What do 1/2, 3/4 and full size mean?
Full size is often called 4/4; 3/4 and 1/2 are smaller models. These are size labels, not exact ratios for every measurement: scale length and body shape vary between makers. Compare actual instruments.
Test the fit in person
Have the child sit with the guitar on their leg. Can they reach the first frets without lifting their shoulder, keep the wrist comfortable and hold the instrument steady? Try more than one size. Smaller can be easier, but it shouldn't feel cramped either.
Check string height as well
Even a well-sized guitar can be hard to play if the strings sit too high above the frets. Ask a teacher or shop to check an instrument that's difficult to fret. Don't buy solely from an online age chart.