Many adults grew up singing rounds—you know, those songs that start singing here, then start there, then over there and all the while, the first singers are still going. In a round, everyone sings the same song, but they start at different times. Young voices singing a simple round creates beautiful music. Young children are very creative and clever, so if you explain the concept to them in clear language and demonstrate the process with an activity, they will pick it up in a flash.
If possible, let the children listen to a voice recording of the round you want them to sing. Point out where each part starts. Let them sing along if they want.
Teach the children the entire song singing in unison. Let them sing it again and again until they are very familiar with the tune and the words.
Start simply when working on counterpoint. Begin with two groups of children, representing the first part and the second part. Young children respond well to physical activity, so demonstrate the concept with action. Play the recording; instruct the first part group to stand up when the song begins; instruct the second part group to stand when the second part starts. Repeat this activity until the children understand the parts completely.
Start the round simply. Ask the first part to sing the entire song two times; the first time, they will sing it alone. Ask the second part to listen to the song the first time through, listening for the point where the second part starts. During the second pass, help the second part students jump in on cue.
Practice, practice, practice, but for best results, keep it fun. As your group becomes more accomplished, add more parts. Then find a more difficult song.