1. When the children are going to draw up a hexagon I do not of course tell them only to mechanically take the length of the radius and divide up the circumference into six equal parts. But I tell them that wise men have found that in every circle the circumference is about three times as long as the diameter, and then the little pupil will find for himself that the radius, being the half of the diameter, will go six times into the circumference.

For juxtaposition of figures no geometrical figure is more available than the hexagon. The children's power of invention will here get a good field for exercise.

2, 3, 4, 5. Two equal hexagons, or three, or four, or five put together can make Table mats, or Easels, or Vase stands.

6, 7. Seven equal hexagons will make a fine Tray, while the half part thereof can be a pretty Bracket.

8. For the construction of the pentagon the protractor is needed.

9. Two equal pentagons put together can be a Table mat.

10, 11. One pentagon and one hexagon can together be either a Decanter stand or an Easel.

12. The octagon may be constructed either by means of a circle or a square.

13. Two equal octagons will make a Table mat.

14. And five equal octagons a Tea pot stand.

But other juxtapositions of that figure are not used until in the next Standard.

15. For the construction of the heptagon the protractor is used.

16, 17, 18, 19. 20. Now the children may be allowed to draw up "Stars" inside the pentagon, the hexagon, the octagon and the heptagon.

It is a great delight for them to saw out these "Stars", which can be used for various purposes. When trimming them the three-cornered file is employed.

21, 22, 23, 24, 25. On the sides of the various geometrical figures, which the children have learnt to know during the previous exercises, viz., the triangle, the square, the pentagon, the hexagon and the octagon, we draw arcs either convex or concave. The. figures thus constructed are sawn out either with the compass saw or the bow saw and can be used for Vase stands, Cutting boards, Table mats, Lamp stands, Trays, etc. The arcs are trimmed with the drawing knife, the curved spoke shave and the half round file.