满足这种感觉了。（The Amplified Bible,扩大本圣经） 人活着是为着一个目的。所以进化论说人是自然而然就有的，与我们里面深处“要有目的”的感觉是相违背的，是不合我们里面“要有目的”的感觉。这是第一点。 第二点，进化论说人是自然而然就有的，是自然而然演化而来的。这种解释，事实上是一种不可知论，也就是不知到自己是怎么来的。这就好像桌子上的两个花瓶，甲花瓶问乙花瓶说，“你是怎么来的？”乙花瓶说，“我是自然而然就有的”乙花瓶就反问甲花瓶说，“你是怎么来的？”甲花瓶说，“我也是自然而然就有的。”这样的答案就是不可知论，这两个花瓶在它们自己里面，凭着它们自己，根本不知道它们为什么存在，从哪里来，要到哪里去，为什么会存在于这个桌子上。 其实，要知道这个花瓶为什么存在，从哪里来，到哪里去，最好就是问那位设计制作花瓶的人。那个设计制造花瓶的人可以清楚地告诉我们，他制造这个花瓶是为着何种的目的。他的目的是要把花装在这个花瓶里。 同样的道理，人在自己里面，想要了解自己是从哪里来，自己为什么在这世界上，自己要往哪里去是不可能的。你如果问我，而我在我自己里面，就没有答案。我如果问你，而你在自己里面，就也没有答案；即使有答案，也不过是一种猜测，一种遐想。 （人是神造的） 真正要清楚我们人是从哪里来，就要问造我们的那位造物主。圣经是神的话，是神－－这位创造宇宙万物的神－－给我们启示。圣经非常清楚地启示人的来源；人的来源是神，人是神所创造的。 启示录４：１１：“我们的主，我们的神，你是配得荣耀，尊贵，能力的，因为你创造了万有，并且万有是因你的旨意存在并被创造的。” 整个宇宙的被造和存在，都是这位创造万有的神为着他的目的和他的旨意创造的，不是随随便便，凭空产生出来的。宇宙是出自智慧的设计，智慧的创造，是造物主为着达到他的目的而产生的。宇宙是如此，人更是如此。神创造人是非常有目的的。圣经启示，神创造人是按着他的形象，照着他的样式创造的，他的目的就是他要进到人里面，就好像花瓶被造，是要让花进来一样；人的被造是要让神进来的。人是照着神的形象被造的，就好像手套是照着手的形象被造的。手套的目的，手套存在的意义乃是要让手伸进来；今天人的目的，人的意义乃是要让神进到人里面，为要使人彰显神。 神造人的目的有两方面： （１）要人彰显神，把这位看不见的神彰显出来，表现出来，显扬出来。这位神的所是，生命，性情，荣耀，美德，要借着他所造的人彰显，表白，显大出来。神乃是为着这样的目的造人 （２）要人代表他，替他掌权管理他所造的宇宙，并代表他对付他的魔鬼撒旦；所以人的被造是非常有目的的。 认为人是自然而然就有的，是进化来的，这种所谓的解释，否定人存在的意义和价值，认为人的生存是没有目的，毫无意义的。相反的，圣经给我们清楚的启示，人是有源头的。人的源头乃是创造万有的神，而且神创造人是有特别地目的的，是为着他的旨意被创造的。 本文摘自：《人啊，你在哪里？－福音问答六十题》－第二十一问　

Chanson 5 - Tu me manques

Malgre tous ces bonnes moments que l'on a passe
Je tourne la page car je prefere tous les oublier
Je ne reviendrais jamais jamais avec toi
Malgres tout tu me manques

Ma vie n'est plus la meme, depuis que t'est parti
Chaque journee qui se leve me plonge dans l'ennui
Tu me manques mais je ne reviendrais jamais plus avec toi

Pour continuee~~

Chanson 4 - Il avait les mots

Il etait vraiment
Plus age que moi
Je suis tout betement
Tombe dans ses bras
Par lui j'ai decouvert
Ce que je ne connaissais pas
Il semblait sincere
Je l'aimais pour ca.

Ce qui m'a toujour deranger
Est que rarement le soir je pouvais le gater
Mais des qu'il me parlait
Je la fermais

Il avait les mots
M'a rendu accro
Je voyais deja
L'avenir dans ses bras
Il avait les mots
M'a rendu accro
Je ne savais pas
Que je ne connaissais pas
Il avait les mots

Je n'avais plus vie
Je ne pensais qu'a lui
Meme si j'ai cramer
Que souvent il mentait
Il se perdait dans qu'il me racontait
Se trompait nom quand il disait qu'il m'aimait
Et je supportais
Je pardonnais

Dans sa caisse, j'ai trouve des jouets
J'ai grille que son ex continuait de l'appeler
Et qu'est-ce qu'il le cachait? Je le decouvrais.

Il avait les mots
M'a rendu accro
Je voyais deja
L'avenir dans ses bras
Il avait les mots
M'a rendu accro
Je ne savais pas
Que je ne connaissais pas
Il avait les mots

Je l'ai suivi chez lui
Bete de jardin et chien de compagnie
Putain de maison, on s'imagine tout de suite la vie de famille
Pendant tout ce temps,
J'etais dans le faux
J'etais dans le faux

Sa femme m'a surprise,
Elle est tout de suite venue m'avouer,
Que j'etais pas la premier conne avec qu'il s'amusait
Pendant tout ce temps,
J'etais dans le faux
J'etais dans le faux

Ce qui m'a toujour deranger
Est que rarement le soir je pouvais le gater
Mais je m'en douter
Mais je la fermais

Il avait les mots
M'a rendu accro
Je voyais deja
L'avenir dans ses bras
Il avait les mots
M'a rendu accro
Je ne savais pas
Que je ne connaissais pas
Il avait les mots.....

Chanson 3 - Une femme amoureuse

Le temps qui court comme un fou,
Aujourd'hui voila, qui s'arrete sur nous,
Tu me regardes qui sait,
Si tu me vois,
Mais moi je ne vois que toi.

Je n'ai plus qu'une question,
Tes yeux mes yeux,
Et je chante ton nom,
Si quelqu'un d'autre venait,
Je l'eloignerais, et je me defendrais.

Je suis une femme amoureuse,
Et je brule d'envie de dresser autour de toi,
Le murs de ma vie,
C'est mon droit de t'aimer,
Et de vouloir te garder,
Pas dessous tout.

Hier, aujourd'hui, demain,
Font un seul jour, que tu prends ma main,
C'est comme un plan fabouleux trace la haut,
Pour l'amour de nous deux,
Qu'on soit ensemble longtemps,
Ou separes, par des oceans,
Si un danger survenait,
Je l'eloignerais et je me defendrais.

Je suis une femme amoureuse,
Et je te parle clair, et tu dois savoir,
Ce qu'une femme peut faire,
C'est mon droit de t'aimer,
Et de voulour te garder.
Je suis une femme amoureuse,
Et je brule d'envie de dresser autour de toi,
Les murs de ma vie,
C'est mon droit de t'aimer,
Et de vouloir te garder
Et de vouloir te garder....