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Many schools offer extracurriculars for free, so take advantage of this. If the child's school has a choir, encourage the child to enroll. If a child can pick optional classes for a given semester, encourage them to take classes that involve singing. Extracurriculars don't always have to be directly related to singing. Things like band and even a music appreciate course can help develop the child's singing skills. If it's within your budget, search online for local voice teachers. It can be hard to teach children the technical aspects of singing if you're not professionally trained. A personal voice teacher can be invaluable when it comes to teaching children to sing. Look for a voice teacher with experience working with children. Children respond to different teaching methods than adults, so they'll benefit from a teacher who knows how to talk to kids. Online lessons are often cheaper than professional voice teachers. You can buy access to an online course that will provide with materials you can teach. Online courses sometimes also include occasional evaluations from a real instructor via things like Skype. Look for children's choirs in your area and consider having the child sign up. If the child's church has a children's choir, for example, have them enroll. Singing with other children, under the direction of a professional, can really help the child hone their singing skills.
Enroll the child in extracurriculars involving singing. Hire a voice teacher. Look for online lessons. Have the child join a choir.