tianzhu:

mathnoobs:

I believe your 11 units is derived from 3 units of plates left and thus, there are also 3 units of bowls left. This is the part I do not understand, if there are 3 units of plates left, some amount must be sold in the afternoon, and some must remain left unsold. I'm totally confused on the comprehension of this question.

Hi

Good Morning.

The shop sold 100 plates and bowls on a particular day. By noon (in the morning), it sold 5/8 of the plates and 12 bowls. The rest were sold in the afternoon.

Hope this helps.

Best wishes

http://farm7.staticflickr.com/6160/6199051565_562fe291d4_z.jpg\">

Hi Tianzhu
thank you very much for your help. I understand now.

Hi Tianzhu

I was going through some old questions and came across this question.
http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=67&t=25121&start=60

After going through your answer, I'm still at a loss.
I believe my understanding of the question is at fault. Anyway, here is the question:

Aik Huat Provision sold 100 plates and bowls on a paticular day.
BY noon 5/8 of the plates and 12 bowls had been sold.
In the end, there was an equal number of plates and bowls.
How many bowls were there at first?

here is my understanding of it:
100 plates and bowls were sold at the end of the day.
In the morning 5/8 plates were sold and 12 bowls were sold.
In the beginning, before plates and bowls were sold, there were 8 units of plates.
In the afternoon, some more plates and bowls were sold.
In the end, an equal amount of plates and bowls were left unsold

Your solution says: 11 units + 12 = 100
how does one arrive at 11 units ? since 5 units of plates were sold in the morning, there are 3 units of plates left. However, since we don't know how many plates were sold in the afternoon, and how many plates are left.

I believe your 11 units is derived from 3 units of plates left and thus, there are also 3 units of bowls left. This is the part I do not understand, if there are 3 units of plates left, some amount must be sold in the afternoon, and some must remain left unsold. I'm totally confused on the comprehension of this question.

tianzhu:

mathnoobs:

Hi Tianzhu
this was posted some time back, and I had a look.
I have a question:
why is 1 unit = 2 1/3 ? why not 1 unit = 2 2/3 ?

Hi

After Bala took 5/6 of the remaining tin of cookies, 1/6 of the tin was left.

This 1/6 of tin comprises of 1/3 of a cookie and the remaining 2 cookies, therefore 1 unit equals 2 1/3.

Please refer to my earlier post.

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&p=369724&hilit=cookies#p369724

Best wishes

ok, got it. Thank you very much Tianzhu. I must say comprehension is a key thing here for the more difficult questions.

tianzhu:

http://farm5.staticflickr.com/4019/4713599224_8f586290c0_z.jpg\">

Hi Tianzhu
this was posted some time back, and I had a look.
I have a question:
why is 1 unit = 2 1/3 ? why not 1 unit = 2 2/3 ?

tianzhu:

Hi


I’ve intentionally labelled the boxes as unit and part so that students can have an option if they choose to work using Units and Parts.

As usual, I’ve done more MD than necessary, once students understand the logic, they may consodilate the steps.

Hope this helps.

Best wishes

http://farm8.staticflickr.com/7035/6812082325_7bb0b1b14f_z.jpg\">

Hi Tianzhu
thank you very much again for taking the time to come up with an excellent diagram. It very clearly illustrate the concept involved.

I find that while modelling is very good for understanding the concept, when it comes to answering exam questions, the unit transfer method is faster, since there is no drawing involved. Drawing takes up more time, compared to writing out a few numbers. More so if the child's motor skills isn't that good and drawing a straight line freehand, is going to be cumbersome.

tianzhu:

mathnoobs:

after some thinking, I think I see the logic.

The labels Units/Parts are assigned based on the comparison made by the question.
Since the question compared Sally's age at present time to Tom's age at some other time, then that comparison should be assigned the same label (ie. either Units or Parts) The second comparision would be assigned another label.

However, I still have this question: in Challenging Maths Made Easy, the chapters on Unchanged Total/Difference/Quantity all used only 1 label for both the Before and After comparision. Should not they have used different labels for the Before and After cases ? I can understand that after normalization (lowest common multiple), all ratios are assigned a single label. But before they are normalized, shouldn't they have different labels ?

Hi

Great, you see the logic. So, there‘s no need for me to draw the MD anymore.

Yes, you may represent them in units and parts to represent before and after ratios. But you still need to change parts into units as you use the concepts of unchanged quantities, unchanged difference or unchanged total quantities. There is more than one way to solve it.

Best wishes

yes, I understand that one needs to change parts into units for unchanged stuff. However, in Ammiel Wan's book, both ratios were presented as units before the common multiple operation was done. Is this correct ? or one of the ratio should be labelled as parts ?

after some thinking, I think I see the logic.

The labels Units/Parts are assigned based on the comparison made by the question.
Since the question compared Sally’s age at present time to Tom’s age at some other time, then that comparison should be assigned the same label (ie. either Units or Parts) The second comparision would be assigned another label.

However, I still have this question: in Challenging Maths Made Easy, the chapters on Unchanged Total/Difference/Quantity all used only 1 label for both the Before and After comparision. Should not they have used different labels for the Before and After cases ? I can understand that after normalization (lowest common multiple), all ratios are assigned a single label. But before they are normalized, shouldn’t they have different labels ?

tianzhu:

mathnoobs:

Hi Tianzhu
how does one know when to use units and parts ? Here the units are assigned to Sally, and parts to Tom. However, since Tom has age in both present time and some other time, how does one tell whether to assign parts/units based on time or individual ? What is the rational for the assignment ?

Hi

I am sorry. I can’t answer in detail at this moment.

If you have a copy of Challenging Maths Made Easy, try to do some reading first.

I’ll try to answer your question at a later time.

Best wishes

Hi Tianzhu
no problem. Thanks for responding first.
I do have the Challenging Maths Made Easy, and here is why I have the confusion.
It is only in Chapter 7, External Transfer with Changed Quantities Concept, that I see both Units and Parts being used.
In the others, ie. Unchanged Total, Unchanged Difference, Unchanged Quantity, only Units are used for the typical Before and After cases. In the unchanged scenarios, the 2 ratios are linked by normalizing them to a common denominator. But before the normalization, I would have thought the After scenario would be labelled as Parts rather than Units.

In the age problem, I see 2 scenarios, the Present age scenario and the some other time scenario. I would have thought that based on the Chapter 7 concept, the label Units, Parts would be assigned based on scenarios (ie. Before, After) in thise case (Present Age, Some Other Time)

tianzhu:

kkme:

1) Tom's present age is thrice Sally's age some years ago. Conversely, Sally's present age is Tom's age the same number of years ago. Given that the sum of their present ages is 30 years, how old is Tom now?

Hi

For Q1, you may use MD or Units and Parts.

Due to time constraints, I’ll skip the MD this time.

At present
Tom ----- 3 units
Sally ----- 1 part

Some years ago
Tom ----- 1 part
Sally ----- 1 unit

The difference in age between two people remains the same.

3 units – 1 part ----- 1 part – 1 unit

4 units ----- 2 parts
2 units ----- 1 part

The sum of their present ages is 30 years.

3 units + 2 units ----- 30
5 units ----- 30
1 unit ----- 6

Tom ----- 3 units ----- 18

Best wishes

Hi Tianzhu
how does one know when to use units and parts ? Here the units are assigned to Sally, and parts to Tom. However, since Tom has age in both present time and some other time, how does one tell whether to assign parts/units based on time or individual ? What is the rational for the assignment ?

MathIzzzFun:

mathnoobs:

Hi Mathizzfun

Thank you for taking the trouble to draw out a diagram.
I'm afraid I still don't get it.
I've drawn a model here that says Nacho combos costs more than Popcorn combos.
http://i42.tinypic.com/2laa1hj.png\">

can you tell me what is wrong with the diagram ?

Is there a way to tell which is bigger without resorting to diagram ? My child's motor skill is not very good, and has difficulty in getting the relevant boxes to be of the same size.

Hi

The model that you have drawn are of different length which means that the total amount is different.

Note that the total amount of money must be the same ie
total amount of money = (money spent on 4 nachos+3 popcorns) +(money left = 4.50) = (money spent on 3 nachos + 4 popcorns) + (money left = 4.50)

In fact, by noting that there is more money left if I buy 4 nachos and 3 popcorns than if I buy 3 nachos and 4 popcorns means that 3 nachos + 4 popcorns cost more than 4 nacho + 3 popcorn.

http://i40.tinypic.com/n2d1md.jpg\">

cheers.

Hi MathIzzzFun
thank you very much for drawing the diagrams. It is clearer now to see the relationships. Appreciate your time in offering your help. Thank you very again.