Q&A - P3 Math

[atutor2001]

Keroppi30:

I got this question from a P3 maths assessment book:-


The mass of 50 twenty-cent and one-dollar coins is 600g. The mass of 2 one-dollar coins is as heavy as 3 twenty-cent coins. How much heavier is a one-dollar coin than a twenty-cent coin? The answer is 5g per the answer booklet.

If the question is modified to :
[quote]There are 50 pupils sharing a total of 600 cards. Every boy is given same number of cards. Every girl is also given same number of cards but different from each boy. The sum of the number of cards from 3 boys is equal to the sum of the number of cards from 2 girls. What is the difference in the number of cards between 1 boy and 1 girl?[/quote]In this modified question, although the ratio of the number of boys and girls is also not given, however, there is only 1 possible answer because the number of cards of each boy and each girl cannot be a fraction and must be a whole number.

Have been wondering whether beside using \"Guess & Check\", is there any other \"mathematical method\" to find the answer.

Thanks in advance.

[Keroppi30]

Hi tianzhu


using your method are we assuming the ratio of one-dollar coins and twenty-cents coins is 2:3

Hi atutor2001

The answer to the original question has to be whole numbers too cos P3 hasn’t touch on decimals yet.

[tianzhu]

Keroppi30:

using your method are we assuming the ratio of one-dollar coins and twenty-cents coins is 2:3

Hi

There is no assumption; the solution is based on the information provided in the question.

When dealing with primary Maths and Science, it’s important to see what they’ve studied in their syllabuses, do not try to go beyond that. See them through the eyes of our young ones.

In this particular question, we are given that the mass of 2 one-dollar coins is as heavy as 3 twenty-cent coins. What does this mean? Imagine 2 one-dollar coins and as 3 twenty-cent coins put into a box (A group).So, you’ll have a total of 5 coins in a box.

Next, we are told that there was 50 coins altogether. Therefore, you’ll have 10 such boxes to make up a total of 50 coins.

The total mass of 50 coins is 600g; therefore the mass per box is 600/10 which is 60g.

Hope this helps.

[atutor2001]

Keroppi30:

Hi atutor2001

The answer to the original question has to be whole numbers too cos P3 hasn't touch on decimals yet.

I agree that the book implicitly expected the answer in whole number.

However, it is important for the book to state clearly by including a statement, for example : \"The difference in the weight is a whole number\".

Otherwise, many students develop the wrong impression that all answers must be in \"whole number\". This is a common problem many average students in upper Pr are facing. Whenever they get an answer in fraction (which is actually correct), they thought that it is wrong because they have been getting whole number answers in the past and nobody highlight to them that answers can also be in fraction. Some students even manipulated the working just to get a whole number and end up with a wrong answer.

It is important for assessment books for lower Pr to state clearly if it only wants answer in \"whole number\" when there are other possible answers. By doing so, it will make the student realise that there are other possible answers that may not be in whole number. In later years, they will have confident to accept answers in \"fraction.\"

[Keroppi30]

:thankyou: tianzhu & atutor2001


I really appreciate your help. I’m not trying to challenge your answers but I’m trying to address the questions raised by my dd. I’m not very good at explaining maths concepts to my dd in fact what I usually do when I encounter such problem sums is I’ll try to obtain the answers via simultaneous equations.

[atutor2001]

Keroppi30:

:... I’m not trying to challenge your answers but I’m trying to address the questions raised by my dd. ....

Hi Keroppi30

Don't be too concerned, questioning our proposed answers. In fact, your query sets me thinking. Which is why I modified the question - hoping to find a solution to a more tricky type of math condition where only the whole number solution is allowed but is not explained explicitly in Pr Math. Lets just continue to question when there is ambiguity. It makes math more interesting and \"alive\".

Regards

[fanren]

Hi

for P3, can we use equation? for example let something be u, let something be w

then come out with 2 equations and solve the two unknown alphabets…

thought now school wants students to use reasoning, trial and error or those draw model type,

please enlighten me! my son going P3 next year

[tianzhu]

Keroppi30:

I’m not trying to challenge your answers but I’m trying to address the questions raised by my dd.

Hi

No worries, I’ve stayed long enough in Maths and Science threads to realise that a solution is only useful if it serves its purpose. The person asking the question must be able to understand it for it to be meaningful.

A vibrant forum where members offer differing views can only benefit us in the long run. So, we welcome your feedback as it helps to improve ourselves.

Best wishes

[Daddy]

HI,


A question need help.
\" Harry and Frank have 480 cards altogether. After Harry gve 90 cards to Frank, Frank has twice as many cards as Harry. How many cards do the two boys have at first.\"

Thanks

[Muffins]

Daddy:

HI,


A question need help.
\"Harry and Frank have 480 cards altogether. After Harry gave 90 cards to Frank, Frank has twice as many cards as Harry. How many cards do the two boys have at first.\"

Thanks

Hi Daddy, the two boys ALWAYS have 480 cards altogether. THAT DOES NOT CHANGE. So, if Frank has twice as many cards as Harry in the end, there must be three units of cards (2 units of Frank + 1 unit of Harry). So, 3 units = 480. 1 unit = 480/3=160. If Frank had 2 units - 90 cards at first, he had (160 X 2) - 90 = 320 -90 = 230 cards at first. And if Frank had 230 cards at first, Harry had 480 - 230 = 250 cards at first.

Regards.