There is a custom that on Shabbath, children go to the Tebah and read all the Mizmorim out loud for the congregation. They start with "Hodu" and continue till the end of the "Shirath HaYam". The purpose is to train the children.
The children take turns, the first boy reads the first Mizmor, the next one reads the second and they continue like this, in rotation, till they have completed all the Mizmorim. This is a fine custom to follow.
The portions of "Hashem Melekh" and "Barukh Sheamar", however, which are contained within the Mizmorim, should not be read by the boys. Instead, the Hazzan should read them. If the Hazzan has not yet arrived, then another man should read them in his stead.
(See Derekh HaTorah, Shabbath 8:5)
children read mizmorim, Shabbath, Shabbat, Shabbos