Q&A - P3 Math

[Tang]

tutormum:

Ooops. Sorry, forgot to quote. My early reply is for the following question.


A teacher gave her students some balloons. If she gave 6 balloons to each student, she will have 2 balloons left. If she gave 8 balloons to each student, she will be short of 2 balloons. What is the smallest possible number of students she has?

Try to do this without using ALGEBRA!

2 + 2 = 4

8 - 6 = 2

4 / 2 = 2 students


Or

Number of students 1 , 2
Multiple of 6 -- 6 , 12,
+ 2 -- 8 , 14

Multiple of 8 -- 8 , 16
-2 -- 6 , 14

[Muffins]

tutormum:

Ooops. Sorry, forgot to quote. My early reply is for the following question.


A teacher gave her students some balloons. If she gave 6 balloons to each student, she will have 2 balloons left. If she gave 8 balloons to each student, she will be short of 2 balloons. What is the smallest possible number of students she has?

Try to do this without using ALGEBRA!

Alright tutormum... I'll use ratios!

6 : 8
(+2) (-2)
1 : 1

6u + 2 = 8u -2

2u = 2+2 = 4

4 x 6/2 = 12

12/6 = 2

This is the other correct way we can use...

[Muffins]

ameryeducation:

Muffins:

[quote=\"tutormum\"]Ooops. Sorry, forgot to quote. My early reply is for the following question.


A teacher gave her students some balloons. If she gave 6 balloons to each student, she will have 2 balloons left. If she gave 8 balloons to each student, she will be short of 2 balloons. What is the smallest possible number of students she has?

Try to do this without using ALGEBRA!

Alright tutormum... I'll use ratios!

6 : 8
(+2) (-2)
1 : 1

6u + 2 = 8u -2

2u = 2+2 = 4

4 x 6/2 = 12

12/6 = 2

This is the other correct way we can use...

Muffins, you are actually using algebra, where U is the number of students.

In fact, you could have just written:

6u + 2 = 8u -2

2u = 2+2 = 4

4 x 6/2 = 12

12/6 = 2

and still get the answer, without the earlier ratio statement.[/quote]Oh ya...

Thanks ameryeducation!

[suiyuan]

ameryeducation:

No problem, Muffin! You may want to refer to my above solution (LCM), which can be employed for all similar questions like \"There are some chairs in a hall, numbering between 300 and 350. If they are arranged in rows of 7, there will be a remainder of 4. If they are arranged in rows of 8, there will be a shortage of 3. How many chairs are there in the hall?\" (Taken from our upcoming book.)

Hi

Will your book be available in Popular Bookstores?
How much will it cost?
What are the differences between your book and those assessment books currently available in the market?

[Dharma]

tutormum:

Ooops. Sorry, forgot to quote. My early reply is for the following question.


A teacher gave her students some balloons. If she gave 6 balloons to each student, she will have 2 balloons left. If she gave 8 balloons to each student, she will be short of 2 balloons. What is the smallest possible number of students she has?

Try to do this without using ALGEBRA!

For 2 additional balloons given out to a student – Teacher will have 4 less balloons.
(Difference between 2 balloons left and short of 2 balloons = 4 balloons)

No. of students = 4/2 = 2

(# If teacher has 4 less balloons after giving out 2 additional balloons to each student, then there must be 4/2 =2 students)

[kitty2]

Great to hear that your book will be out soon as it’s just on time for my P6 kid next year.I like your simple and elegant solution ,hopefully all your questions come with detailed answers.I can’t find an assessment book which has detail answers.


All the best to you and thank you for your kindness.

[Muffins]

Dharma:

tutormum:

Ooops. Sorry, forgot to quote. My early reply is for the following question.


A teacher gave her students some balloons. If she gave 6 balloons to each student, she will have 2 balloons left. If she gave 8 balloons to each student, she will be short of 2 balloons. What is the smallest possible number of students she has?

Try to do this without using ALGEBRA!

For 2 additional balloons given out to a student – Teacher will have 4 less balloons.
(Difference between 2 balloons left and short of 2 balloons = 4 balloons)

No. of students = 4/2 = 2

(# If teacher has 4 less balloons after giving out 2 additional balloons to each student, then there must be 4/2 =2 students)

Dharma, hey!

I forgot that method...

Short, simple, and easy to remember. You really are one of the best sum solvers on this site! :udaman:

[mamona]

Sakina has 15 coins. There are 20c coins and 50c coins. The total amount is $4.80. How many 20c coins are there?


The above sum can be done using the guess method like

10 20c coins = $2.00
5 50c coins = $2.50

then by increasing 20c coins number & decreasing the 50c coins number. But this method is very time consuming & a P3 student may not able to guess correctly which coin to increase & which one to decrease.

So can any one let me know some method which can be used for these kind of sums.

Thanks in advance.

[tutor_your_child]

mamona:

Sakina has 15 coins. There are 20c coins and 50c coins. The total amount is $4.80. How many 20c coins are there?

Perhaps you could explain the following method for P3 :
The first step is to assume that all the coins are either 50c coins or 20c coins.
Assuming all 15 coins are 20c coins, total value is only $3
Find the difference compared to $4.80; i.e. $1.80.
(easier to do show this in a table - see below)

2nd step
Since the total is less than $4.80, there should be more 50c coins and fewer 20c coins ( i.e. need more of those with higher value)
Conversely if the total is more than $4.80, there should be fewer 50c coins and more 20c coins. (This scenario is not possible for we had assumed that all are 20c coins).

3rd step
The 3rd step cuts down the number of iterations required for the 'guess and check' method.

For every 50c coin you increase, you have to decrease the 20c coin as well.
As such, the value increased per coin is only 30c (50c-20c)
As above, assuming all are 20c coins, total value is only $3, we are short of $1.80.
$1.80 / 30c = 6
i.e. increase 6 50c coins and decrease 6 20c coins
As such, the number of 20c coins is 15-6=9

4th step
Complete in table to check
http://www.postimage.org/

[mamona]

Many Many Thanks for your reply. Yes I understood the method. :lol: