Pray the rosary with your children daily.   If you explain clearly what the rosary is about, your children will embrace it with wonder. 

Where did the rosary come from ?  It is believed that Mary gave the rosary to St. Dominic as a response to the Albigensian heresy.  During this initial devotion, it is believed that 100,000 heretics returned to the Catholic Faith.  Many other miracles have been attributed to rosary prayer.

Linked below are two websites that will help get you started.  I think the first link provides the easiest explanation, however the second link has more information and includes passages of Scripture.  Providing the Scripture passages as recitation of the mysteries is a good way to teach your children the story of the mysteries through the rosary.  Once your children are older, it is not as necessary to read entire passages as they will have already learned the stories and can envision the mysteries with ease when you call to mind one verse or meditation.

I have explained to my own children that the rosary is a good way to pray with total focus on God.  As we pray the Hail Marys and contemplate the mysteries, the possibility of distraction becomes far more remote and we can love God with our whole selves as we pray the rosary.

How To Pray The Rosary

Children Learn To Pray -- A Scriptural Rosary