I am a preschool teacher with a love for music and I assume that each normal hearing child can learn to sing. Regarding maths, you won't kick off by teaching a 3 year old multiplication and division. For the same reason one should introduce singing using age appropriate songs. Considering range is very important, otherwise they will produce an undesirable chest sound or throat sound, or they will just sing or shout off tune.
If your group is 3 and younger, start off with songs ranging from D above middle C up to B below the next C. Challenge them later in the year with higher notes, as they expand their range upwards at this stage. Songs for 3 - 6 year olds can range over an octave from D above middle C to the next D or from E above middle C to the next E. 7 - 8 year olds can sing as low as middle C. By 10 - 12 years some might expand their range up to the second G above middle C, while others might be able to sing down to G below middle C.
Unfortunately CDs and YouTube songs which stay within a preschoolers' range are almost non-existing. It's therefore better to introduce the songs without help (if you could call it help!) while you sing within the appropriate range. With very young children or children who can't sing in tune yet, start off with songs consisting only of soh and me, then expand to soh - me - lah - soh - me (the kindergarten chant) and then songs including the whole pentatonic scale.
Young kids are still developing proprioception of the intrinsic muscles of their vocal cords and half tones do not come easy - that's why songs within the pentatonic scale (doh, re, me, soh and lah) is wise to begin with, e.g. "Old MacDonald had a farm".