The celebration of the Holy Communion (The Eucharist, Lord's Supper) in the Christian church is one of the most sacred of all activities that takes place in the Body of Christ.
It is the second ordinance that we observe as Christians and particularly, as Baptists. The first ordinance that we adhere to as Baptists is Baptism by immersion. We know that Jesus shared a memorial meal with His closest followers on the night He was betrayed (by one of His disciples) into the hands of the Roman government. According to the book of Acts, this meal was also celebrated in the home of Mary, the mother of John Mark. The same Mark who would later write the first Gospel.
The early church did not worship in fine buildings such as we have today. They worshipped in real homes. They worshipped from house to house. They shared not a symbolic meal but a real meal. In those homes were children, and as always at mealtime, the children had their share. They may have eaten earlier, later on, or in another room, but they had their meal.
During our celebration of the Holy Communion, we offer our children a share in our celebration of Christ's love. We offer our children the white seedless grape. Symbolically (and theologically) speaking, we do not offer our children the "red bruised" grape. The "red bruised" grape (for us) represents Jesus' body which was bruised for our iniquities and His blood which was shed for our sins. However, we offer the "white seedless grape" which represents (for us) a clear conscience and the absence of accountability for sin. Therefore, in the words of our Savior, we invite the children who have yet to accept Jesus Christ as their Savior to partake at the Lord's table by receiving a grape.