erial as a
whole to allow the child to play with a third gift in which one cube
cut in halves and one in quarters have been substituted for two whole
cubes. He will joyfully discover the new forms, study them carefully,
and find out their distinctive peculiarities and their value in
building. When he has used them successfully once or twice, and has
learned how to place the triangular prisms to form the cube, then the
mass of new material as a whole can have no terrors for him.

How great is his pleasure when he withdraws the cover and finds indeed
something full of immense possibilities; he feels, too, a command of
his faculties which leads him to regard the new materials, not with
doubt or misgiving, but with a conscious power of comprehension.

Its New Features.

At the first glance the most striking characteristics are its greater
size and greater number of divisions, into thirds, ninths, and
twenty-sevenths, instead of halves, quarters, and eighths.

These divisions open a new field in number lessons, while the
introduction of the slanting line and triangular prism makes a decided
advance in form and architectural possibilities.

Importance of Triangular Form.

The triangle, by the way, is a valuable addition in building
exercises, for as a fundamental form in architecture it occurs very
frequently in the formation of all familiar objects. Indeed, the new
form and its various uses in building constitute the most striking and
valuable feature of the gift.

We find it an interesting fact that all the grand divisions of the
earth's surface have a triangular form, and that the larger islands
assume this shape more or less.

The operation of dividing the earth's surface into greater and lesser
triangles is used in making a trigonometrical survey and in
ascertaining the length of a degree of latitude or longitude. The
triangle is also of great use in the various departments of mechanical
work, as will be noted hereafter in connection with the seventh gift.

Difficulties of the Fifth Gift.

The difficulties of the fifth gift are only apparent, for the
well-trained child of the kindergarten sees more than any other, and
he will grasp the small complexities with wonderful ease, smoothing
out a path for himself while we are wondering how we shall make it
plain to him.

Effect of Good Training.

But here let us note that we can only succeed in attaining
satisfactory results in kindergarten work by begi