  In a recent work, the author has constructed two families of algebraic cycles
in Bloch cycle algebra over the prjective line minus 3 points that are expected
to correspond to multiple polylogarithms in one variable and have a good
specialization at 1 related to multiple zeta values. This is a short
presentation, by the way of toy examples in low weight (5), of this contruc-
tion and could serve as an introduction to the general setting. Working in low
weight also makes it possible to push ("by hand") the construction further. In
particular, we will not only detail the construction of the cycle but we will
also associate to these cycles explicit elements in the bar construction over
the cycle algebra and make as explicit as possible the "bottow-left"
coefficient of the Hodge realization periods matrix. That is, in a few relevant
cases we will associated to each cycles an integral showing how the
specialization at 1 is related to multiple zeta values. We will be particularly
interested in a new weight 3 example .
