Q&A - PSLE Math

[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

[ozora]

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

Adoc thanks for the pictorial explanation. Must really get use of using this approach to teach the children.

[tianzhu]

ozora:

thanks for the clear explanation

Hi

You're welcome.

Best wishes

[is_me_lblue]

Hi,


Question as follow :

The ratio of the area of A to B is 1:2. If 30% of B overlaps with A, what percentage of the whole figure is not overlapped ?

Thk u

Anwer given is 75%.

[Belle2011]

is_me_lblue:

Hi,


Question as follow :
The ratio of the area of A to B is 1:2. If 30% of B overlaps with A, what percentage of the whole figure is not overlapped ?
Thk u
Anwer given is 75%.

I try to explain as detailed as possble because I do not know how to insert a diagram which speaks a thousand words.
B is a bigger circle as compared to A.
The overlapping area is 30% of B and thus put 3 in that overlapping area and the remaining of B will be 7. Since A:B is 1:2, the total parts for A will be 5 and since the overlapped area is 3, the not overlapped of A is 2.

Total parts = 7+3+2 = 12.
Total Not Overlapped parts = 7+2 = 9.

9/12 = 75%.

Cheers,
Belle.

[ADoc]

ozora:

Adoc thanks for the pictorial explanation. Must really get use of using this approach to teach the children.

cheers! Hope it's useful..

[ADoc]

Belle2011:

is_me_lblue:

Hi,


Question as follow :
The ratio of the area of A to B is 1:2. If 30% of B overlaps with A, what percentage of the whole figure is not overlapped ?
Thk u
Anwer given is 75%.

I try to explain as detailed as possble because I do not know how to insert a diagram which speaks a thousand words.
B is a bigger circle as compared to A.
The overlapping area is 30% of B and thus put 3 in that overlapping area and the remaining of B will be 7. Since A:B is 1:2, the total parts for A will be 5 and since the overlapped area is 3, the not overlapped of A is 2.

Total parts = 7+3+2 = 12.
Total Not Overlapped parts = 7+2 = 9.

9/12 = 75%.

Cheers,
Belle.

Hi is_me_Iblue!
just a \"rough\" diagram. Hope this is useful for your visualisation.

cheers!
ADoc
http://postimage.org/image/312yr9mpw/

[Emelyn]

Hi,


Brain jammed....cannot solve the problem. Sign of old age too....
Asking for help here .......


http://postimage.org/image/2kyiwxjj8/

In the figure above, which is not drawn to scale, 1/4 of the circle is shaded. The ratio of the area of the square to the area of the rectangle and circle is 5:7. 40% of the square is shaded. 1/3 of the rectangle is shaed. What is the ratio of the area of the circle to the square to the rectangle ?

MTIA !!