Q&A - PSLE Math

[isetan]

2cor41618:

isetan:

Hi, another question:


Tan, Lim and Wong had some pens to sell. Tan had the least no. of pens. Wong's no. of pens was 30% less than Lim's. After Tan and Lim had each sold 50% of their pens, Lim had 95 more pens than Tan. If the three men had a total of 330 pens left, what is the total no. of pens they had at first?

At first

Wong---70%
Lim---100%

After T and L sold 1/2 of their share,

Lim---50%
Tan---95 less than 50%
Wong---70%

Thus, 50% + 50% + 70% ----330+ 95
170%---425 (Wong + Lim at first)
1%----2.5
Tan---2x ( 50 x 2.5 - 95) = 60

Total at first----60 + 425 = 485

Thanks 2cor41618!

[CoffeeCat]

ooioo:

Dear Math Masters, Great Math Teachers and Great Problem Solvers,


Help!!!

First I would like to thank all of you for the great insight and solutions to the very difficult math problems we all face daily.

I too have a math problem but it is not a math question, the problem is how to \"teach\" math? When my child is having problem with a math problem, do I ;

A) show my child how to get the solution straight away?
B) show my child half way to the solution?
C) don't show anything but keep hinting (but how to hint?)?
D) don't do anything and both of us just sit there and wait until we both go old or go crazy?

Please advice, thanks thanks in a million in advance!

Hi,
It is ideal if we can actually guide the student along the way by hinting, but in some circumstances like a totally unseen new type of question, explaining the logic might give the whole game away, or you are required to explain the reasoning behind the solution itself. Either way, explaining the thought process is important, which requires the \"teacher\" to be able to solve the problem in the first place

[cimman]

ooioo:

Dear Math Masters, Great Math Teachers and Great Problem Solvers,


Help!!!

First I would like to thank all of you for the great insight and solutions to the very difficult math problems we all face daily.

I too have a math problem but it is not a math question, the problem is how to \"teach\" math? When my child is having problem with a math problem, do I ;

A) show my child how to get the solution straight away?
B) show my child half way to the solution?
C) don't show anything but keep hinting (but how to hint?)?
D) don't do anything and both of us just sit there and wait until we both go old or go crazy?

Please advice, thanks thanks in a million in advance!

here's my take on teaching maths:

first, you need to teach the child a method that he or she can use to solve the same category of problems. Before that you need to teach how to identify that category of problems. Within that category, there are several permutations. Teach some of the permutations and how the method handles those permutations.
Once the child is confident in identifying that particular category of problems, work on the different permutations of that category. Don't give the solution. Ask leading questions, so that the child is led to the solution. Ask questions that you know the child would know because it was taught before. If you find that the child doesn't know the answers, then the relevant concept needs to be revised again or probably was not taught.

If the child still doesn't know the solution, then the last resort is to explain the solution. However, you need to explain it based on the method that was taught to him and show him how the method was extended to solve that particular problem. A lot of complex maths problems are actually familiar problems dressed up with a lot of secondary relationships that made it seem like another animal altogether. Teach the child to look for the primary core of the problem. The problem core is the main formula that has to be used to solve that particular problem. The other relationships in the problem sum are just noise, meant to confuse the students.

If you're not sure how to ask leading questions, start watching TV serials on court cases where lawyers will ask questions that leads to the defendant giving answers that the lawyers wants to hear. Don't ask questions that you don't have the answers to. The questions should lead the child to the core of the problem.

if you do encounter problems where it requires a concept that was not taught before, then teach that concept first, followed by a few problem sums where the concept is used in different permutations.

I kinda like option (D). Look at each other and grow old together. What better way to spend time together as a family ? great bonding exercise

[cimman]

as you going higher up the complexity ladder in maths problems, you’ll find that the complexity comes not from the maths but from comprehending the problem statement. Some problems are ambiguous, some are just worded so strangely. The only way out of this, is to do more of such problems so that you’ll know how to interpret such problems. Sometimes, focusing on the keywords, key ideas will help to break down the problem into simpler components.

It is unfortunate that the problem setters see it fit to test English comprehension skills together with maths concepts. As with English comprehension, developing the right inferences is a very critical skill to have in tackling higher order problems.

[beanbear]

ooioo:

Dear Math Masters, Great Math Teachers and Great Problem Solvers,


Help!!!

First I would like to thank all of you for the great insight and solutions to the very difficult math problems we all face daily.

I too have a math problem but it is not a math question, the problem is how to \"teach\" math? When my child is having problem with a math problem, do I ;

A) show my child how to get the solution straight away?
B) show my child half way to the solution?
C) don't show anything but keep hinting (but how to hint?)?
D) don't do anything and both of us just sit there and wait until we both go old or go crazy?

Please advice, thanks thanks in a million in advance!

In the past 8 months, I've been learning how to teach my children maths problems. I'm still learning and there are good days and there are bad days. I've tried A, B, & D. When it's a time crunch and we're trying to get alot of work done, I do A. When it's a highly complex sum, I do A first as a demonstration and explain my thinking step by step, especially interpreting each sentence of the sum, highlighting areas when one can get tripped by the interpretation and why we use a certain approach. When we do a similar sum after demonstrating, my child will demonstrate back to me what he had learnt, at times I would hint at next steps. When the sum is within the child's ability, I would observe my child doing the sum and asking lots of questions to help him make explicit his thinking process. This is the critical learning aspect. There are times I've left my child to make mistakes and when we re-do the sum, we do a gap analysis on how the mistake was made. This is critical for learning.

Lately, I've started a journal writing in all those sums that my child has made mistakes in so that he will re-do the sums about one week later to see whether he has learnt from the mistakes he made. I learnt from other forum contributors that this cumulative review strategy will really help the child to internalize the learning.

There have been days, I'm stumped and my child and I will do D - stare blankly at the sum for a good 30 mins. Then we move on to the next sum. But I will persist thinking about it and try to find a solution. Then I go back to my child and tell him excitedly that I've discovered the answer. I do this to show him the value of persistence. If at first, you don't know, it's ok but keep trying.

[2cor41618]

brastilava:

Hi 2cor41618,


I finally figure out:) Thanks so much!

Glad to hear that:-) It's a pleasure:-)

[isetan]

Hi, appreciate help into this question:-


Lawerance had some money. He spent 3/5 of it on 4 similar highlighters. With the rest of his money, he bought another 2 such highlighters and 10 rulers.

a) What fraction of his money was spent on buying 10 rulers? Give your ans
in its simplest form.

b) In a sale, Lawerance would be given 1 free ruler for every 12 rulers bought. how many rulers would he get altogether if he had spent all money at first on rulers?


DD has worked out answer for (a) is 1/10 and (b) is 91.

Wonder if her answer is correct?

TIA

[tianzhu]

isetan:

Hi, appreciate help into this question:-


Lawerance had some money. He spent 3/5 of it on 4 similar highlighters. With the rest of his money, he bought another 2 such highlighters and 10 rulers.

a) What fraction of his money was spent on buying 10 rulers? Give your ans
in its simplest form.

b) In a sale, Lawerance would be given 1 free ruler for every 12 rulers bought. how many rulers would he get altogether if he had spent all money at first on rulers?


DD has worked out answer for (a) is 1/10 and (b) is 91.

Wonder if her answer is correct?

TIA

Hi

I've the same answer for (a).

12 units ------ 4 highlighters

3 units ------ 1 highlighter

2 units ------ 10 rulers

2/20 ------ 1/10

For (b), my answer is 108.

2 units ------- 10 rulers

20 units ------ 100 rulers

1 free ruler for every 12 rulers bought.

96 + 8 + 4 ------ 108

Best wishes

[isetan]

thanks Tianzhu. Appreciate your help.

[isetan]

tianzhu:

isetan:

Hi, appreciate help into this question:-


Lawerance had some money. He spent 3/5 of it on 4 similar highlighters. With the rest of his money, he bought another 2 such highlighters and 10 rulers.

a) What fraction of his money was spent on buying 10 rulers? Give your ans
in its simplest form.

b) In a sale, Lawerance would be given 1 free ruler for every 12 rulers bought. how many rulers would he get altogether if he had spent all money at first on rulers?


DD has worked out answer for (a) is 1/10 and (b) is 91.

Wonder if her answer is correct?

TIA

Hi

I've the same answer for (a).

12 units ------ 4 highlighters

3 units ------ 1 highlighter

2 units ------ 10 rulers

2/20 ------ 1/10

For (b), my answer is 108.

2 units ------- 10 rulers

20 units ------ 100 rulers

1 free ruler for every 12 rulers bought.

96 + 8 + 4 ------ 108

Best wishes

Tianzhu,

Just clarify again....for the last sentence, why do you need to 'plus 4' (ie. 96+8+4).

thanks.