a. Addition. Practical value of checks on all operations.

b. Subtraction, as discussed in section XI.

c. Multiplication. Should the tables extend to 12 × 12? Devices.

d. Division. Algorism considered historically and practically.

e. Historical note as to the number of operations.

9. Extent of Work with Fractions.

10. Nature of the Problems.

References: Smith, Teaching of Arithmetic, chap. xvii, p. 73. Handbook to Arithmetics, p. 29.

XVIII. The Work of the Fourth School Year

1. Leading Mathematical Features.