Q&A - PSLE Math

[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.

[tianzhu]

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.................................

Hi

Good Morning.

I've compiled some examples of similar questions discussed earlier in the forum.

You may wish to have more practice.

1) A farmer has some chickens and ducks. If he sells 2 chickens and 3 ducks every day, there will be 50 chickens left when all the ducks have been sold. If he sells 3 chickens and 2 ducks every day, there will be 25 chickens left when all the ducks have been sold.
a) how many ducks are there?
b) how many chickens are there ?

2) Vicky and Jane were given a certain amount of money to spend. If Vicky spent $90 and Jane spent $30, Vicky would have $100 left when Jane had spent all her money. If Vicky spent $30 and Jane spent $90, Vicky would have $580 left when Jane had spent all her money, Find the total amount of money given to Vicky and Jane.

3) Tammy and Sharon have some money. If Tammy spent $60 each day and Sharon spent $30 each day, Tammy is left with $400 when Sharon spent all her money. If Sharon spent $60 each day and Tammy spent $30 each day, Tammy is left with $1150 when Sharon spent all her money. How much money do the two girls have?

Best wishes

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[andyle.024255sg]

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.................................

If J and R spend $60 and $30 each day respectively, J will still have $600 when R has spent all his money.
This means J spends 2 units, and R spends 1 unit, J has extra $600. (note that 60:30 = 2:1)
Model:
J: 2 units + 600
R: 1 unit

If J and R spend $30 and $60 each day respectively, J will still have $1500 when R has spent all his money.
This means J spends 1 unit, and R spends 2 units, J has extra $1500. (note that 30:60 = 1:2)
Model:
J: 1 unit + 1500
R: 2 units

Combine the two models by making the numbers of units of R the same by sub-dividing the units.
J: 4 units + 600
R: 2 units
J: 1 unit + 1500
R: 2 units

Hence, J has 4 units + 600 = 1 unit + 1500

Cheers.

[Mary Joy]

1.A swimming club has 30 girls and a no of boys.tHe number of boys increased by 15% to 46. And the no of girls decreased by 30%.what is the overall increase or decrease in the club's membership?


Please help me to solve this Qn.Thank you :thankyou:

[starfish53]

1) Can anyone help me with the following question? 800 more females than males went for a workshop on the first day. On the second day, the number of females decreased by 10% while the number of males increased by 40%. 3641 people went to the workshop on the second day.


a) How many females were there at the workshop on the second day?

b) Of each participant for the workshop had to pay $8, how much money was collected from the workshop on the first day?


2) Nick had some $5 and $10 notes in his wallet. He had a total of 60 pieces of notes at first. He used half of the number of $5 notes and his uncle gave him another twelve $10 notes. After that, the number of $10 notes he had was 2/3 of the remaining numer of $5 notes he had left. How much money did he have at first?

Thanks in advance.