# Notes of Lessons: Geometry, Class II

*tour de force*, but is always an illustration or an expansion of some part of the children’s regular studies (in the

*Parents’ Review*School), some passage in one or other of their school books.—Ed.]

Group: Mathematics • Class II • Average age: 10 • Time: 30 minutes

**By W. T. Wilkinson**

*The Parents’ Review, *1903, pp. 545-547

#### Objects

I. To teach the pupils to reason inductively.

II. To cultivate the inventive powers and encourage self-reliance.

III. To train the hand in neatness and the eye in precision.

IV. To train the pupils in a habit of forming correct judgments.

V. To introduce the pupils to a new subject, viz., geometry.

#### Lesson

*Step I*.—Find out if the pupils know that the word “geometry” means the measurement of the earth, and is derived from two Greek words—gē = the earth, and metron = a measure.

Give a brief sketch of the history of geometry as far as it is known. It is supposed to have been invented by the Egyptians when they wanted to restore their landmarks effaced by the inundations of the Nile. Later they used it for measuring such things as areas, solids, etc.; we know that this was in 1700 BC, because of a papyrus preserved in the British Museum. The ancient Greeks used geometry a great deal, but for them it meant the measurement of surfaces, corners, etc.

In the time of Roman power it was not used, but was revived again in the 17th century, and adopted in England and France, and has been used ever since.

*Step II*.—Find out if the pupils know some of the uses to which geometry is put, *e.g.*, to find out the distances of the heavenly bodies from the earth, to measure from place to place when both places are inaccessible, to measure the surface of the earth, fields, etc., etc.

Tell the pupils that there are many different branches of geometry, and the one about which they are going to learn is called “plane” or “flat” geometry, because the things treated of can be drawn on paper.

*Step III*.—Give the pupils a cube and let them find out for themselves, by observation and measurement, the definitions of a surface, a straight line, and a point. Let the measurements be put down neatly in a book and the corresponding definitions written in beside them.

*Step IV*.—Put two dots on the board to represent points, and let the pupils find out the three kinds of lines that can be drawn between them, viz., straight, curved and zigzag, and that the straight line is the shortest distance between the two points. Let the pupils illustrate these three lines by reference to roads, etc.

*Step V*.—As the pupils know that a straight line has no breadth or thickness, give them each two matches, and let them put these in as many different positions with relation to each other as they can: (1) meeting with four, two and one corners or angles respectively; and (2) not meeting; (*a*) where the two lines would meet if lengthened or produced, and (*b*) where they would never meet. Let diagrams of these be put neatly into the book.

*Step VI*.—Let the pupils give the definitions of an angle and parallel lines from their drawings, and illustrate them from the cube and numerous other objects, such as the corners of the room, of the table, railway lines, the sides of a room, a picture, etc.

*Step VII*.—Recapitulate by asking for definitions and illustrations of a surface, a line, a point, a straight line, an angle and parallel lines.