Choose a simple children's song in a simple key; for example, "Twinkle, Twinkle, Little Star" in the key of C.
Change the words to numbers based on the notes of the song. C equals 1, D equals 2, E equals 3 and so on, up to the next C which equals 8. Notice that "Twinkle, Twinkle, Little Star" follows a very easy pattern. Here's the first line: 1-1-5-5-6-6-5 ("Twinkle, twinkle, little star"). The second line would be: 4-4-3-3-2-2-1 ("How I wonder what you are"). Third and fourth lines: 5-5-4-4-3-3-2 ("Up above the world so high, like a diamond in the sky"). Repeat lines one and two.
Play the C scale and have the child sing the numbers of the scale, so that he sees the relationship between the notes and the numbers of the scale.
Play that same song in the key of C, starting on C as 1. Ask the child to sing the numbers instead of the words. If she's not willing or able to sing, she can speak them. (Sometimes a child's sense of pitch is not yet well developed.)
Change to a key with just a few sharps and flats. G major has only 1 sharp -- F sharp. Play the song again in this key, starting on G as 1. Again, have the child sing or speak the numbers.