Math: Which makes you tick?

[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.

[metz]

ksi:

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

:offtopic:

(sorry to digress here)

I would agree with that for most questions. But some have been designed in such a way that model drawing offers the best solution.Try using algebra for this question (hopefully I remembered correctly) -

Ben ate half a bunch of bananas.
Sam ate half of the remaining bananas and 1/3 of a banana.
David ate the half of the remaining bananas and 1/3 of a banana.
Only one banana was left.
How many bananas were there in the bunch at first?

[corneyAmber]

chamonix:

ksi:

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

:offtopic:

(sorry to digress here)

I would agree with that for most questions. But some have been designed in such a way that model drawing offers the best solution.Try using algebra for this question (hopefully I remembered correctly) -

Ben ate half a bunch of bananas.
Sam ate half of the remaining bananas and 1/3 of a banana.
David ate the half of the remaining bananas and 1/3 of a banana.
Only one banana was left.
How many bananas were there in the bunch?

Sorry, just looking at the question, if 2/3 of a banana has been eating, the remainder should at least have a 1/3 left, how come the left over banana is a whole number (1)?

[metz]

Sorry, wrong question.


Here's the correct question -

Ben ate 2/3 of a bunch of bananas and 1/3 of a banana.
Sam ate 2/3 of the remaining bananas and 1/3 of a banana.
David ate 2/3 of the remaining bananas and left with 1/3 of a banana.
How many bananas were there in the bunch at first?

Question can be solved by both algebra and model drawing. Try both ways and have fun.

[corneyAmber]

chamonix:

Sorry, wrong question.


Here's the correct question -

Ben ate 2/3 of a bunch of bananas and 1/3 of a banana.
Sam ate 2/3 of the remaining bananas and 1/3 of a banana.
David ate 2/3 of the remaining bananas and left with 1/3 of a banana.
How many bananas were there in the bunch at first?

Question can be solved by both algebra and model drawing. Try both ways and have fun.

Question: Is the 1/3 of a banana eating a standalone banana or part of the bunch of bananas?

[metz]

The one banana is part of the bunch.

[toddles]

both diagrams on the tens are completely confusing to me.

[corneyAmber]

toddles:

both diagrams on the tens are completely confusing to me.

Alamak, if there are more people like you after this polling, then the learning dept really have to re-think of the pedagogy.