Math: Which makes you tick?

[Busymom]

ksi:

Busymom, you always very spot on to what I am alluding to...it is consistency I am looking for in the visual to interpret the info.

ksi:

In any case I learn something from this experience.
When one is learning the concept, perhaps Picture 1 is clearer.
When one is applying the concept, perhaps Picture 2 is clearer.

So if the school is testing regurgitation, then Picture 1
But if the school is testing application, then Picture 2. GWIM?

I also learn something from the posts here... place value... erm... :idea:

Anyway, even if pic 2 is testing application, I still think the heading for the table should not show the 10 squares for tens and 1 square for ones, otherwise it is inconsistent again. It would be better to state tens and ones for the heading, and have 2 squares under the tens and 10 squares under the ones. JMO.

[Busymom]

buds:

... model drawing is model drawing hor.. Purposely make things
more confusing & mix it with place value indications, har.. :evil:

:roll: ... jargon that I don't understand... guess I need to learn all these next year.

[buds]

Yes.. Yes.. Must learn.. :evil:


Or else... :faint:

But i have a feeling you can take it.

[sunflower]

Busymom:

Anyway, even if pic 2 is testing application, I still think the heading for the table should not show the 10 squares for tens and 1 square for ones, otherwise it is inconsistent again. It would be better to state tens and ones for the heading, and have 2 squares under the tens and 10 squares under the ones. JMO.

Agree! :celebrate: Was just going to say that the bar of ten squares in the Tens heading can be deleted so we understand the diagram as each square rep 1 unit under each heading.

If the 10 sqs are shown in heading, the length of each box under Tens heading should be prolonged to be of the same length as that in the Tens heading, but need not have the lines in between to show the 10 sqs division.

[corneyAmber]

Busymom:

Anyway, even if pic 2 is testing application, I still think the heading for the table should not show the 10 squares for tens and 1 square for ones, otherwise it is inconsistent again. It would be better to state tens and ones for the heading, and have 2 squares under the tens and 10 squares under the ones. JMO.

Boxes in tens for Picture 2 was left there to remind that tens=10.
So I have updated with Picture 3 to make it clearer.

Picture 2 is still consistent because 1 box = 1 unit whether it is placed againt the tens or placed under tens but this is a bit abtract to understand, I agree.

In picture 1, 1 box under tens = 1/10 unit

[metz]

I won't advise losing sleep over Place Values but Model Drawing, that is something I'm still trying to learn. Tried some P6 model questions myself and ...

[corneyAmber]

chamonix:

I won't advise losing sleep over Place Values but Model Drawing, that is something I'm still trying to learn. Tried some P6 model questions myself and ...

Yes model diagram is tougher and in some situations, it takes longer to derive the diagram than to solve it using algebra under exam conditions.

The good thing about model diagram is it is very good for explaining concepts for a teacher to a student visually but not necessarily the best and fastest method to adopt for exam conditions. JMHO

[metz]

For me, I think the hurdle in Pic 2 lies here - one square under Tens is equivalent to 10 similar squares under Ones.

[corneyAmber]

chamonix:

I would say the method in Pic 1 is the introduction to understanding Place Value, which is easier for kids. It is more visual. Once the understanding has been established, I would consider the method in Pic 2 as application of the place value concept taught.


Method 1 - First pic,
When there are 10 boxes under Ones, we can easily regroup them to a 10-boxes bar under Tens and 0 boxes under Ones.
When there are 15 boxes under Ones, we can regroup 10 boxes into a 10-boxes bar under Tens and 5 boxes under the Ones.

Method 2 - Second pic,
When there are 10 boxes under Ones, we put one box under Tens and discard the 9 other boxes.
When there are 15 boxes under Ones, we put one box under Tens, 5 boxes under Ones, and discard 9 other boxes.


In Method 1, we can show the changes and relationship clearly,
i.e, 10 ones = 1 ten and 15 ones = 1 ten and 5 ones.
For a visual learner, it would be easier for him/her to understand that 1 ten = 10 ones (1 bar of ten), 5 tens = 50 (5 bars of ten), 50 tens (50 bars of ten) = 500.

But in Method 2, the box has no meaning or value. Its meaning or value depends on the place (i,e. Ones, Tens, Hundreds) that it has been assigned to. Because there are no difference in the boxes used, it might be (my speculation) more difficult for the more visual learners to grasp this abstract idea and understand 1 ten = 10 ones, 5 tens = 50, 50 tens = 500.

If we take a step further, Method 2 is actually the next step that follows after Method 1. Except numerals are used instead. A digit itself has no meaning or value. Its meaning or value also depends on the Place it takes. So, in Pic 2, we can replace the boxes with numerals 2 and 10 instead.

Erm, hope I didn't confuse you.

No, you did not confuse, it is in fact a detail explanation of my realisation that Method 2 is application of concept.

[corneyAmber]

chamonix:

For me, I think the hurdle in Pic 2 lies here - one square under Tens is equivalent to 10 similar squares under Ones.

That is assuming the concept of Tens is not understood yet.