Start off with simple patterns. Children often mimic what they hear, so clap first and have them echo you. Try 4/4 time – four even claps, then progress to three quick claps for 3/4. Once they've mastered these patterns, add more and have them echo those. You can put on music that has these patterns, then clap to the music and encourage them to listen to the patterns in the music itself. Older children can learn to write out these patterns themselves as they hear them.
Sing a song and clap along with it in the pattern that fits. Have the children listen to identify the pattern, then sing a song and see if they can identify, and clap, the pattern themselves. A simple 4/4 beat may be best to start with, and then move up to other beats and other songs.
Rhythm sticks and tambourines are good instruments to use to teach children music by clapping. The different sounds they produce add interest to the lesson, yet still enable the children to listen to and then mimic the clapping sequence. You can introduce music concepts like slow, soft, fast and other music dynamics at the same time. A soft tap of a rhythm stick or tambourine makes a different sound than a loud one, even if the tempo is the same.
Games and chants are fun-filled added tools to teach children about rhythm and music through clapping. Many clapping games and chants have both simple and complicated rhythms that the words flow along. Add in stomps, slapping the hands to the floor or tapping out a rhythmic pattern on another child's back for them to identify. Soon the children will have a working, basic knowledge of clapping, rhythm and music.