LESSON TWELVE THIRD YEAR NUMBER WORK 1. Text-Book Work.-One great difficulty which teachers encounter in number work lies in the introduction of the text-book. Often children who have previously done very good work seem almost unable to proceed when the book is put into their hands. This will be avoided if the right sort of preparatory work is done. (a) PRELIMINARY STEPS. Be sure that the pupils can read and understand the problems before the text-book is placed in their hands. As a rule, the pupils will be more or less embarrassed by the book, although it contains but few words with which they are not familiar. The embarrassment arises from the fact that the book is to be used for a new purpose. The attention is centered upon the number facts more than upon the reading, and the first few pages should contain nothing with which the pupils are not already familiar. (b) PREPARATORY LESSONS. Special preparatory lessons should always precede the introduction of the book. These lessons should be so planned as to make adequate preparation for the different pages, and they will naturally vary considerably. For some pages merely a word or two of explanation will suffice; for others, a brief oral review will do; again, for others, two or three preparatory lessons which include oral work, blackboard and written work will be found necessary; but bear in mind that there is scarcely a page of text-book matter but what will need some prepara 343314 tion before the children can take it up and carry it through successfully and easily. It is no wonder that children stumble over work that ought to be easy, when we consider how often they are given work to do for which they have had no preparation. Suppose that it has been six weeks or two months since a child has had problems in liquid measure, and he suddenly comes to this problem in his book: "How many gallons in twelve quarts ?" Six out of ten children would probably stumble on the question, guess at the answer, and waste a good deal of time before they got it. If the teacher had spent a very few minutes recalling the table of liquid measure and rapidly giving a few problems before the lesson was taken up, the problem, with similar ones that would undoubtedly follow, would be readily solved. Or the teacher might, on the preceding day, give a few problems which would recall all of the work in liquid measure and use these problems for the busy work for that day. This preparation would serve just as well. (c) ILLUSTRATIVE LESSON. The following will illustrate how a text-book lesson may be taken up: "1. One dollar is equal in value to half-dollars. fourth-dollars. fourth-dol lars. A fourth-dollar is sometimes called a 'quarter,' or a quarter of a dollar. "4. One half of a dollar and one fourth of a dollar are fourths of a dollar. “5. One half of a dollar less one fourth of a dollar is of a dollar. "6. Four times one fourth of a dollar equals of a dollar, or dollar dollar. fourths 7. One fourth of a dollar is contained in one half of a times. "8. One half of one half of a dollar is dollar. "" of a Material. When ready for the lesson, the teacher should state that before using their text-books a short review is to be held. She should bring to the class a dollar, a halfdollar and a quarter. Method. After briefly stating the purpose of the lesson, the teacher may ask, "John, what is the name of this coin ?" (Holding up a dollar.) "What is the name of this coin ?" (Holding up a halfdollar.) "One half-dollar or fifty cents.' "How many of these does it take to make one dollar ?" "It takes two." "We say that one dollar is equal in value to two halfdollars. One dollar is equal in value to how many cents ?” "To one hundred cents.” "Two half-dollars are equal in value to how many cents ?" "To one hundred cents.' "What is the name of this coin ?" (Holding up a quarter.) "A quarter or a twenty-five-cent piece." 1 The Werner Arithmetic, Book II. "You say it is a quarter. A quarter of what ?” "A quarter of a dollar." "What is another name for a quarter of anything?" "A fourth." "Then this (holding up the quarter) is equal in value to what part of a dollar ?" "It is equal in value to one fourth of a dollar." "It is equal in value to how many cents ?" "To twenty-five cents." "This piece of money (holding up a half-dollar) is equal in value to how many quarters ?" "It is equal in value to two quarters." "This (holding up the dollar) is equal in value to how many quarters ?" "One dollar is equal in value to how many half-dollars ?'' "To how many fourth-dollars ?" "One half of a dollar is how many fourths of a dollar ?" "Two." "One half of a dollar and one fourth of a dollar are how many fourths of a dollar ?" "They are three fourths of a dollar." "If I had one half of a dollar and took away one fourth of a dollar, how much would I have left ?" "One-fourth of a dollar or twenty-five cents.' "How many times must I take one-fourth of a dollar to make one half of a dollar ?" "Two times." "Another way of saying that is to say that one fourth of a dollar is contained in one half of a dollar two times. One fourth of a dollar is contained in one dollar how many times ?" "It is contained in one dollar four times." "One half-dollar is contained in one dollar how many times ?" "It is contained two times." "Read this first problem (pointing to the board) and in place of this line, put the words 'how many.'" A child reads, "One dollar is equal in value to halfdollars," supplying the words as directed. Enough problems are given to accustom the children to supplying the words, "how many." Other problems are read in which they have to supply the words, "what part." A few problems requiring the words, "is contained in," are given, the word "contained" being told by the teacher if the pupil hesitates. The text-book may now be used, the attention of the children being called to the pictures at the top of the page. They tell what they see, then solve the problems. Since the meaning of the new phrases has been made clear, the children will have little difficulty in understanding the problems. So, in every lesson, new expressions and new forms of prob. lems should first be made perfectly clear. A teacher needs to be constantly on guard to see that every problem is understood. Ask often for the meaning of the problems or the meaning of a word. Teach the child that in every problem he must look for three things, viz.: what is given, what is required, and the process by which the result is obtained. It is well occasionally to have problems in which these three factors are told by the child with no attention paid to the answer. 2. Reduction of Denominate Numbers.-During the preceding years the children have been thoroughly grounded in the tables of liquid measure, dry measure, United States. money and possibly one other table. They can readily change quarts to gallons, gallons to pints, dimes to nickels, etc., but having no knowledge of the meaning of multiplication and division at the time when these facts were learned, they did not formulate any rule for the reduction of denomi |