My daughter in grade 3 is learning about telling time at her school. She eagerly showed me this method she has discovered on her own to tell the minutes part of the time on an analogue clock. I wasn't sure at first because I have never heard about it before but it works really well.

Here is her method:

Look at the minute hand and see what number it is pointing to, let's say it's $3$.

Add a zero at the end to make it $30$.

Halve it to get the minutes, so $3$ becomes $30$ and halving it gives $15$, $6$ becomes $60$ and halving it gives $30$ and so on.

It works well but I am not sure why. What mathematically justifies the method used?