They may feel that their words aren't good enough. When we simply let our merely recite memorized prayers at mealtimes, we may teach them that people have to have set words to pray. When we pray our own prayers in everyday language, they begin to learn that any language and any concern is okay to bring before God. However, it is important to help our children memorize prayers as well as make up their own. These memorized prayers can take many forms.
Scripture can often be memorized prayer.
In times of stress when other words failed me, the Twenty-Third Psalm became my prayer linking me with God. Hymns are also prayers. Think about the words to a hymn you love. When I sing that hymn, it becomes a prayer of thanksgiving, and I feel full of gratitude for the world and my place in it. Our role as model and encourager will help our children know the joy that comes in talking and listening to God.