Tell your students that the time signature is found at the beginning of a piece of music. Explain that it works like a fraction. The top number indicates how many beats in a measure; the bottom number indicates which note is equal to one beat. For example, 4/4 means four beats in a measure and the quarter-note gets one beat.
Teach the students to "feel" the music by playing multiple recordings. For example, play a piece of classical music in 4/4 time, then switch to a waltz in 3/4, and then play a piece in 2/2. Have the students clap to the rhythm of the music and determine the time signature. Once they start to "feel" the time signature, the written notation will be easier to teach later.
Gather the students into groups of three. Choose three predetermined songs, each with a different time signature, and play them for the class. At least one of the pieces of music should have a change of time signature in the middle, like in Peter Gabriel's "Salisbury Hill." Give each group the appropriate number of pencils and paper, and have them listen and decipher what is happening with the music, in terms of both the mood and the time signature.
Have the groups give a presentation in front of the class. Each group should choose to present one of the three songs while tapping along to the beat. The time signature and any changes in the music should be pointed out during the presentation.