Q&A - PSLE Math

[tianzhu]

LaiHeng:

2. A bag contains 200 blue balls and 450 yellow balls. A tin contains 850 blue and 340 yellow balls. After some blue and yellow balls are moved from the tin to the bag, the percentage of the blue balls in the bag becomes 50% and the blue balls in the tin becomes 70%.

a)How many blue balls are moved from the tin to the bag?
b)How many yellow balls are moved from the tin to the bag?

Hi

In answering this question, a student should note that the total number of blue and yellow balls remains the same in the before and after scenarios.

Before
Bag
Blue ----- 200
Yellow ----- 450

Tin
Blue ----- 850
Yellow ----- 340

Total number of blue balls ------ 200+850 ------1050
Total number of yellow balls ------ 450+340 ------790

After
Bag
Blue ----- 1 unit
Yellow ----- 1 unit

Tin
Blue ----- 7 parts
Yellow ----- 3 parts

Here, we’ve two equations with two variables, and we cannot run away from simultaneous equations.

Some students may find it difficult to grasp SE concepts; the challenge is to help the less mathematically inclined students deal with such handicaps.

Needless to say, students who have learned SE from external courses or their parents would go ahead with SE.

Students who are able to grasp SE concepts may use letters of the alphabets to solve the equations or work using units and parts to represent the quantities of the blue and yellow balls as shown above.

Let’s begin.

1 unit + 7 parts ------1050
1 unit + 3 parts ------ 790
4 parts ------ 260

Tin
Yellow ------ 3 part ----- 3*65 ------ 195
Blue ------ 7 parts ---- 7*65 ----- 455

a)How many blue balls are moved from the tin to the bag?
850 – 455 ------ 395


b)How many yellow balls are moved from the tin to the bag?
340 – 195 ------- 145

For those students who have difficulties understanding SE, you may solve it by visualising such equations in pictorial form.

Please help to check the calculations as they had been done in a rush.

Best wishes

[ozora]

tianzhu:

Hi LaiHeng


Good Morning.

Here's the solution to Q1.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5095/5490097769_cb20f73bac_b.jpg\">

thanks
the explanation for both questions are clear. I really got a lot to learn from you.

[ozora]

tianzhu:

LaiHeng:

2. A bag contains 200 blue balls and 450 yellow balls. A tin contains 850 blue and 340 yellow balls. After some blue and yellow balls are moved from the tin to the bag, the percentage of the blue balls in the bag becomes 50% and the blue balls in the tin becomes 70%.

a)How many blue balls are moved from the tin to the bag?
b)How many yellow balls are moved from the tin to the bag?

Hi

In answering this question, a student should note that the total number of blue and yellow balls remains the same in the before and after scenarios.

Before
Bag
Blue ----- 200
Yellow ----- 450

Tin
Blue ----- 850
Yellow ----- 340

Total number of blue balls ------ 200+850 ------1050
Total number of yellow balls ------ 450+340 ------790

After
Bag
Blue ----- 1 unit
Yellow ----- 1 unit

Tin
Blue ----- 7 parts
Yellow ----- 3 parts

Here, we’ve two equations with two variables, and we cannot run away from simultaneous equations.

Some students may find it difficult to grasp SE concepts; the challenge is to help the less mathematically inclined students deal with such handicaps.

Needless to say, students who have learned SE from external courses or their parents would go ahead with SE.

Students who are able to grasp SE concepts may use letters of the alphabets to solve the equations or work using units and parts to represent the quantities of the blue and yellow balls as shown above.

Let’s begin.

1 unit + 7 parts ------1050
1 unit + 3 parts ------ 790
4 parts ------ 260

Tin
Yellow ------ 3 part ----- 3*65 ------ 195
Blue ------ 7 parts ---- 7*65 ----- 455

a)How many blue balls are moved from the tin to the bag?
850 – 455 ------ 395


b)How many yellow balls are moved from the tin to the bag?
340 – 195 ------- 145

For those students who have difficulties understanding SE, you may solve it by visualising such equations in pictorial form.

Please help to check the calculations as they had been done in a rush.

Best wishes

thanks for the prompt help.

[tianzhu]

LaiHeng:

thanks

the explanation for both questions are clear. I really got a lot to learn from you.

Hi

You're welcome.

Best wishes

[ozora]

Hi

I managed to solve this question but I wonder is there a another method.
The question is as follows: There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

I used SE concepts to solve it : 2/5o+ 2/3a=44----eq1
3/50+ 1/3a=36-----eq2
I managed to get 35 oranges.

Is it possible to use model to get the answer? If so how? Thanks

[ADoc]

LaiHeng:

Hi

I managed to solve this question but I wonder is there a another method.
The question is as follows: There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

I used SE concepts to solve it : 2/5o+ 2/3a=44----eq1
3/50+ 1/3a=36-----eq2
I managed to get 35 oranges.

Is it possible to use model to get the answer? If so how? Thanks

Hi! Since model is algebra (including SE) in disguise, so we can still use the so-called model method to help the students visualise this problem instead of calling it SE. So instead of using \"O\" and \"A\", we can always use the pictorial form. Also, I think students are more familiar & comfortable manipulating whole numbers compared to fractions (SE or model).

Here's a quick diagram so to speak. We can always translate to \"models\" to aid visualisation. not sure if this will be helpful. cheers!

Original
oranges [ ] [ ] [ ] [ ] [ ]
apples { } { } { }

[ ] [ ] [ ] [ ] [ ] + { } { } { } = 80 fruits
or 5 [ ] + 3 { } = 80 fruits

after eating 2/5 oranges & 2/3 apples
oranges [ ] [ ] [ ]
apples { }

[ ] [ ] [ ] + { } \t\t = 36 fruits

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] + { } { } { } \t= 36 x 3 = 108 fruits
|-------------9---------------| |----3-----|
or 9 [ ] + 3 { } = 108 fruits

subtracting original of 5 [ ] & 3 { }, we have:
therefore 4 [ ] = 108 - 80 = 28
1 [ ] = 7
therefore 5 [ ] = 5 x 7 = 35 oranges at first

[tianzhu]

LaiHeng:

Hi

I managed to solve this question but I wonder is there a another method.

The question is as follows: There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

I used SE concepts to solve it : 2/5o+ 2/3a=44----eq1
3/50+ 1/3a=36-----eq2
I managed to get 35 oranges.

Is it possible to use model to get the answer? If so how? Thanks

Hi

Besides solving SE in algebraic manipulation, alphabet method or in pictorial form, you may also solve this question with Systematic Listing.

SL is less efficient but may offer a lifeline for less mathematically inclined students. It may take a bit more time but it’ll give one precious few marks as long as a student is able to have the patience to list down the equivalent fractions in a systematic manner.

But, use it as a last resort, .... imagine a striker or midfielder taking long shots at goals in the dying minutes of the game hoping for that elusive winning goal or equaliser.

Best wishes

[ozora]

tianzhu:

LaiHeng:

Hi

I managed to solve this question but I wonder is there a another method.

The question is as follows: There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

I used SE concepts to solve it : 2/5o+ 2/3a=44----eq1
3/5o+ 1/3a=36-----eq2
I managed to get 35 oranges.

Is it possible to use model to get the answer? If so how? Thanks

Hi

Besides solving SE in algebraic manipulation, alphabet method or in pictorial form, you may also solve this question with Systematic Listing.

SL is less efficient but may offer a lifeline for less mathematically inclined students. It may take a bit more time but it’ll give one precious few marks as long as a student is able to have the patience to list down the equivalent fractions in a systematic manner.

But, use it as a last resort, .... imagine a striker or midfielder taking long shots at goals in the dying minutes of the game hoping for that elusive winning goal or equaliser.

Best wishes

is alphabet method the same as my stated method?
thanks for answering Tianzhu.

[tianzhu]

LaiHeng:

is alphabet method the same as my stated method?

Hi LaiHeng

Good Morning.

No, I think your method is geared more towards manipulation of algebraic fractions.

Aiyo, memory jammed early in the morning, I cannot recall where this term ”alphabet method” surface from. Jialat, really a sign of old age.

Anyway , we are using the letters of the alphabet to represent units and parts because the fractions for apples and oranges are of different measures.

There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

1O represents 1 unit of oranges and 1A represent 1 part of apples.

2O+2A ------ 44
3O+1A ------ 36

Representing the equations in this form avoids working with fractions in the calculations.

We have
1O+1A ------22
2O ------36-22-----14
1O ------7
5O ------ 35.

A student may translate these equations into pictorial method if he prefers.

Do not be too particular about the names of the terms, different books may call the same term different names. What’s more important is that a child is able to apply the concepts to solve questions.

Let the child take the method he/she is most comfortable with to the exam hall.

Best wishes

[ozora]

tianzhu:

LaiHeng:

is alphabet method the same as my stated method?

Hi LaiHeng

Good Morning.

No, I think your method is geared more towards manipulation of algebraic fractions.

Aiyo, memory jammed early in the morning, I cannot recall where this term ”alphabet method” surface from. Jialat, really a sign of old age.

Anyway , we are using the letters of the alphabet to represent units and parts because the fractions for apples and oranges are of different measures.

There are 80 apples and oranges in a basket. 2/5 of the oranges and 2/3 of the apples are eaten. In the end, they are 36 fruits left. How many oranges were there at first?

1O represents 1 unit of oranges and 1A represent 1 part of apples.

2O+2A ------ 44
3O+1A ------ 36

Representing the equations in this form avoids working with fractions in the calculations.

We have
1O+1A ------22
2O ------36-22-----14
1O ------7
5O ------ 35.

A student may translate these equations into pictorial method if he prefers.

Do not be too particular about the names of the terms, different books may call the same term different names. What’s more important is that a child is able to apply the concepts to solve questions.

Let the child take the method he/she is most comfortable with to the exam hall.

Best wishes

thanks for the clear explanation