Q&A - PSLE Math

[tianzhu]

Michaelia0816:

Pls help but this time method pls give me step by step answer

A shopkeeper had some apples and oranges. If 34 apples were sold, the ratio of the number of apples to number of oranges would be 3:1. If 85 oranges were sold, the ratio would be 29:4. How many apples did he have?

Hi

Hope this helps.

Best wishes.

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[Michaelia0816]

Dear everyone here, a question again cause my stupidness.

Sorry!
Father gave Nicholas and Rachel $630 to buy some clothes. Nicholas was given $60 more than Rachel. At the shop, Nicholas spent twice as much as Rachel. Rachel was left 3 times as much money as Nicholas. How many did Nicholas. How much did Nicholas spend ?

[Michaelia0816]

Thank you tianzhu !

[Michaelia0816]

Ok I use guess and check and found the answer

[tianzhu]

Michaelia0816:

Dear everyone here, a question again cause my stupidness.

Sorry!
Father gave Nicholas and Rachel $630 to buy some clothes. Nicholas was given $60 more than Rachel. At the shop, Nicholas spent twice as much as Rachel. Rachel was left 3 times as much money as Nicholas. How many did Nicholas. How much did Nicholas spend ?

Hi

Please confirm phrase highlighted in pink.

A neat way to solve it is to use MD.

Nicholas

Amount ------ 345
Spent ----- 2 parts
Left ------ 1 unit.

Rachel

Amount ------ 285
Spent ----- 1 part
Left ------ 3 units.

Rearrange the MD, you’ll see 1 part is equal to 2 units + 60

3 units + 2 units + 60 ------ 285
5 units ------ 225
1 unit ------- 45

Nicholas -------- 345
Nicholas spent ------ 345 – 45 ------ 300

If you need the MD, please let me know.

Best wishes

[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?