Q&A - PSLE Math

[MathIzzzFun]

Zack7:

peggy:

Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

2/3 x = 3/5y
Y-x = 100

Solving,

X=900

Now that you mention how models are used in conjunction with equalizing the numerator, it has become clear.

And I never claimed algebra is superior. Y do u see it that way? In fact I gave a solution which I thought was 'clearer' that contained no algebra.

Anyway, I must agree eugene's method is better now that isee how it works.

Hi Zack7,
I copied the initial solution you provided... and I did not say that algebra is superior or that another method is superior.
let's not pick words.. I m not here to debate which method is better and which is not..there are different approaches to solving a problem.. there is no one single method that can used for all types of problem sums... sometimes, the algebra/unit approach is more efficient, some times MD will provide a quicker and clearer solution, and sometimes simple logic will do... this forum provides for all to contribute their ideas/methods so that everyone can benefit. In particular, it offers different perspectives on problems and this is something that classroom will not be able to provide to the students who are reading this forum.

Take for example this question: \"There are some marbles in a box. The marbles can be put into packets of 4 or 7 with no marbles left over. When the marbles are put into packets of 13, there are 11 marbles left. What is the smallest possible number of marbles in the box?\".

The usual approach is to make a list and find the number that fits the scenarios. A quicker way is to draw a simple model to get the solution- 336

Have a great weekend !

cheers.

[MathIzzzFun]

PiggyLalala:

ADoc:

[quote=\"peggy\"]Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3/3 = 6/9 } ali
(3/5) x 2/2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene


Hi! My bad! tks for pointing out Zack. What i meant was 3/3 and 2/2 (as corrected above) to change to equivalent fractions. The concept is logically sound and in practice and can be construed as algebra in disguise in fact. It's just that most primary students prefer working in this manner to the ill-perceived horrors of algebra, especially cross multiplying and simultaneous linear eqn (which are not taught \"formally\" in most schools except by some primary teachers in certain schools that I know of).

cheers
eugene

No worries. We can understand your solution very well. And this is the way that the primary school kids are taught. In my opionion, we should not introduce the concept of algebra, like cross multiplication in Primary schools. Primary schools use units and parts or model method which is actually simple simple algebra that the kids can understand. Personally, I do not encourage solving primary school questions using simultaneous linear equations involving fractions and decimals, especially so for the weaker students. These methods are too complicated and there are always easier methods to solve such questions.[/quote]Hi PiggyLalala,

actually, the units/parts method, onsponge unit table, cross multiplication are really the same methods presented in different ways, but the cross-multiply approach allows one to solve without introducing a 2nd variable eg units & parts/algebra which involves two variables.

Bon weekend !

cheers.

[oceanh2o]

Anyone can help me With this question ? Thanks


The ratio of the number of boys to the
number of girls in a hall was 1:4.
After 87 more boys joined and 12 girls left the hall, the ratio of the number of boys to the number of girls was 5:2.
How many children were there in the hall at first?

[tianzhu]

oceanh2o:

Anyone can help me With this question ? Thanks


The ratio of the number of boys to the
number of girls in a hall was 1:4.
After 87 more boys joined and 12 girls left the hall, the ratio of the number of boys to the number of girls was 5:2.
How many children were there in the hall at first?

Hi

You may use “Units and Parts”

At first
Boys:Girls ----- 1 unit: 4 units

Change
Boys:Girls ----- +87: -12

In the end
Boys:Girls ----- 5 parts: 2 parts

1 unit + 87 ------ 5 parts
(x2)
2 units + 174 ----- 10 parts

4 units – 12 ----- 2 parts
(x5)
20 units – 60 ----- 10 parts

2 units + 174 ----- 20 units – 60
18 units ----- 234
1 unit ----- 13

Number of children at first ----- 5*13 ----- 65

Best wishes

[Zack7]

MathIzzzFun:

Zack7:

[quote=\"peggy\"]Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

2/3 x = 3/5y
Y-x = 100

Solving,

X=900

Now that you mention how models are used in conjunction with equalizing the numerator, it has become clear.

And I never claimed algebra is superior. Y do u see it that way? In fact I gave a solution which I thought was 'clearer' that contained no algebra.

Anyway, I must agree eugene's method is better now that isee how it works.

Hi Zack7,
I copied the initial solution you provided... and I did not say that algebra is superior or that another method is superior.
let's not pick words.. I m not here to debate which method is better and which is not..there are different approaches to solving a problem.. there is no one single method that can used for all types of problem sums... sometimes, the algebra/unit approach is more efficient, some times MD will provide a quicker and clearer solution, and sometimes simple logic will do... this forum provides for all to contribute their ideas/methods so that everyone can benefit. In particular, it offers different perspectives on problems and this is something that classroom will not be able to provide to the students who are reading this forum.

Take for example this question: \"There are some marbles in a box. The marbles can be put into packets of 4 or 7 with no marbles left over. When the marbles are put into packets of 13, there are 11 marbles left. What is the smallest possible number of marbles in the box?\".

The usual approach is to make a list and find the number that fits the scenarios. A quicker way is to draw a simple model to get the solution- 336

Have a great weekend !

cheers.[/quote]Then why ask me to be open to other methods?

Just because I use algebra mainly means i am not open to other methods?

And why not quote my other solution that is based on logic?

I question Eugene's method because I don't understand how it worked. I then proceeded to suggest a 'clearer' method which I now believe Eugene's method is better.

Where did I mention that any method was better? Or I am not receptive of any method?

[Ngserene617]

Hihi, pls help on these questions:


1. Alicia had 20% more stickers than Randy. Then Alicia gave away 30% of her stickers to her sister. Randy received 28 stickers from Peter. As a result, Randy now had 25% more stickers than Alicia.
How many stickers did Alicia have at first?

2. Shelly has some vanilla and chocolate sweets in her bag. If she adds 20 vanilla sweets into the bag, the percentage of vanilla sweets in the bag becomes 40%. If she adds 30 chocolate sweets in the bag, there will be 70% of chocolate sweets in the bag. How many vanilla sweets and chocolate sweets does she have?

3. On average, a bakery sells 500 fish fillet buns at$1.50 each day. When each bun increases by 20%, the total sales volume drops by 25%.
A. Find the new price of each bun.
B. find the number of buns sold at the new price.
C. What is the percentage change in the amount collected from the sales with the increase in the price?
D. Find the percentage discount required on the new price to adjust the price to its original level

TIA

[Ngserene617]

Hihi, pls help on these questions:


1. Alicia had 20% more stickers than Randy. Then Alicia gave away 30% of her stickers to her sister. Randy received 28 stickers from Peter. As a result, Randy now had 25% more stickers than Alicia.
How many stickers did Alicia have at first?

2. Shelly has some vanilla and chocolate sweets in her bag. If she adds 20 vanilla sweets into the bag, the percentage of vanilla sweets in the bag becomes 40%. If she adds 30 chocolate sweets in the bag, there will be 70% of chocolate sweets in the bag. How many vanilla sweets and chocolate sweets does she have?

3. On average, a bakery sells 500 fish fillet buns at$1.50 each day. When each bun increases by 20%, the total sales volume drops by 25%.
A. Find the new price of each bun.
B. find the number of buns sold at the new price.
C. What is the percentage change in the amount collected from the sales with the increase in the price?
D. Find the percentage discount required on the new price to adjust the price to its original level

TIA

[Andrew Lee]

Ngserene617:

Hihi, pls help on these questions:


1. Alicia had 20% more stickers than Randy. Then Alicia gave away 30% of her stickers to her sister. Randy received 28 stickers from Peter. As a result, Randy now had 25% more stickers than Alicia.
How many stickers did Alicia have at first?

2. Shelly has some vanilla and chocolate sweets in her bag. If she adds 20 vanilla sweets into the bag, the percentage of vanilla sweets in the bag becomes 40%. If she adds 30 chocolate sweets in the bag, there will be 70% of chocolate sweets in the bag. How many vanilla sweets and chocolate sweets does she have?

3. On average, a bakery sells 500 fish fillet buns at$1.50 each day. When each bun increases by 20%, the total sales volume drops by 25%.
A. Find the new price of each bun.
B. find the number of buns sold at the new price.
C. What is the percentage change in the amount collected from the sales with the increase in the price?
D. Find the percentage discount required on the new price to adjust the price to its original level

TIA

Hello, can help me solve Q10
http://i41.tinypic.com/2lw2dn8.jpg\">

[tianzhu]

Andrew Lee:

Hello, can help me solve Q10
http://i41.tinypic.com/2lw2dn8.jpg\">

Hi

Good Morning.

An interesting question, from the image you posted, it doesn't look that it from a past year paper.Could you share with us where is it from?

Sometimes, questions on circles look intimidating at first glance.Try to reorganise into familiar looking shapes.

Join the point of intersections(outermost) of the 3 circles to form an equilateral triangle.Join the centepoints (ABC) of the circles to form a smaller equilateral triangle.Add in an identical circle to touch the centrepoints of the two circles (BC) if you think it'll help you to see better.

Do some cut and paste of areas formed by the small arcs and triangles and you'll see that the area of shaded portion is equal to the area of a semi circle of radius 7 cm.

Area of shaded region = 1/2*22/7*7*7 = 77 sq cm

Best wishes

[cimman]

Andrew, here's something to help you visualize:

http://i40.tinypic.com/nnm7pe.png\">

The Tao of Maths
http://i40.tinypic.com/zn7zpf.png\">
on one side, are the people who don't know the solution. On the other side, are the people who knows the solution. Outside of the circle, are people who are not sure if they have the solution.