Here are some activities that my son (almost 3 years) has enjoyed. They are all motivated by the idea: make mathematics visceral (especially for the young ones).
As Kevin says, count, count, count things. Count backwards. Count by twos. Do it while your you're moving.
Rather than show them the symbols $3 \times 2 = 6$, take 6 bottle caps and arrange them into a rectangle. Can you do the same with 7 bottle caps?
Let them play with a nice length of rope. Show them the "trick" of a slip-knot. Do it repeatedly (you've taught them to crochet!)
Take off your T-shirt while keeping your sweater on. Or put on a shirt that is upside-down and inside out so that it comes out right.
Draw big shapes with chalk on the sidewalk. A perennial request from my son: "Draw it bigger!"
When you do get to the stage of learning the strange code called "alphabet," keep it tactile. Cut out big letters with scissors. Recognition of symmetry seems to be a pretty natural phenomenon when you can hold the object in your hands. "What happens when you turn M upside down, flip over the b?"
Most importantly, don't push it. If their interest wanders elsewhere, then let it go.