Q&A - PSLE Math

[KP2]

:thankyou: MathIzzzFun

[fullhope]

Thanks Tianzhu for the answer.

[fullhope]

Thanks Tianzhu for the answer.

[YumYum]

Tianzhu, thks for yr help the Qn on the marbles, the ratio is indeed 18:85. My mistake in typing it out. Thanks :rahrah:

[smileplease]

Please help in this Q.


J and R are given some money each. If J and R spend $60 and $30 each day respectively, J will still have $600 when R has spent all his money. If J and R spend $30 and $60 each day respectively, J will still have $1500 when R has spent all his money.

a) How much is given to J at first?
b) If J and R spend $35 and $20 respectively, how much money would J have left when R has spent all his money?

Thank you…

[iCreative Math]

Yum Yum, your question below:-


1) Mary bought some red marbles and have half to Noel.
Noel bought some blue marbles and gave half to Mary.
Mary lost 16 red marbles and Noel lost 55 blue marbles.
The ratio of Mary's red marbles to blue marbles became 18:85 and the ratio of Noel's red marbles to blue marbles became 7:20.
How many red marbles did Mary buy?

is adapted from the 2009 PSLE question with changes to the numbers and the resultant ratios but they are essentially similar questions.

I have posted the explanation of the solution to the 2009 PSLE question in YouTube (see the link below).

I hope the verbal explanation will be helpful for your child to understand the solution to this sort of questions.

http://www.youtube.com/watch?v=epaXFwd5j_0

Best Regards,

iCreative Math

[cimman]

ozora:

PapayaDad:

Need guide to solve the following questions.

q1. in 20 years time, Tom's age will be 34 years less than twice Joan's age.
If Joan is now 3 times older than Tom, what is Tom's present age?

q2. A is the oldest among three people. When B's age was twice of C's age, A was 30 years old. When A's age was twice of B's age, C was 21 years old. How old was C when A was 62 years old.


the above questions, I have used models to get the answers as follows: Q1 . Tom (1 unit+20years)
Joan( 4unit +20 years) x 2
Tom is 2 years

Sorry, but answer not correct leh.
now Tom is 2, 20 years he is 22
22 + 34 = 56
J = 56/2 = 28
now J is 28 -20 = 8
now Tom = 2
Joan is now 3 times older than Tom...not true
Joan is now 4 times older than Tom.... typo? cuz ur method use 4 units...

3 times older meaning is 4 units.
is a common mistake we assume 3 times older is same as 3 times as..
in fact they are totally different.

More Than / Less Than statements are very common in Maths problem sums.
All of them share certain characteristics. I call More Than / Less Than statements, Difference Statements.
The objective of Difference Statements is to give us 2 pieces of information:
1. the difference between 2 values
2. which value is the larger value

let's have a look at a typical Difference Statement:
Michelle had 238 more cards than Adila
this means : Difference = 238, Michell > Adila
this can be translated to the mathematical statement: Michell - Adila = 238

here's a few more Difference Statements:
Sally paid $0.20 more than May
The boys planted 30 more trees than the girls
He spent $9.10 more on the pens than the erasers.
Danny earned $5 less than Richard each day
Each large bag has 5 more cookies than each small bag.

notice that there is a consistent structure to Difference Statements.
The Difference Statement contains the key words \"more than\"/ \" less than\"
The Difference value is a whole number. The more than/ less than indicates which value is larger.

let's have a look at the below problem:
Jack bought some pens and erasers for a total of $100.10. He spent $9.10 more on the pens than the erasers. Each pen costs $3.70 more than each eraser. Jack bought 6 times more erasers than pens. How much does each pen cost? Ans: $4.20
the solution is here for those who are interested: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&start=480

Jack bought 6 times more erasers than pens.
Difference = 6u, Erasers > Pens
this translates to the mathematical statement:
Erasers - Pens = 6u (larger value - smaller value)

why 6u ? because it is 6 times of something. Since we don't know what that something is, we let 'u' be that something. The smaller value, Pens, represents \"u\",
thus: 7u - u = 6u
Pens = u, Erasers = 7u

a more advance form of Difference Statement is when the keywords \"more/greater than\" or \"less/fewer than\" is not used. Instead a comparative adjective is used. Comparative adjectives are adjectives that ends in \"er\". Some examples are \"shorter than\", \"bigger than\", \"faster than\", \"older than\". The keyword \"than\" remains. This tells us that the statement is a Difference Statement and we must evaluate it as such. We need to extract the Difference value and figure out which value is the larger value.

Joan is now 3 times older than Tom
Difference = 3u, Joan > Tom
Joan - Tom = 3u
since Tom is the smaller value, we let Tom = u.
4u - u = 3u
thus, Joan = 4u

what if we use another comparative adjective \"younger than\" instead ?
Joan is now 3 times younger than Tom
Difference = 3u, Joan < Tom
since Joan is now the smaller value, we let Joan = u,
Tom - Joan = 3u
Joan = u, Tom = 4u

so, depending on the comparative adjective used, the student has to discern which value is the larger value.

[cimman]

ozora:

Besides the algebra, is it possible to use units transfer method? I wouldn't mind learning algebra as well.

Units Transfer method uses Units and Parts or \"u\" and \"p\", unknown variables.
This is essentially the concept of using unknown variables as place holders, which is what algebra is all about.

Since you prefer the Units Transfer approach, it shows that you've discovered that using an abstract approach is a less cumbersome method than using a spatial approach (modelling). You're on the right path I've always believed that highly abstract problems requires abstract analysis techniques.

The only difference between Units Transfer Method and an algebraic approach is that Unit Transfer do not have the concept of negative numbers -u(3p -2u) and simultaneous equation is not used.

The Units Transfer analysis process is similar to an algebraic approach, but the method to remove unwanted variables differ.

What this means is that if you can understand Units Transfer Method, you'll be able to understand the algebraic approach, provided simultaneous equations and negative number multiplication is not used.

However, traditional algebraic analysis is not easy to understand. The teacher reads out the problem sum, and then proceeds to write out 2 equations. Between the problem sum and the equations is normally a black box for students. A tabular approach will help to formulate the equations in an easier manner, sort of like a pair of training wheels on a bicycle.

[cimman]

as for the alternative method, I’ll send it to you in a file as the graphics involved would be too large to fit in here. However, if you come to the 25 May workshop, I’ll be happy to spend some time with you to go through the table structure for age questions. It is not easy to understand the table structure on a piece of paper. Send me a PM with your email address.

[MathIzzzFun]

YumYum:

Hi, can someone pls help with these Qns:


1) Mary bought some red marbles and have half to Noel.
Noel bought some blue marbles and gave half to Mary.
Mary lost 16 red marbles and Noel lost 55 blue marbles.
The ratio of Mary's red marbles to blue marbles became 18:55 and the ratio of Noel's red marbles to blue marbles became 7:20.
How many red marbles did Mary buy?

thanks, thanks!

AT first (,
Mary's red marbles : blue marbles --> 18u + 16 : 85u
Noel's red marbles : blue marbles --> 18u + 16 : 85u
Red marbles bought by Mary --> 36u + 32
Blue marbles bought by Noel --> 170u

After Noel lost 55 blue marbles,
Noe's red marbles : blue marbles
--> 18u + 16 : 85u - 55
= 7 : 20

cross multiply:
360u + 320 = 595u - 385
1u --> 3

Red marbles bought by Mary --> 36 x 3 + 32 = 140

cheers.