Q&A - PSLE Math

[ozora]

Mathizzfun thanks solved

[cimman]

ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

http://i40.tinypic.com/i42046.png\">

this problem is made up of a number of equations, similar to this type of problem sums:
Three boys, Alan, Bernard and Calvin sat for a test. The average score of Alan and Bernard was 78 marks, the average score of Bernard and Calvin was 74 marks and the average score of Alan and Calvin was 80 marks. Find the marks scored by each of them.

The key is to figure out how to combine specific equations together to eliminate some variables. Since this problem is about angles, we need to do some inference on angles before we begin to combine equations together.
In any angle problems, we always look for same angle properties. The key is to look for parallel sides or sides with same lengths (isosceles triangles). However, none of that exists in this diagram. However we do note that n = m.
The other property that we need to take note of, is that the interior angles of a triangle adds up to 180 or the interior angle of a quadrilateral adds up to 360. This property gives us another inference (on equation) that is not normally stated in the figure diagrams.
In this case, we don't have a quadrilateral shape, but we do have triangle shapes.
There are 3 triangles:
a + f + n = 180
p + e + d = 180
m + b + c = 180

so, with the 2 inferences that we have made (m=n, and the equations that gives 180), we can move on to the next step.

amongst all the 4 equations given in the problem sum, a + m = 135 is the most useful to start of with because it can be translated to a + n = 135, since m = n. (a + n) is useful because it gives us part of the equation that will lead us to 180. All we need now, is to link it to f.

We find that equation 4, will give us that variable, f. So, we will start off with adding equation 1 and equation 4, which will utilize our inference that
a + f + n = 180

http://i44.tinypic.com/33mr12o.png\">

there are other combinations to solve this, but the main idea is to make the necessary inferences on angles and interior angles of a triangle, and then look for equations with variables that will utilize the inferences.

[ozora]

cimman:

ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

http://i40.tinypic.com/i42046.png\">

this problem is made up of a number of equations, similar to this type of problem sums:
Three boys, Alan, Bernard and Calvin sat for a test. The average score of Alan and Bernard was 78 marks, the average score of Bernard and Calvin was 74 marks and the average score of Alan and Calvin was 80 marks. Find the marks scored by each of them.

The key is to figure out how to combine specific equations together to eliminate some variables. Since this problem is about angles, we need to do some inference on angles before we begin to combine equations together.
In any angle problems, we always look for same angle properties. The key is to look for parallel sides or sides with same lengths (isosceles triangles). However, none of that exists in this diagram. However we do note that n = m.
The other property that we need to take note of, is that the interior angles of a triangle adds up to 180 or the interior angle of a quadrilateral adds up to 360. This property gives us another inference (on equation) that is not normally stated in the figure diagrams.
In this case, we don't have a quadrilateral shape, but we do have triangle shapes.
There are 3 triangles:
a + f + n = 180
p + e + d = 180
m + b + c = 180

so, with the 2 inferences that we have made (m=n, and the equations that gives 180), we can move on to the next step.

amongst all the 4 equations given in the problem sum, a + m = 135 is the most useful to start of with because it can be translated to a + n = 135, since m = n. (a + n) is useful because it gives us part of the equation that will lead us to 180. All we need now, is to link it to f.

We find that equation 4, will give us that variable, f. So, we will start off with adding equation 1 and equation 4, which will utilize our inference that
a + f + n = 180

http://i44.tinypic.com/33mr12o.png\">

there are other combinations to solve this, but the main idea is to make the necessary inferences on angles and interior angles of a triangle, and then look for equations with variables that will utilize the inferences.

Thanks for giving detail explanation. I was kinda of stuck with so many equations. Really have to take time to solve one at a time. I wonder how much could those average kid manage .

[cimman]

Chalupa:

I need a help to solve this problem. A fruit seller had 600 apples & oranges altogether. After he sold 1/5 of his apples and bought another 60 oranges, the number of oranges was 2/5 the number of apples. How many more apples than oranges were there at first.( Ans.400) .Thanks in advance. :thankyou: :?:

if you don't mind using a bit of algebra, here's an alternative method.
The table is consistent for all such Before/After problems.
First step is to transfer the values from the problem sum to the table.
http://i44.tinypic.com/34ph0sx.png\">
http://i41.tinypic.com/fz8ts.png\">
http://i44.tinypic.com/30u75hs.png\">

once we have copied over all the values from the problem sum, the next step is to circle the equations:
(note: Before + Transfer = After)
http://i44.tinypic.com/xqcb2d.png\">

now, we fill in the blank boxes that is within the circles.
http://i39.tinypic.com/2gx44jl.png\">

you can avoid simultaneous equations by finding the lowest common multiple for 5p and 2p. ie. 2p (x5), and 5p (x2)
(x5) 660 - 5u = 2p (x5)
3300 - 25u = 10p

(x2) 4u = 5p (x2)
8u = 10p
3300 - 25u = 8u

another common technique is to find the lowest common multiple for 4u, 5p (commonly known as equalizing the units and parts)
since 4u = 5p ----------------------- equation 2
(x5) 4u = 5p (x4)
660 - 5u (x5) = 2p (x4) ----------- equation 1
660 - 25u = 8u
660 = 33u
20 = u
Apples = 5u (x5) = 5x20 (x5) = 500
Oranges = 600 - 5u (x5) = 600 - 500 = 100

The table allows you to view all possible equations for the problem sum. By filling in different values into the table, and with some creative way of solving simultaneous equations (as shown above), you can arrive at the simple equations that one normally gets from modelling heuristic.

I am conducting a workshop at the end of the month (last Saturday of this month, 25 May) on this technique. It's a workshop to help parents cope with difficult problem sums using a simple table.

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=43&t=32278&start=200

the technique is straight forward: copy the values from problem sum to the table, circle the equations, solve the equations. It's a 3 step approach.

[YumYum]

Hi, can someone pls help with these Qns:


1) on the first day of a camp, there were 240 more boys than girls. On the second day, 20% of the boys left the camp and the number of girls increased by 10%. in the end, there were 42 more girls than boys. How many children were there at the camp on the first day?

2) on the first day of a camp, there were 240 more girls than boys. On the second day, 20% of the boys left the camp and the number of girls increased by 10%. given that the total number of children on both days remained the same, how many children were there at the camp on the first day? Thanks!

[cimman]

ozora:

Thanks for giving detail explanation. I was kinda of stuck with so many equations. Really have to take time to solve one at a time. I wonder how much could those average kid manage .

the difference between the GEP kids and the average kids is that the neurological pathways for logical thinking is inborn. Somehow, they are able to connect disparate information to form a coherent relationship. It requires very little effort on their part to do this.

For the average kid, the logical pathways have to be built. It requires effort to build the relationships. However, with training and the right pedagogical techniques, the average kid can achieve the same result as the GEP child, within certain predefined boundaries.

You'll find that each problem category has certain key concepts to be mastered. Once they are mastered at the abstract level, then the analysis process is quite consistent. In the multiple equations problem, once the initial equation is identified, it will link to the next equation and the next and the next. There is a logical link between the equations.

In the same way, Before/After type problems too have a consistent logic in them. All them follow the logic inherent in the table structure that I've shown in the problem on Apples and Oranges. Once one learns to see the logical relationships, then Before/After type problems are pretty straight forward. The table simply outlines the relationships in a way that is much easier to analyse.

Speed problems too have a consistent logic. They are often twisted around, and there seems to be many seemingly disparate problem permutations. However, they are all just variations on the same theme. Once the student understands what this main theme is, then all speed problems can be linked back to that theme, and solved in the same manner, ie. a single reasoning technique is used.

I tend to see this in the manner of the Matrix movie. There is this memorable scene where Neo stops the flying bullets coming at him and he picks one up in mid air and looks at it. That is when Neo finally understood the Universe for what it is, and in the process, how to control it.

It is the same with Maths problems. See through the fudge and the murk, and recognize the logic for what it is. Embedded in all that ambiguous words and phrases is a consistent logic. Seems pretty abstract. Luckily there is a step by step approach to this

[tianzhu]

YumYum:

Hi, can someone pls help with these Qns:


1) on the first day of a camp, there were 240 more boys than girls. On the second day, 20% of the boys left the camp and the number of girls increased by 10%. in the end, there were 42 more girls than boys. How many children were there at the camp on the first day?
Thanks!

Hi

First day
Boys ---- 10 units + 240
Girls ---- 10 units

Second day
Boys ---- 8 units + 192
Girls ---- 11 units

11 units ------ 8 units + 192 + 42
1 unit ------ 78

Number of children@first day ------- 20units + 240 ------- 1800

Best wishes

[tianzhu]

YumYum:

2) on the first day of a camp, there were 240 more girls than boys. On the second day, 20% of the boys left the camp and the number of girls increased by 10%. given that the total number of children on both days remained the same, how many children were there at the camp on the first day? Thanks!

Hi

First day
Boys ---- 10 units
Girls ---- 10 units + 240

Second day
Boys ---- 8 units
Girls ---- 11 units + 264

20 units + 240 ------ 19 units +264
1 unit ------ 24

Number of children@first day ------- 20units + 240 ------- 720

Best wishes

[iamproudparents]

hi all, please help to enlighten us on these few maths questions, thanks alot.


1) the ratio of jim’s savings to ken’s savings is 1:2. jim received some money and his savings increased by 60%. what percentage of ken’s money must be decreased so that their savings are equal?

2) alice had some apples and bananas. 3/4 of the apples and 6/7 of the bananas are in good condition. 9/11 of the good fruits are apples. if the number of apples alice had was 522 more than bananas, how many fruits did alice have in all?

3) sandy started to drive from city Q to city P. at the same time, jack also started to drive in an opposite direction from city Q to city R. after travelling for 4 hours, sandy and jack were 620km apart from each other. if sandy’s speed was 12km/h slower than jack’s speed, what was jack’s speed for the journey?

4) there were 846 glasses in a basket. some of the glasses were found to be broken and thrown away. of the remainder, 2/3 of the glasses were sold and 1/4 of the glasses was given away. there were 56 glasses left.

a) how many glasses were sold?

b) what fraction of the glasses in the basket was thrown away? give your answer in its simplest form.

[The Right Equation]

iamproudparents:

hi all, please help to enlighten us on these few maths questions, thanks alot.


1) the ratio of jim's savings to ken's savings is 1:2. jim received some money and his savings increased by 60%. what percentage of ken's money must be decreased so that their savings are equal?

http://i40.tinypic.com/6j3o1x.jpg\">