Help needed to solve Primary 6 problem sum

Baiye1232003 SG

Hi,

Can anyone help to solve this problem sum and provide the workings (done in a way that a Primary school student can understand)? Many thanks for your help!

Qn: Chan had 120 marbles more than Bob. Chan lost 1/5 of his marbles and Bob lost 1/4 of his marbles. Chan had 164 marbles more than Bob in the end. How many marbles did Chan had at first?

Seowlah SG

Hi,

Can anyone help to solve this problem sum and provide the workings (done in a way that a Primary school student can understand)? Many thanks for your help!

Qn: Chan had 120 marbles more than Bob. Chan lost 1/5 of his marbles and Bob lost 1/4 of his marbles. Chan had 164 marbles more than Bob in the end. How many marbles did Chan had at first?

All P5 and P6 Primary school maths students know and understand this method but they always deem it too time consumimg and too lazy too guess and check the answers. (P5 and P6 maths students are allowed to use calculators now).

Using Guess and Check Method

Before After

Chan Bob Difference Chan Bob Difference

240 120 120 192 90 102 (not 164 wrong)

480 360 120 384 270 114(not 164 wrong)

960 840 120 768 630 138(not 164 wrong)

1480 1360 120 1184 1020 164 correct

So, Chan had 1480 marbles at first.

MaNyZeR SG

Let the number of marbles Chan has be X, and let the number of marbles Bob has be Y

Therefore,

X - Y = 120, which can also be written as X = 120 + Y

Given that after Chan lost 1/5 of his marbles, he still have 164 marbles more than Bob, whom had lost 1/4 of his marbles, an equation shown below can be made:

4/5(X) - 3/4(Y) = 164

Sub in [X = 120 + Y] into the above equation and we would get the below equation:

4/5(120 + Y) - 3/4(Y) = 164

Start solving the equation and we would get:

4/5(120) + 4/5(Y) - 3/4(Y) = 164

96 + 4/5(Y) - 3/4(Y) = 164

4/5(Y) - 3/4(Y) = 164 - 96

1/20(Y) = 68

Y = 68 X 20

Y = 1360.

Therefore Bob has 1360 marbles to begin with, and Chan has 1360 + 120 marbles to begin with (1480 marbles).

wee_ws SG

Hi,

Guess and check may be a little daunting to students because it requires mathematical intuition, which takes time to develop. Anyhow, how does one know that he/she has to start with the figures 240 and 120? How does one know that he/she has to double the set of figures next?

I believe the algebra approach is not taught to students to solve word problems like this, although they are exposed to some basic algebra.

Below is the model approach that students are much exposed to.

Before:
Chan -> 5 units
Bob -> 5 units - 120

After:
Chan -> 4 units
Bob -> 4 units - 164

Now (4 units - 164) : (5 units - 120) = 3 : 4,

so 4(4 units - 164) = 3(5 units - 120), giving

1 unit = 296 marbles.

The rest of the working is easy. Thanks.

Cheers,
Wen Shih

Seowlah SG

Hi,

I believe the algebra approach is not taught to students to solve word problems like this, although they are exposed to some basic algebra.

Below is the model approach that students are much exposed to.

Before:
Chan -> 5 units
Bob -> 5 units - 120

After:
Chan -> 4 units
Bob -> 4 units - 164

Now (4 units - 164) : (5 units - 120) = 3 : 4,

so 4(4 units - 164) = 3(5 units - 120), giving

1 unit = 296 marbles.

The rest of the working is easy. Thanks.

Cheers,
Wen Shih

Hi,

Basically, the P5 and P6 students are taught to let some numbers for Chan eg 240 marbles and Bob eg 120 marbles so that the difference is 120 marbles as required in the question.

Next, after losing 1/5 ie 4/5 left for Chan is 4/5 x 240= 192 and after losing 1/4 ie 3/4 left for Bob is 3/4 x 120 marbles = 90 and the difference is 102 marbles not 164 marbles, so the answer is wrong.

So, the students will try other numbers for Chan and Bob and go through the whole process again and again until they got the difference of 164 marbles.

It is very true that it is a very time consuming process but it is a method that the PSLE maths teachers taught the students as a last resort method. The guess and check method is to be used as a last resort if the students cannot solve the question with the bar model method.

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I have given the question x^2 - y^2 = 37 (but the question is modified as box x box - triangle x triangle = 37) to a PSLE student who usually scores 60 plus marks. The PSLE student found the x and y answers with the use of a calculator.

I have also given the same question x^2 - y^2 = 37 to an "O" level student who usually scores a B3. The "O" level student is so conditioned to solve the simultaneous equations x^2 - y^2 = 37 using the elimination and substitution methods and the "O" level student cannot solve the question. The student forgets that there is the guess and check method that can be used as a last resort to solve the question.

PS : The question x^2 - y^2 = 37 can be solved by noting that 37 is a prime number.

wee_ws SG

Hi,

Thanks for clarifying and sharing your teaching experience :)

It is indeed useful to teach students a variety of problem-solving approaches so that they have an arsenal of methods to tackle challenging, elusive examination questions.

Cheers,
Wen Shih

Baiye1232003 SG

Wow, thank you Seowlah, MaNyZeR and wee_ws, your answers helped me alot!!

jayh272416 SG

Hi,

Basically, the P5 and P6 students are taught to let some numbers for Chan eg 240 marbles and Bob eg 120 marbles so that the difference is 120 marbles as required in the question.

So, the students will try other numbers for Chan and Bob and go through the whole process again and again until they got the difference of 164 marbles.

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PS : The question x^2 - y^2 = 37 can be solved by noting that 37 is a prime number.

(x+y)(x-y) = 37

therefore x+y=37,x-y=1

x = 19, y = 18

this should be the best way.

Seowlah SG

(x+y)(x-y) = 37

therefore x+y=37,x-y=1

x = 19, y = 18

this should be the best way.

Wee_ws and I are discussing the approaches that students can use to solve the questions. At times, students cannot use their usual methods to solve the questions and what other approaches are available to solve the questions.

For the question x^2 - y^2 = 37, in my eariler post I have already said that the question can be solved if the student has noted that 37 is a prime number.

The problem is that a student who has not done a question like x^2 - y^2 = 37 will be at a loss and the "O" level student is so conditioned to the use of elimination and substitution methods to solve the simultaneous equation. The student could have used common sense ie the guess and check method to find the answers even though the student did not note that 37 is a prime number.