math question

[space cadet]

I'm trying to find out what the proper term is for the following situation:

a problem like this: 4 + 3 = 3 + 4 is demonstrative of the commutative property.

But what property, if any, applies to a problem like this? 6 + 3 = 5 + 4

It's certainly not the commutative property, however, six plus three and five plus four are both nine, so they are still equal to each other.

I'm trying to teach this concept to my fifth graders (I'm a student teacher) and I have to write up a report on the lesson for my college class as well. The cooperating teacher I'm working with doesn't know the technical term for it either. But I really want to know what the right term for this concept is or I'll feel like I'm not qualified to teach it.

Thanks!

[Roving Philosopher]

Hmmm... I don't think that has any special name beyond equivalence.

If you generalize 6 + 3 = 5 + 4, you get a + b = c + d, which really doesn't tell you a whole lot.

Edit to add: I suppose if you want to sound kinda technical, you could refer to it as the non-uniqueness of sums (warning - I just made that up, as far as I know) - for any two numbers a and b, there exist at least two other numbers c and d, distinct from a and b, such that a + b = c + d

[A Thousand Pardons]

Hmmm... I don't think that has any special name beyond equivalence.
Yeah, and by addition both 6+3 = 9 and 9 = 5 + 4 so 6 + 3 = 5 + 4, which is a consequence of the transitive property of equivalence (if a=b and b=c then a=c)

[space cadet]

thanks guys.

I'll just refer to it as equivalency then. It sounds fancy enough for a paper. Anything's better and less long winded than, "that thing that you have when two different numbers on either side of an equal sign add up to the same number thus making the equation true."

[Taks]

you could probably use the commutative property again...

6 + 3 = (5+1) + (4-1) = 5 + 4 + 1 - 1 = 5 + 4...

taks

[Disinfo Agent]

I'm trying to find out what the proper term is for the following situation:

a problem like this: 4 + 3 = 3 + 4 is demonstrative of the commutative property.

But what property, if any, applies to a problem like this? 6 + 3 = 5 + 4

It's certainly not the commutative property, however, six plus three and five plus four are both nine, so they are still equal to each other.
That's the associative property:

6 + 3 = (5 + 1) + 3 = 5 + (1 + 3) = 5 + 4

But I'm not sure if this way of thinking is suitable for your pupils.

[Taks]

oops... i knew that... duh.
taks

[A Thousand Pardons]

But you did use the commutative property as well, when you switched the order of the additions and subtractions.

[Taks]

But you did use the commutative property as well, when you switched the order of the additions and subtractions.
dang... i'm off today. it's just getting too complex. give me some simple linear algebra. :)

taks