Distributive Property

What is the distributive property? Why do we need it when we already have an order of operations for simplifying expressions? When can't we use it?

http://www.youtube.com/watch?v=Ohw6whHKuyY

Associative Property

What is the associative property? Why does it have that name? How can I recognize it when I see it and distinguish it from other situations that look like it?

http://www.youtube.com/watch?v=B5CwR-15vd8

Commutative Property

What is the commutative property? How does it work? When does it work? How can you recognize it and accurately name it when you see it?

http://www.youtube.com/watch?v=ef7Y2_h_wp8

Identity Property

What is the identity property? How can you recognize it when you see it? What is the difference between the identity property of addition and the identity property of multiplication? Why did mathematicians name this seemingly simple concept?

http://www.youtube.com/watch?v=LVx4bTKUMs8