One of thinking activities today involved manipulation of our place value blocks as we worked out some true/false statements about odd and even numbers. The groups were asked if the following statements were true:
An even number plus an even number is always even
An odd number plus an odd number is always odd
An odd number plus an even number is always odd
All children could "prove" to me that the first and third statements were true and the second statement was false by giving/showing me examples with the little blocks. However, it was definitely trickier to be able to articulate WHY.
If you do a quick internet search, you can come up with the following reasoning, and I certainly could have simply "taught" this to the children:
For any even number n, the following integer is odd (n+1), so for any odd number other than 1, you are adding the preceding even number, plus 1. Think of the odd number as an even number plus one and remember that all even numbers are multiples of two. Therefore: Any two odd numbers added together will be the same as adding two even numbers plus 1 plus 1.
Instead, I gave them gentle questions and thinking time, and this is what one child came up with. Enjoy and learn.