Before we get into the answer to your question, let us first understand what the gunas are all about. Sattva is the state of selflessness and serenity. A sattvika person is one who has mastered himself or herself and has control over his or her desires. Such a person will perform obligatory duties selflessly. Sattvika people find satisfaction within themselves. They understand the transitory nature of the world and hence become independent of the world. Rajas is the state of selfishness, agitation, stress and strain. Such a person is obsessed with the fruit of action and will go to almost any extent to get what they want. Rajasika people are driven, compelled and pushed into frenzied activity by their desires. Rajasika persons are usually extroverted i.e. they are constantly looking out into the world for satisfaction. Tamas is the state of indolence, laziness and sloth. These people have tremendous desires but they lie dormant within them. They are too lazy to work to fulfil their desires. They will not even act for their own welfare. They achieve nothing.
Every person is a combination of all three gunas in varying proportions.
The varnas are structured in such a way that Brahmanas are predominantly sattvika with a little rajas and minimum quantum of tamas. Kshatriyas have more rajas and a lower sattvika content. Vaishyas have even greater rajas, less sattva and a considerable amount of tamas. Finally, shudras are those who are predominantly tamasika. They have some rajas and traces of sattva.
To identify the predominance of a particular guna in a child, you will see the expression of these gunas in and through his or her interactions with the world. A sattvika child will for example rise early, be predominantly selfless or unselfish, have simple tastes. A rajasika child on the other hand may be loud, highly active, excitable, always needing something to do, will think primarily of his or her welfare etc. A tamasika child may be lazy, sleeping a lot, procrastinating.
However, there is one thing that must be noted. In life where we are is not as important as where we are headed. A child, or any person, may be tamasika or rajasika but there must be a constant effort towards becoming sattvika. Towards cultivating fine thoughts, living a healthy life, achieving spiritual goals. Once this is done, sooner or later we will establish ourselves in sattva.
We should avoid trying to slot people into a particular mould. Instead, we should focus on developing fine qualities. Concentrate on exposing children to finer things in life. Classical music, good literature and most importantly the fundamental truths of jnana (knowledge), bhakti (love & devotion) and karma (service). We must set a good example, demonstrate the things we would like our children to learn by living them ourselves. We must walk the talk.