Thank you for solving the maths problem.

Say, Salim has 60 units, which means Desmond has 100 units. Ronny has 40% × 60 units = 24 units Desmond must give Salim 20 units in order for Desmond and Salim to have equal number of marbles. 20 units = 840 marbles 1 unit = 42 100 units - 24 units = 76 units = 3192 marbles (ans)

Why Desmond needs to give 20 units?? Pls explain.

Initially, Salim has 60 units and Desmond has 100 units. If Desmond gives Salim 20 of his units, he will be left with 100 - 20 = 80 units. Salim upon receiving 20 units from Desmond will end up with 60 + 20 = 80 units. The end result is that both Salim and Desmond have the same number of marbles.

Somehow I got this answer which is diff from yours, Xavier. Can you pls advise where went wrong ? Thanks

Hello Pauline. First off, 3360 - 1008 = 2352 Secondly, the transfer of marbles from Desmond to Salim us hypothetical (because of the word "if") so if you add 840 to 2352, or if you find the number of marbles for 19 units (25 units - 6 units) you will arrive at 3192. I hope that helps.

Oh yeah... 'If' means if it happens but didn't happen eventually. I see. Got it. Thanks

Glad to help. Just watch out for the "fine prints" because there is only this much that the setter can do to challenge your children :)

I do like your approach using ratio.

Ratio of children to all people is 1 : 4 = 5 : 20 Ratio of boys to all children is 3 : 5 Hence ratio of boys to all people is 3 : 20 (ans)

If Marcos is 40 kg, then Javier who is 12 lighter is 28 kg. Aaron is 46 kg heavier than Javier, which makes him 74 kg. Javier and Marcus together have a mass of 68 kg, so they are 68/74 Aaron's mass. This can be reduced to 34/37.

You are correct, the answer should be 3/8. I would stick my neck out to say that the question should at least mention that the the two pies are of the same masses and sizes.

Perfect model.

The question asks for "fraction of the pieS eaten altogether"

The answer should be 3/4. Strawberry pie: 3/4 left, means 1/4 eaten. Blueberry pie: 1/2 left, means 1/2 eaten, i.e 2/4. Hence, total pie eaten: 1/4 + 2/4 = 3/4 . Hope this explains ☺️

I see it both ways. I don't understand why the teacher was wrong. Could it just be the wording?

Teacher is correct. They want to find wat fraction was eaten. 1/4+1/2 = 1/4 + 2/4 = 3/4

The diagram looks fine at first glance. But please take note the 8 parts is equal to 2 whole. So by just looking at the model is not accurate. The teacher is correct to say 3/4.

Maybe the teacher advice was based on the diagram shaded part..this is my understanding.and seems like the shaded part was the 'eaten part'.

I will agree to the answer 3/4 if the wording is "determine, in fraction of a pie, the total amount of pie eaten." The question clearly asks for fraction of the pies eaten, so based on the wording, 3/8 is correct. If the teacher has intended for 3/4 to be the answer, the question can be better phrased.

If based on diagram, it's 3/8 eaten. But read carefully the questions. Fraction of the pies. There are 2 pies, not 1. So answer has to be 3/4.

Yes. I agree the English is the problem here. There can be two interpretations.

The two pies cannot be assumed to be of the same size because when pupils are taught, the emphasis is always on fractions representing equal parts. The question stem needs to be improved.

Thank you guys so much for the input.😊 I actually found a similar qn in an assessment book. The only slight difference in the qn is what Xavier has pointed out.. identical pies. Hmm.. so should I conclude that if there is the word "identical", the answer is 3/8...otherwise it's 3/4? 😕

Present both cases. It will be good to cement your child's understanding. Should your child gets a little confused, stick to the identical pies way of working out the solution. Cheers.

Ans shd be 3/4. Qn did not say e pies were of equal size. If they were, it wld be 3/8.

That does not make sense. If the pies are not identical, why would one add the individual fractions of the pies eaten?

Consider this question : Peter had $100 and John had $80. Peter spent half of his money while John spent a quarter of his. What fraction of their money was spent altogether?

Wrong understanding on how fraction is calculated. u don add up the denominator that way. 1/4 + 2/4=3/4 NOT 1+2/4+4=3/8. Nothing wrong with this question in fact

No one here added 1/2 to 1/4 and claimed that the total is 3/8. Please kindly follow the thread again, thank you.

I think I see where Xaxier Sng is coming from..

What Caryn's son did was to cut the two pies into four quarters each, resulting in eight quarters. One quarter of the strawberry pie was eaten, as were two quarters of the blueberry pie. Three quarters out of eight quarters were eaten as a result.

Ans is 3/4 because there are 2 whole pies from start. So 2 -1/2 -3/4 = 3/4.. It is a tricky qns to test understanding of whole n parts

There is nothing tricky in the question. Base on the wording of the question, 3/4 is not the answer.

I guess it comes down to how one read the question. 2 individual pies or putting them together and regard as 1 whole.

The question asks for "fraction of the pies", not "fraction of a pie." Big, big difference.

The question should have stated that both pies are of the same size, i.e. Same diameter and thickness. By not stating that at all, both the one wholes are different, they could be many possible answers.

Agree with William Chong. The question can be interpreted both ways. Using the money example, it could mean adding up the money and finding the fraction spent or simply adding the fractions together without meaning that 3/4 of $180 was spent?

Well Sharon, if we look at the said example, we all know that 3/4 cannot be the answer. That is what I am saying, we need to solve the question based solely on the wording.

How did u get 3/8 then?

Do you think the wording issue lies in "altogether"? It would be 3/8 if the question did not have the word "altogether"?

The strawberry pie: cut into 4 quarters,The blueberry pie: also cut into 4 quarters. Total of quarters obtained? Eight. 3/4 of strawberry pie left, so one of the quarters was eaten. Half of the blueberry pie was eaten, so two of the quarters were eaten. Total quarters eaten? Three out of eight.

That's y i said u add 2/4 + 1/4 =3/8

Goodness...I am speechless.

Sharon, I just think the word "altogether" was used to inform the students that both pies are to be taken into consideration during the calculation.

One pie, one whole. Not two pies equal one whole.

"What fraction of the pies...." refer to the two pies as one whole.

4/4 + 4/4 = 8/4

What is the difference between "What fractions of the pies...." and "What fraction of the pies...."?

3 quarters were eaten and 3/8 were eaten are very different.

There were a total of eight quarters. Three were eaten. So the fraction of the pies eaten is 3/8.

If so, answer cannot be 3/4. Logically they have not eaten 3/4 of the 2 pies combined since one pie was left with half and the other 3/4.

Excellent observation, Sharon.

That is why, the problem is with the wording of the question.

1 - 3/4 = 1/4 1/4 of the strawberry pie was eaten. 1 - 1/2 = 1/2 1/2 of the blueberry pie was eaten. 1/4 + 1/2 = 3/4 3/4 of the pies were eaten. The question is very literal. This is the way how many international papers' questions are structured too.

I beg to defer. Questions from internationally renowned organisations are very particular with the wording. The structure of this question, in my humble opinion falls into the CMI category.

When you start to count the quarters, you are thinking in terms of fraction of a set.

Exactly, as the question has asked.

This question is not testing fraction of a set.

The wording is.

And hence the question is too.

Val Soh, you are correct. The issue is here is knowing what is the one whole and knowing what to count.

1/2 a pie was eaten, 1/4 of a pie was eaten. Together 3/4 of a pie was eaten.

Hi Caryn and all, the problem with most questions I have seen in Pri school Math is English. Sad to say most Math teacher didn't speak perfect English and hence the language is always an issue. I am also confused at times trying to interpret question rather than solving question.

Alexander, as you had clearly written: "together 3/4 of a pie was eaten" and not "together 3/4 of the pies was eaten." Please do take a closer look at what the question asks for.

Sorry i re-read the qns. To make it simple..Think about it, there is more eaten or more left? If 3/4 is eaten then it doesn't make sense anymore

When you consider the fraction of the pies eaten altogether, the total fraction of pie eaten was only 3/4 of a pie out of both pies.

Val, I rest my case, thank you.

That is not what the question asks for, Alexander.

I just tried on 2 of my kids' small pizza sweets. I ate 1/4 of the first one and ate 2/4 of the second one. What's left was 3/4 on the 1st and 2/4 on the second. Which adds up to be 5/8. So I must have eaten 3/8!

Or let say if the question asked for what is the fraction of pies left, and we calculate based on 3/4+1/2= 5/4. It doesnt make sense too. U shld ask the teacher does it work this way 😂

I wouldn't mind if I get my paws on some of the pizza sweets! My blood sugar is getting low with the length of this discussion!

This question is a test on part-whole fraction concept, not fractions of a set concept. Thinking in quarters and counting 8 of them as your whole is thinking in fractions of a set concept.

Which is what the question asks for. Please read it again.

Alexander Ho if 3/4 is eaten then 1/4 is what is left. Does it make sense?

Caryn Mok, I suggest you ask your child's math teacher if this question is testing the part-whole concept or the fraction of a set concept. If she says it's a fraction of the set concept, question her why is a p4 topic being tested at p3?

Val Soh, I am not sure if we are thinking of the same thing. 3/4 of which whole? Two whole pies or one set of two pies? There is a difference between 8/4 and 8/8. 8/4 means I have 8 quarters. 8/8 means I have 8 eighths.

Alexander, are we debating over the issue of which concepts are being tested at P3 and at P4, or are we debating over what is this particular question seeking, based on the wording?

Caryn's son, at P3 is able to understand the part-set concept, so I thought the discussion is solely on the wording.

This qns is interesting. I think the tcher got confused herself. Pls clarify with her/him n let us know Caryn

1-3/4 = 1/4 = 2/8 eaten 1-1/2 = 1/2 = 4/8 eaten 2/8 + 4/8 = 6/8 = 3/4 eaten That is probably the logic of this Q...using equivalent fractions. However, the model method suggests otherwise...do further discuss with the teacher and let us know.

Xavier, no debate is going on, at least I am clear on that. I like to believe that we are here to help Caryn and her son and maybe his classmates if his math teacher explains this question again in class. The questions I am asking Caryn to ask her son's teacher, are to help her and the math teacher come to a quick resolution and also for the math teacher to see where the confusion is at.

Pang Shing Hsiu, the model is drawn correctly. Two pies, two wholes, two bars.

Alexander, noted with thanks. Agreed, we want to make clear the situation for Caryn and her son.

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Eh...teacher may not always be right..sometimes they might just make a careless mistake .it's definitely 3/8 of the pies eaten or 3/4 of a pie but I doubt at this level they will want to "trick" the student by getting them to identify 3/4 of a pie. Whether the pies are same or not doesn't change the method ..but the question should be phrased that the pies are the same sizes so that a comparison can be made.

Hi all, really appreciate all the help here. Thank you.. 😊. I have emailed the teacher. Will update when he replies. The reason why I posted in this group is because this is from my boy's CA2 Pratice Paper and his CA2 assessment is tomorrow. I was hoping to clarify b4 his test as the sch teacher may not reply me in time. I remembered there was a similar yet somewhat different qn posted by another member and one of the answers required multiplying the indv fractions by 1/2 to get the answer. Please see the pics attached. Can the same principles be applied here then?

All correct methods should lead to the same correct answer.

Good luck to your son's exam tomorrow.

This question is clear on that answer to be the fraction of total number of ice cream.

Thank you Alexander :). After the discussion here and with friends, I can see how 3/4 is what the teacher is looking for. See my pic in which the top shows the 2 pies and the bottom shows the part that is eaten taken aside to form a 3/4 shape.

While what my boy and I (and Xavier Sng) have in mind in solving the qn is like this... part of what is eaten = 3 counters. Total counters = 8. So fraction is 3/8.

So I hope both answers will be accepted as correct by the teacher given the ambiguity of the qn. :p

3/4 should be the answer as it mentioned two different pies. 3/8

3/8 , noted that the denominator '8' is usually treated as the same pie 8 pieces.

All the best to your son, Caryn. Break a leg!

In any fraction problem, the student must know which item is the One whole. You child got confused as he thought the One whole is total of both the pies. But it's quite clear that the question indicated 3/4 of the Strawberry pie and 1/2 of the blueberry pie. So there are 2 different One whole in this case. Hope that you are clear now

"Fraction of a pie" means that 'a pie' is taken as one whole. "Fraction of the pies" however refers to 'the pies' being taken as one whole. The question asks for "fraction of the pies", hence 3/4 cannot be the answer.

If there are two different one wholes as claimed, should the question not have two answers, one for each of the pies?

Eimaths Sg so which 1 whole you are referring to? What is your answer? Anyway i think its a poorly worded question, should just feedback to the teacher, please do not set such questions in future. These kind of qustions just confuses students. I am quite sure this question is probably grabbed from some book with some alterations. If you ask the teacher she will maybe realise.. "O Yar.." Trust me...teachers make mistakes.. they are not "know all" and perfectionists.. unless she is in charge of maths papers in some PSLE board then.. O well.. i got nothing to say :P

I couldn't have said it better myself, Jeannie. I just feel that many of us are conditioned to think that if the student is marked wrong by the teacher, the student must be the one who has misunderstood the concept. Let us give our children more credit. They have often ended up teaching us adults a thing or two.

SEAB did set a wrong math question once during one of the PSLE math exams. It was featured in the Straits Times. It is human to make mistakes.

Alexander Ho then maybe it's e same setter :p #justjoking

Mistakes are inevitable, no matter how hard we try to root them out.

So the teacher called me to explain and gave my boy a photocopied page of a P4 textbook. I didn't debate with him on the phrasing of the above qn as I have separately emailed the Math HOD to clarify. Written in blue is a similar phrasing of the above qn and that will lead to a different answer (13/18) as it's a fraction of the 3 choc bars altogether. When it is asked "how much chocolate is left" ... similarly the abv qn shd be phrased "how much pie is left"? Then the answer is 3/4. This is how i interpret. :) So the problem is how (the wordings) and thus what the qn is essentially asking. Thks once again for everyone's help and inputs. Greatly appreciated. :)

Basically, your son's teacher fails to recognize the major differences in the wordings of the two questions concerned. It is the usual one-size-fits-all approach that is frequently found in school, and the teacher merely copies the questions, tweaks the subject and the numbers and then expects the same solutions..... exactly how Jeannie Ng had vividly described.

Also, the chocolate question should ask "How many bars of chocolate were left?" Only then will 2 and 1/6 bars of chocolate be the undisputed answer.

I often wonder how our text books, with such glaring cases of ambiguity and controversy, be touted as the next big thing around the world in mathematics education. Don't get me wrong, thousands of our educators have put in uncountable hours of toil to bring about developments in the way we teach our children, but I believe we have gotten to be too complacent just because so many countries are trying to learn what we have been doing that we forget to check our basics, namely language.

There is something wrong w ur tr ans..in black tb is 13/6 her ans is 13/18 If use 2 -1/2-3/4 = 3/4 ( for pie qn) But something just seems wrong...maybe tb is wrong! Haha..:p ( which is also possible k!)..ok back to wrk....

13/18 is for the fraction of chocolate bars not eaten. 13/6 is the number of bars of chocolate not eaten.

Wah win liao lor..if u tell me the difference is e word bar

Based on the teachr's explanation, shldn't 3/8 be the right answer for the pie qn? since it asked for fraction of the pies

Oops! To clarify, the wordings in blue are written by me to show the difference in answer if phrased in a similar manner as the original qn I posted. Sorry of the misunderstanding! The teacher didn't write anything.. he just passed my boy the paper with yellow highlighted parts.

Xavier, seems like you are good in English too . Haa. I noticed you wrote in full sentences and perfect grammar. Anyway, this thread reminded me the concept of fraction. So I still think is 3/8 for the pies question (unless it's worded how much pies were eaten?? 3/4 of one pie was eaten. Similar to the chocolate bar phrasing). Anyway I think most of us understand the difference already. Cheers :)

Sharon, thank you. You flatter me. I wish most certainly that I am half as good as you think, and I will be over the moon. I try very hard to write in the manner that will not embarrass my former teachers, though I know I do fall short. Regards

How many of us have seen the math programs in other countries? How many of us have been down to the Singapore public schools before? There are about 360 of them and about 150 of them are primary schools. How many of us have seen how hard and the amount of time the majority of our public school teachers have put into their teaching? How many of us have seen foreign math teachers in action? There will always be good, average and not-so-good teachers everywhere. There will always be one or more mistakes made in textbooks and test. Until we have walk the path of a teacher, gone through what they have been through, let's not knock them and the system down based on our very limited experiences. Is our education system perfect? No, it's not. Is it better than many others? Yes, it is. Is it standing still and getting complacent? Definitely not.

I think you are barking up the wrong tree, Sir. I have not dissed the system nor the teachers, I had merely pointed out we are far from the completed article. If we refuse to even face up to the faults that the system has, we are indeed complacent.

It's just the language.. Which not everyone is good at (and hence cannot see the problem at one glance). At least I'm enlightened by the diverse views and discussions here although we can get frustrated putting our views across. Normal. In the spirit of open sharing. Haaa.

Or the spirit of the opera! lol

In the chocolate problem, Jim ate 5/6 bar of chocolate, and there were 2 1/6 bars left. We may ask, "how much chocolate was left?", or "how many bars of chocolate were left?". It is correct that 5/18 of the chocolate bars was eaten, and that 13/18 was left. Here the whole comprises 3 bars or 18 units, of which 5 units were eaten.

As for the pie problem, it is somewhat confusing, and the language is more difficult. It is necessary to assume that the two pies are identical except for their types. Here the whole is 2 pies, or 8 units of 1/4 pie each. The correct answer should be "3/8 of the pies was eaten", or "5/8 of the pies was left". If we ask, "how much pie was eaten?", or "how many pies were eaten?", then the answer is 3/4 pie. I hope this clarification helps.

Thank you so much for your clarification, Dr Kho! I'm so honoured to have you commenting here. 😊

Thank you Dr Kho for sharing with us your understanding of these questions. I really like the clarity of your explanations. We have much to learn. 👍🏻👏🏻😊

I really enjoy your long chain of conversation and appreciate very much your concern. These problems should be in P4 after students have learnt the concept of fraction of a set. The language and understanding are beyond many P3 students. Please look at the ice-cream problem which is of the same nature. Let your child try on the problem also. You draw two equal bars to represent the number of two types of ice-creams. After making common units (15 units for each bar), we can see that the whole set comprises 30 units, of which 11 units are left and 19 units are eaten. Therefore 19/30 of the total number of ice-cream was eaten.