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。