(3) Familiarity with /100s and /1000s by reductions of 750/1000, 50/100, etc., to lowest terms and by writing the missing numerators in 500/1000 = /100 = /10 and the like, and by finding 1/10, 1/100, and 1/1000 of 3000, 6000, 9000, etc. (4) Writing 1/10 as .1 and 1/100 as .01, 11/100, 12/100, 13/100, etc., as .11, .12, .13. United States money is used as the introduction. Application is made to miles. (5) Mixed numbers with a first decimal place. The cyclometer or speedometer. Adding numbers like 9.1, 14.7, 11.4, etc. (6) Place value in general from thousands to hundredths. (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 _x_th of _y_ a fraction? Can the same words mean both a common fraction and a decimal fraction? Express 1 as a common fraction. Express 1 as a decimal fraction. These same children can, however, be taught to operate correctly with fractions in the ordinary uses thereof. And that is the chief value of arithmetic to them. They should not be deprived of it because they cannot master its subtler principles. So we seek to provide experiences that will teach all pupils something of value, while stimulating in those who have the ability the growth of abstract ideas and general principles.