Notes of Lessons: Algebra, Class IV

[We have thought that it might be of use to our readers (in their own families) to publish from month to month during the current year, Notes of Lessons prepared by students of the House of Education for the pupils of the Practising School. We should like to say, however, that such a Lesson is never given as a 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 IV • Time: 30 minutes

By Gertrude E. M. Francis
The Parents’ Review, 1904, pp. 793-794

Objects

I. To introduce division to Class IV.

II. To show the connection between multiplication and division.

III. To help the girls to work examples in division accurately and intelligently.

IV. To give them practice in mental work.

Lesson

Step I.—Let one of the girls work a multiplication sum on the board, and then find out from them the connection between multiplication and division, and how division is the reversal or undoing of multiplication.

Step II.—Show that the division of one expression by another is represented by placing them as a vulgar fraction in arithmetic, the dividend being the numerator, the divisor the denominator. Also show that in algebra, as in arithmetic, a common factor may be struck out of the numerator and the denominator:—as in

\(\frac{ax}{cx}\)

strikeout the common factor x, and remainder is

\(\frac{a}{c}\)

Step III.—Find out from the children how to work

\(\frac{9a^3}{3a}\)

and then let each of the girls work an example on the board. Then find out from them the rule for dividing one simple expression by another. Ask them the meaning of the terms “coefficient” and “index.”

Step IV.—Ask the girls the “rule of signs” in multiplication, and tell them it is the same in division. “Like signs produce plus, unlike signs produce minus.” Let them each work an example involving the “rule of signs.”

Step V.—Ask the girls for a definition of a simple and of a compound expression. Find out from them how to divide a compound expression by a single factor.

Step VI.—Work several examples in the division of one compound expression by another, and afterwards find out from the girls the rule for dividing such expressions.

Rule.—(1) Divide the term on the left of the dividend by the term on the left of the divisor, and put the result in the quotient. (2) Multiply the whole divisor by this quotient, and put the product under the dividend. (3) Subtract and bring down from the dividend as many terms as maybe necessary. Repeat this till all the terms from the dividend are brought down.