(7) Review of (1) to (6).
(8) Tenths and hundredths of a mile, subtraction when both numbers extend to hundredths, using a railroad table of distances.
(9) Thousandths. The names 'decimal fractions or decimals,' and 'decimal mixed numbers or decimals.' Drill in reading any number to thousandths. The work will continue with gradual extension and refinement of the understanding of decimals by learning how to operate with them in various ways.
Such may seem a slow progress, but in fact it is not, and many of these exercises whereby the pupil acquires his mastery of decimals are useful as organizations and applications of other arithmetical facts.
That, it will be remembered, was the third principle:—"Develop abstract and general ideas by experiences which will be intrinsically valuable." The reason is that, even with the best of teaching, some pupils will not, within any reasonable limits of time expended, acquire ideas that are fully complete, rigorous when they should be, flexible when they should be, and absolutely exact. Many children (and adults, for that matter) could not within any reasonable limits of time be so taught the nature of a fraction that they could decide unerringly in original exercises like:—
Is 2.75⁄25 a common fraction?
Is $.25 a decimal fraction?
Is one xth of y a fraction?
Can the same words mean both a common fraction and a decimal fraction?
Express 1 as a common fraction.