Here's a way to introduce even and odd numbers to preschoolers and kindergarteners (or any age!) using Cuisenaire rods. The pattern is much easier to remember when you can see it in color pictures rather than abstract symbols. Right-brained, visual-spatial learners will find this a breath of fresh air compared to what they are used to in school!
The significance of understanding whether an answer is going to be odd or even is not often instantly understood. If children understand this, they will have an instant way to know whether their answer may be wrong. They will know that 459+243 has to be even because they are both odd numbers. It develops numbers sense. That's a good thing!
After watching this video, I see how I could have done things a little better. Writing all even numbers in red and odd numbers in black would have helped tie in the Cuisenaire rods to the symbols. Our numerals themselves show no similarity to quantities (what does the shape of a 5 have to do with five things?) so bridging that gap with colors or letters to indicate odd or even would be a good idea.
Cuisenaire Rods provide a concrete way to talk about the concept of ratios. The "I get, you get" idea comes from Crewton Ramone's House of Math - lots of great ideas there!
Using manipulatives to teach complex math concepts will bring a wider range of children to understanding than the traditional formula-driven way of teaching. Children with visual and kinesthetic learning styles will especially benefit from this style of instruction.