hould reproduce the
lessons with the solids in outline with the sticks. When the child is
more advanced, the connection of the sticks with the preceding objects
will be more clearly explained and intelligently comprehended, and
then they may be used in connection with softened peas or tiny corks,
which serve to illustrate the points of contact of the sides of
surfaces and edges of solids whose skeletons the child can then
construct with these materials.

5. The geometrical forms illustrated in this gift are:--

Angles of every degree.
Triangles, quadrilaterals, and additional polygons.
Skeletons of solids by means of corks or peas.

6. The law of the mediation of contrasts is shown in the fact that
every line is a connection between opposite points. As in the other
gifts, the law governs the use of the line in the formation of all
outlines of objects and all symmetrical designs.

* * * * *

As we have already noted, the gifts of Froebel are thus far solids,
divided solids, planes and divided planes.

Relation of the Single and Jointed Slats to the other Gifts. How both
are used.

With the single and jointed slats we shall not deal separately, merely
stating that they form a transition between the surface and the line,
having more breadth and relation to the surface itself than to the
edge, but manifestly tending towards the embodied line of which the
little stick given by Froebel is the realization.

The jointed slats, generally ruled in half and quarter inches for
measuring, may be used to show how one form is developed from
another,--for instance, the rhombus from the square, the rhomboid from
the oblong, and they are very useful also for explaining and
illustrating the different kinds of angles, as the opening between the
joints may be made narrower or wider at pleasure.

The disconnected slats are used for the occasional play or exercise of
interlacing, forming a variety of figures, geometrical and artistic,
which hold together when carefully treated.[66]

[66] "The slats form, in some sort, the transition from the
surface-pictures of the laying-tablets to the lineal
representations of the laying-sticks, but have this advantage
over both tablets and sticks, that the forms constructed with
them are not bound down to the surface of the table, but
possess sufficient solidity to bear being removed from
it."--H. Goldammer, _The Kindergarten_