Tutor MathsGuru: Ask me for your burning Maths questions!

[tianzhu]

Kiasu Friend:

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

Hi

Guess and Check is one of the problem solving strategies in the Primary Maths syllabus. It may be less efficient as compared to other methods, but it can help one much especially when one can’t crack a problem despite repeated trying with other strategies.

When you are in a desperate situation, with a bit of luck and some educated guesses, it may help you to secure some marks.

In this case, you need to have some number sense. What is the average speed of a car? In the exam, present your solution in a tabulated list and make at least three guesses. Even if are so lucky to get the right answer with the first guess, also try to show your answer in a systematic way so as to get the marks.

If you see a GC solution from me, it means it’s my last resort to secure some marks in an exam.At this moment, I can’t think of any other solution other than forming equations.

Best wishes

[kancheongmum]

tianzhu:

Kiasu Friend:

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

Hi

Guess and Check is one of the problem solving strategies in the Primary Maths syllabus. It may be less efficient as compared to other methods, but it can help one much especially when one can’t crack a problem despite repeated trying with other strategies.

When you are in a desperate situation, with a bit of luck and some educated guesses, it may help you to secure some marks.

In this case, you need to have some number sense. What is the average speed of a car? In the exam, present your solution in a tabulated list and make at least three guesses. Even if are so lucky to get the right answer with the first guess, also try to show your answer in a systematic way so as to get the marks.

If you see a GC solution from me, it means it’s my last resort to secure some marks in an exam.At this moment, I can’t think of any other solution other than forming equations.

Best wishes

hi kiasu friend

Totally agreed with tianzhu. I always tell my ds to use guess and check as last resort and in desperate situation. He got back 10 marks for this prelim. I also realise I have to learn to accept his way and level of thinking when he is solving problems sums. Sometime my shortcut method is too difficult for him to understand and sometime he does. I don't know if it is because of the standard of his class, his Maths teacher always teach them using guess and check, even for the speed question:
speed of 2 vehicles were given, travelling from opposite direction at the same time, distance between them were given,at what time they meet? Anyway I have given up on this teacher and even pull him out of the supplementary class after 2 terms which he had to stay in school till 4.30 pm 3 times a week. I use the time to let him rest and teach him myself. The results have been very rewarding.

[Kiasu Friend]

tianzhu:

Kiasu Friend:

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

Hi

Guess and Check is one of the problem solving strategies in the Primary Maths syllabus. It may be less efficient as compared to other methods, but it can help one much especially when one can’t crack a problem despite repeated trying with other strategies.

When you are in a desperate situation, with a bit of luck and some educated guesses, it may help you to secure some marks.

In this case, you need to have some number sense. What is the average speed of a car? In the exam, present your solution in a tabulated list and make at least three guesses. Even if are so lucky to get the right answer with the first guess, also try to show your answer in a systematic way so as to get the marks.

If you see a GC solution from me, it means it’s my last resort to secure some marks in an exam.At this moment, I can’t think of any other solution other than forming equations.

Best wishes

Hi Tianzhu,

Thank you very much for a neat explanation about the value of using G&C in exams. My respect for G&C methodology has vastly increased after reading your explanation. I will adopt your suggestions immediately.

Hi kancheongmum,

Thanks for narrating the experience of your DS. I never knew that G&C can be so handy in solving P6 problems. I somehow thought G&C is more of a P4 method. I see how valuable G&C can be.

Thanks & Regards.

[Dharma]

Kiasu Friend:

tianzhu:

[quote=\"trytry\"]Hi, need help.

This question was given as prelim practice:

Tom was driving from his office back to his house. As he was sick, he drove 20km/h slower. As a result, he reached home 10 minutes later.The distance between his office and house is 40km. What is his usual speed?

Tia.

Hi

Try Guess and Check

40/60 ---2/3h ----- 40min
40/80 --- 1/2h -----30min

Difference -----10min -----OK

Therefore speed -----80km/h

Best wishes

Hi tianzhu,

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

I am sorry for taking your time. Thank you very much for your tireless contribution to this forum.[/quote]Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h

[Kiasu Friend]

Dharma:

Kiasu Friend:

[quote=\"tianzhu\"]
Hi

Try Guess and Check

40/60 ---2/3h ----- 40min
40/80 --- 1/2h -----30min

Difference -----10min -----OK

Therefore speed -----80km/h

Best wishes

Hi tianzhu,

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

I am sorry for taking your time. Thank you very much for your tireless contribution to this forum.

Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h[/quote]Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.

[acehkr3009]

tianzhu:

acehkr3009:

The ratio of Apples to Pears in a fruit stall is 5 : 8. If 60% of the pears are sold, what percentage of the apples must be sold for the number of pears and apples in the stall to be the same?

Hi

You may use MD or Units Method to solve this question.

Apples: Pears ----- 5:8 -----25:40

60% of pear% sold ----- 60/100*40 ----- 24
40% of pear left ---- (40-24) ------16

Number of apples to be sold ----- (25-16) -----9
9/25*100% ---- 36 %( percentage of apples to be sold)

Best wishes

Thanks for the answer. I fully understand now.

But for the Apples : Pear -----5:8, is there a way for choosing x5 instead of others, in order to convert to 25:40 ? If we use other factors, we may chanced upon fractions later on, which can complicate the working.

Any other method to recommend?

Thanks again.

[acehkr3009]

tianzhu:

acehkr3009:

Solution looks simple, but when I am trying it at first, brain just got stuck and freeze!

Hi

The KS way.

Keep (in) Syllabus
Keep (it) Simple
Keep (it) Short

Keep Supporting your kids

Best wishes

Hi Tianzhu,

Thanks for the KS way.....it really summarizes it all....

One of my kid has special needs (Asperger), which really require alot of attention and motivation, even though he is mathematically incline. More often, I have to built up his trust in me on the topic we doing, before I can start working with him, and to learn from each other. Thereafter, everything becomes easier and fun. So, I think Support and his interest really comes first on the list for me.

Thanks.

[ABCDE]

Kiasu Friend:

Dharma:

[quote=\"Kiasu Friend\"]

Hi tianzhu,

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

I am sorry for taking your time. Thank you very much for your tireless contribution to this forum.

Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h

Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.[/quote]Hi Kaisu Friend,
Can u explain the algebra method used..I blur on what is 1u assumed as...
TIA

[favianboy]

2 candles A & B, A is fatter and takes 5 hours to burn. B is thinner and takes 4 hours to burn. They are the same height. At which point A is twice the height of B.


Pls help

[Kiasu Friend]

ABCDE:

Kiasu Friend:

[quote=\"Dharma\"]

Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h

Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.

Hi Kaisu Friend,
Can u explain the algebra method used..I blur on what is 1u assumed as...
TIA[/quote]Hi ABCDE,

1u stands for the average of the two speeds, i.e., the usual speed of Tom and the slower speed at which Tom drives when he is sick.

I can explain the solution in more detail, but I think it is better that you request Dharma to explain it because:

(a) He is the author of the excellent algebra solution provided above
(b) I consider him an 'authority' on this when compared to an amateur like me.

Thanks and Regards.