Teacher. Show me twenty-two ones. Children place twentytwo one ones, side by side. Tr. Show me twenty-two by using two kinds of ones. Children tie two ten ones together, thus having two bundles of tens and two ones. Tr. What have you now? Children. Two one tens and two one ones. Either of the two one tens is worth ten times as much as either of the two one ones. Either of the two one ones is worth only one-tenth as much as one of the one tens. Each child should be able at the end of the year to make any number from 11 to n by thinking it in relation to its kinds of ones. By the skillful use of sticks the principle that when any term of the minuend is less than the corresponding term of the subtra hend, the minuend must be changed, etc., can be easily comprehended. Illustration : 102 13=? To be read-The whole number is 102; the known part is 13; what is the unknown part? The unknown part can only be found by separating. As the parts are unequal the kind of separation is subtraction. In subtraction, first separate the ones; then the tens; next the hundreds. Two ones will not contain three as one of its parts and there are no tens to make into units, for the tens are all tied up in the hundred. In order to find the unknown part the whole must be changed by untying the hundred so that it shall become ten tens, and by making one of these tens into ones. The new whole, nine tens and twelve ones, differ from the first whole in form but not in value. Twelve ones less three ones is nine ones. whole-102 131 89 The wooden cubes are valuable in teaching the combination and separation of numbers under 100 and in teaching addition, subtraction, multiplication, and division tables. Illustration : Arrange 20 cubes in the form of an oblong prism, 5 in. by 4 in. . Lead the pupils to see that by separating the prism you have 12= =of ? five sections of four blocks each, each section representing onefifth of the whole. Let the pupils, by actually performing the operations indicated with the blocks find the parts called for. ( } how many cubes ? 16 = f of ? + ļor} = how many cubes? Whole, 20 cubes how many cubes ? 8 = } of ? how niany cubes ? 4= what part of 20 cubes ? + = how many cubes ? In teaching tables of 5's and 1o's use the parts of $1, or dimes and half-dimes. In teaching tables of 6's and 12's call the cubes eggs, apples, etc., and think them as so many dozens and half-dozens. The squares of paper are valuable in furnishing individual work in studying fractions. A skillful teacher can easily teach the fractional parts of one, with their combinations and equivalents through tenths in this grade. Illustration: Material, a four-inch square. Place the opposite edges together, crease in the center. Talk about the oblongs you now have. Compare with the square as to form and size. Lead the pupils to observe and tell in their own words the following: In one whole paper there are two halves. Work with one half until the children thoroughly understand all of its combinations and separations, performing the operations with apples, sticks, lines, etc. CORA Hill. WORK IN DERIVATIVES-THIRD YEAR GRADE. By the time the pupil is able to use the Third Reader, he has obtained such facility in reading that he may begin the study of derived words. The work may be taken orally as a general les. son, or incidentally in connection with reading lessons. The following illustration will tend to suggest the nature of the work on affixes and prefixes during the third and fourth year: (in the fifth and sixth years the general plan would be similar, the material, however, presenting more difficulty.) It may be that in some reading lesson the word river has occurred. During the recitation or at another time, as a general lesson, lead the pupils to consider rivers as to their size, and to call that body of moving water that is too small for even small boats to float upon, a little river. Consider the meaning of ritulet. Write the word river at one part of the board and the word rivulet in another place. Have the children 1. State the difference in meaning. Under the word river write the word stream. Obtain from the children its meaning and lead them to infer the word that means a little stream. Write the word streamlet under rivulet. Deal in a similar way with brook, tart, wave, cloud. Let the class give orally, and then write on their slates, the meaning or force of let, i. e., define it. In like manner consider kin, as with lamb, pan, man, etc, In this stage lead the children to observe that in each case let and kin are added or fixed to a syllable, and then state and have them write “Let and kin are affixes, meaning small or little.” Have the sentence given orally many times. Ask then for two affixes meaning small. Write the two as the beginning of a column. Suggest others, writing them in the column as obtained, by asking the name for a little duck, a little goose, etc. Inquire what is meant by lordling, darling, etc., sug. gesting, if necessary, that the first means a lord or person who is little in mind but great in his own thought, and that the second is a slight modification of dear, with the affix. Have the pupils infer the meaning of nursling. State that a sack or bag is also termed a poke. Also, what those little bags sewn in their coats, vests, trousers, aprons and dresses, in which they may carry handkerchiefs, knives, marbles, etc., are called. In this way obtain the word pock(e)et. From it and floweret, lead them to infer the meaning of et. In a similar way obtain ock from hillock, of ? five sections of four blocks each, each section representing onefifth of the whole. Let the pupils, by actually performing the operations indicated with the blocks find the parts called for. 了; how many cubes ? 16 + for = how many cubes ? 12= of ? Whole, 20 cubes how many cubes ? 8 = { of ? how niany cubes ? 4= what part of 20 cubes ? + g = how many cubes ? In teaching tables of 5's and ro's use the parts of $1, or dimes and half-dimes. In teaching tables of 6's and 12's call the cubes eggs, apples, etc., and think them as so many dozens and half-dozens. The squares of paper are valuable in furnishing individual work in studying fractions. A skillful teacher can easily teach the fractional parts of one, with their combinations and equivalents through tenths in this grade. Illustration; Material, a four-inch square. Place the opposite edges together, crease in the center. Talk about the oblongs you now have. Compare with the square as to form and size. Lead the pupils to observe and tell in their own words the following: In one whole paper there are two halves. Work with one half until the children thoroughly understand all of its combinations and separations, performing the operations with apples, sticks, lines, etc. Cora Hill. WORK IN DERIVATIVES—THIRD YEAR GRADE. on affixes and prefixes during the third and fourth year: (In the fifth and sixth years the general plan would be similar, the material, however, presenting more difficulty.) It may be that in some reading lesson the word river has occurred. During the recitation or at another time, as a general lesson, lead the pupils to consider rivers as to their size, and to call that body of moving water that is too small for even small boats to float upon, a little river. Consider the meaning of ritulet. Write the word river at one part of the board and the word rivulet in another place. Have the children 1. State the difference in meaning. Under the word river write the word stream. Obtain from the children its meaning and lead them to infer the word that means a little stream. Write the word streamlet under rivulet. Deal in a similar way with brook, tart, wave, cloud. Let the class give orally, and then write on their slates, the meaning or force of let, i. e., define it. In like manner consider kin, as with lamb, pan, man, etc. In this stage lead the children to observe that in each case let and kin are added or fixed to a syllable, and then state and have them write “Let and kin are affixes, meaning small or little." Have the sentence given orally many times. Ask then for two affixes meaning small. Write the two as the beginning of a column. Suggest others, writing them in the column as obtained, by asking the name for a little duck, a little goose, etc. Inquire what is meant by lordling, darling, etc., sug. gesting, if necessary, that the first means a lord or person who is little in mind but great in his own thought, and that the second is a slight modification of dear, with the affix. Have the pupils infer the meaning of nursling. State that a sack or bag is also termed a poke. Also, what those little bags sewn in their coats, vests, trousers, aprons and dresses, in which they may carry handkerchiefs, knives, marbles, etc., are called. obtain the word pock(e)et. From it and floweret, lead them to infer the meaning of et. In a similar way obtain ock from hillock, In this way |