Tutor MathsGuru: Ask me for your burning Maths questions!

[iFruit]

ADoc:

meimeitan:

Hi Maths Guru


....May I know the meaning of \"What fraction of the club members who did not take part in the competition were boys.?\" The denominator should be the whole club members or the club members who did not join the competition...

Hi there! I shall take the plunge.

From a grammar perspective, the denominator would be \"club members who did not join the competition\", since the relative pronoun \"who\" is used to introduce a further comment or description of an earlier person or group of persons.

I agree. The denominator should be \"club members who did not join the competition\".

[small]

CJM:

To motivate her son to study mathematics, Mrs Mani agreed to reward her son 50 cents for every problem solved correctly and to fine him 35 cents for each incorrect solution. At the end of 17 problems, neither owed anything to the other. How many problems did her son solve correctly?

Please try to use guess and check method.

From working,her son solved 7 problemd correctly.

[atutor2001]

small:

CJM:

To motivate her son to study mathematics, Mrs Mani agreed to reward her son 50 cents for every problem solved correctly and to fine him 35 cents for each incorrect solution. At the end of 17 problems, neither owed anything to the other. How many problems did her son solve correctly?

Please try to use guess and check method.

From working,her son solved 7 problemd correctly.

I recommend \"replacement method\". This is a 3 mark question and guess and check might take too much time.

If the son gets all correct : 17 x 50 = 850
For every 1 wrong, the son must return 50 + fine 35 = 85

At the end, the son gets nothing means he return 85 cents 10 times. (850/85 = 10) That is, he got 10 wrong. Therefore, no. of correct is 7.

[NickleBee Tutors]

andante:

Pls help for the following question. I have solved it using algebra simultaneous equations but I heard that the pupils cannot use this method to solve during PSLE exam or else marks will be deducted.



20% of the number of balls Kyle had is equal to the 35% of the number Pauline had. After Kyle sold another 30 marbles and Pauline bought 20 marbles, 30% of the number of marbles Kyle had is equal to the 50% of the number Pauline had. What is the number of marbles each of them had at first?

Thanks in advance

During the \"parents meet teachers\" sessions for Pri 5 and 6 pupils, the oft-mentioned query on whether algebra is accepted in the PSLE maths paper is very commonly posed by anxious parents.

Most Primary School mathematics teacher will parrot MOE's stand that \"In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.\"

That being said, Primary school maths teachers and PSLE markers will also highlight the fact that what they are looking for is the ability of the child to show that he understands the context of the problem sum and is able to apply an appropriate method to reason and solve it in a logical and sequential manner.

Now as i understand from my chats with primary school teachers, for a 5 mark question, 4 marks are method marks and a correct answer is allocated 1 mark. So the marker will go down the question and tick each sequential step off if the marker is satisfied that the child is on the right logic/reasoning track. Anyway just to share, if the child makes a careless mistake right at the first step, and yet all his remaining steps are logical and shows that he understands the question and has applied proper reasoning to solving the question, he would of course not get the 1 answer mark (because the answer will definitely be wrong) but he may be able to get all 4 method marks!

If algebra is used and if it is done perfectly and with proper application to the question, i am sure the examiner is more than willing to award the full 5 marks. But if the PSLE marker is unsure and errs on the side of caution by bouncing the script up to the supervisor to rule on whether the algebra is acceptable. If they still find it unacceptable because they cannot be sure that the child has truly understood the context of the question and shown how he has arrived at the answer in a logical manner, then i guess its up to the supervisor on how many marks can be awarded.

Another point to note. More often than not, unless the child is very well grounded in algebra, careless mistakes and wrong application of algebraic concepts will lead to a wrong answer (1 mark gone). Also, most of the algebraic statements as written will become grossly off tangent as well and are no longer answering the question, and the child will start to lose all his method marks as well.

So the impression i get is that MOE accepts algebra but to be fair to those using other problem solving methods, it is marked to the same rigorous standard as the rest of the cohort. If the child uses algebra and is unable to demonstrate his understanding of the question and proper application of his chosen method which allows the marker to be satisfied that the child can solve the question with acceptable reasoning and logical thought processes, the marker has every right to decide how many marks are to be awarded. This gives rise to the misconception that marks will automatically be deducted once algebra is used. That is not true.

Now, i would like to re-emphasize the fact that throughout the Primary School syllabus, pupils are taught various problem solving skills, approaches and heuristics to solving maths problems. And most if not all of the PSLE questions can be solved by understanding the context of the question, applying reasoning and procedural knowledge. So as i tell my students, why give the marker an excuse not to award you any marks?

Yours
Zhou Shicai
NickleBee Tutors

[small]

CJM:

the tickets for a show are priced at $22 and $8. The number of $12 tickets available is 1 1/2 times the number of $8 tickets. 2/3 of the twelve-dollar tickets and the eight-dollar tickets were sold. The ticket sales amounted to $6400. How much more would have been collected if all the tickets were sold ?

Hi CJM,

Hope this helps...

At first
$12 --- 3U
$8 --- 2U

Total tickets were sold:
$12 --- 3 x 2/3 = 2U
$8 --- 2U

Convert to price unit:
$12 --- 12 x 2 = 24U
$8 --- 8 x 2 = 16U

(24U + 16U) = 6400
40U = 6400
1U = 160

160 x $12 = $1920

$1920 more would have been collected if all the tickets were sold.

[ADoc]

andante:

ADoc:

[quote=\"andante\"]...using algebra simultaneous equations but I heard that the pupils cannot use this method to solve during PSLE exam or else marks will be deducted...

Hi,
Thank you for your reply. I hope you can help to solve the problem using model approach.

Thanks and regards,[/quote]Hi there! Hope this is useful for your explanation to your kid using models. Pls note there isn't really a need for such an \"elaborate\" model as I have done. The key is able to draw the initial model representing Kylie's Units and Pauline's in terms of Kylie. The student should be able to proceed from there.

The primary concept tested here is \"equivalence of percentage and fractions (and this allows the student to draw a model with suitable number of units for subsequent calculations).

Cheers!

http://postimage.org/image/2fqei0i3o/
[/img]

[Dharma]

CJM:

To motivate her son to study mathematics, Mrs Mani agreed to reward her son 50 cents for every problem solved correctly and to fine him 35 cents for each incorrect solution. At the end of 17 problems, neither owed anything to the other. How many problems did her son solve correctly?

Amount of reward received = Amount of fine paid

Amount = Qty x Rate
For amounts to be the same , quantity and rates must be inversely proportional to each other.

Ratio of rates => Correct: Wrong= 50 : 35 = 10 : 7
Ratio of quantity => Correct : Wrong = 7 : 10

No. Of problems solved correctly and was rewarded = 7

[andante]

ADoc:

andante:

[quote=\"ADoc\"]

Hi,
Thank you for your reply. I hope you can help to solve the problem using model approach.

Thanks and regards,

Hi there! Hope this is useful for your explanation to your kid using models. Pls note there isn't really a need for such an \"elaborate\" model as I have done. The key is able to draw the initial model representing Kylie's Units and Pauline's in terms of Kylie. The student should be able to proceed from there.

The primary concept tested here is \"equivalence of percentage and fractions (and this allows the student to draw a model with suitable number of units for subsequent calculations).

Cheers!

http://postimage.org/image/2fqei0i3o/
[/img][/quote]Thank you very much.

[meimeitan]

hi


Then, may I know answer for that question:

There were 12 more girls than boys in a club. 1/3 of the girls and 1/4 of the boys took part in a competition. Among those who took part in the competition, there were 6 more girls than boys. What fraction of the club members who did not take part in the competition were boys?

Thanks.

[atutor2001]

meimeitan:

hi


Then, may I know answer for that question:

There were 12 more girls than boys in a club. 1/3 of the girls and 1/4 of the boys took part in a competition. Among those who took part in the competition, there were 6 more girls than boys. What fraction of the club members who did not take part in the competition were boys?

Thanks.

Let girls be 3U
Girls taking part in competition will be 1U

Let boys be 4V
Boys taking part in competition will be 1V

There were 12 more girls than boys in a club: 3U = 4V + 12 ----> (1)
Those who took part in the competition, there were 6 more girls than boys : 1U = 1V + 6 ----> (2)

(2)x 3 : 3U=3V+18 ----> (3)

Put (3) into (1) : 3V+18 = 4V+12 --> 1V = 6

From (2) : 1U = 6+6 = 12

No of boys who did not take part : 3V = 3x6 = 18
Total club members = 3U + 4V = 3x12 + 4x6 = 36+24 = 60

Fraction of the club members who did not take part in the competition were boys : 18/60 = 3/10