Applications. 1. How many working days are there in a week? What part of such a week is one day? How many sixths of such a week are five days? 2. A cake was cut into equal parts for a family of six. Each had what part of the cake? There were 3 boys in the family; how many sixths of the cake did they have? 3. A man lost one day in a week through illness; what part of the work-day week did he work? 4. From a keg containing 6 gallons of vinegar a grocer sold one gallon; what part of the whole did he sell? What part was left? 5. If a school day consists of six hours, what part of the day is one hour? If schools begins at 9 o'clock, what part of the school day is passed by 10 o'clock? At 11 o'clock? To teach the relation of thirds and sixths.-Use the rectangle as folded for thirds and sixths. Into how many parts do the short creases divide the rectangle? Each part contains how many sixths of the rectangle? How many sixths of the rectangle are there in one-third of it? How many sixths are there in two-thirds of it? Two days are what part of a work-day week? How many sixths of a work-day week? Two-thirds are how many sixths? Similarly teach the relation of halves and sixths. Applications. 1. A man worked one-third of a week; how many days did he work? How many sixths of a week? 2. A man worked three-sixths of a week; how many days did he work? 3. Another man worked one-half of a week; how many sixths of a week did he work? 4. By use of a rule draw a rectangle 6 in. long and 2 in. wide. Divide it crosswise into six equal rectangles. Shade one-sixth of the rectangle. Show by shading that one-half equals three-sixths; that one-third equals two-sixths; that two-thirds equal four-sixths. 2. Draw a figure like this (K). Shade it so as to show that twothirds equal four-sixths. In grade 2B the second idea of the fraction should be taught, that is. one or more of the equal groups of a single group. For this purpose the denominate numbers familiar to the children will be found helpful. To teach the meaning of one-half of a group.—A picture like this (L) may be used. How many steps are there in the picture? What part of the way up has Mary gone? How many steps has she taken? How many more must she take to reach the top? Two steps are what part of four steps? Or a sketch of a tray (M) of 4 quart-baskets of berries may be drawn. If two of these baskets are taken away, what part of the whole is taken? Two quarts are what part of 4 quarts? Or a sketch of 6 milk bottles in a case may be shown. If three of them are sold, what part remains? Three bottles are what part of six bottles? The numbers may be varied so as to picture halves of other numbers as 8, 10, 12, 14, 16 and 20. Applications. 1. How many six-inch lengths are there in a foot? A six-inch length is what part of a foot? How many inches are there in a foot? Six inches are what part of 12 inches? 2. Answer in the same way; 3 inches are what part of six inches? 3. How many oranges are there in half a dozen oranges? 4. A crate contains 12 bottles of milk; how many bottles are there in half a crate? 5. How many days are there in one week? In two weeks? One week is what part of two weeks? Seven days are what part of 14 days? 6. There are 8 quarts in a peck; how many quarts are there in half of a peck? 7. How many cents are there in a dime? In two dimes? Ten cents are what part of 20 cents? 8. There are 8 ounces in half of a pound; how many ounces are there in a pound? 9. There are 9 men in a baseball team; how many are there in two teams? 9 is what part of 18? 10. Give a large number of drill questions like: One-half of 6 is? One-half of 10 is? One-half of 12 is? To teach fourths of a group-Mark What part of a foot is a 3-inch length? foot? Three inches are what part of 12 part of a dozen oranges? 3 is half of? 4 is half of? off 3-inch lengths on a foot rule. How many inches are there in a inches. Three oranges are what Show the pupil 4 five-cent pieces. Each coin is what part of the whole? Four five-cent pieces are how many cents? Five cents are what part of 20 cents? Four ounces are one-fourth of a pound; how many ounces are there in a pound? Draw a diagram of a window with two sashes of 4 panes each. Have the pupils show that 4 panes are half of 8 panes. Applications. 1. How many working days are there in 2 weeks? How many days does a man lose who is ill one-fourth of the time? 2. How many working days are there in 4 weeks? One week is what part of four weeks? 6 days are what part of 24 days? 3. Four ounces are what part of 16 ounces? What is one-fourth of 16 cents? 4. What is one-fourth of 20 cents? What is 3 times 5 cents? What is three-fourths of 20 cents? 5. Clarence had a vacation of 12 days, and it rained one-fourth of the time; how many days did it rain? 6. Ralph bought 4 ounces of spice for his mother; what part of a pound did he buy? 7. Draw a square 16 in. around. Each side is what part of the distance around? Each side is how many inches long? How many inches are there in one-fourth of 16 inches? 8. How many feet are there in 4 yards? How many feet are there in one-fourth of 12 feet? Problems involving the relations of halves and fourths of groups may now be given without development. To teach thirds of a group.-Draw a square and divide it (N) into 9 square parts. If the blackboard will permit, a yard square should be drawn and divided into square feet. How many squares are there in each row? How many rows are there? Each row is what part of the whole square? Three squares are what part of 9 squares? How many square feet are there in one square yard? In one-third of a square yard? What is onethird of 9 square feet? Each of the sides of a triangle is 3 in. long, what is the distance around the triangle? Each side is what part of the distance? Three inches are what part of 9 inches? Find the number of inches in the length of a yard stick. One foot is what part of a yard? Twelve inches are what part of a yard? Twelve inches are what part of 36 inches? Applications. 1. How many 4-inch lengths are there in one foot? Each is what part of a foot? Four inches are what part of 12 inches? 2. One five-cent piece is what part of 3 five-cent pieces? Five cents are what part of 15 cents? 3. How many working days are there in one week? In three weeks? What is one-third of 18 days? 4. Richard sold papers at 3 cents each and was paid one-third for selling; how much did he receive for each paper? How much did he receive for selling 5 papers? 5. One day Richard sold 18 cents' worth of papers: how much did he receive for his part? 6. Draw a line 12 in. long. Mark off one-third of it; two-thirds of it. By means of a yard stick find two-thirds of 36. 7. 8. By means of a school calendar find one-third of 15: two-thirds of 15. To teach sixths of a group.-Canned foods are often packed in boxes of 12 cans each. Count the cans in this box by twos. How many twos are there in twelve? Two cans are what part of twelve cans? By examining a foot rule find the number of 2-inch lengths in 12 inches. Two inches are what part of 12 inches? By reference to the calendar find one-sixth of 12 days; one-sixth of 18 days. Applications. 1. What is one-sixth of 12 cans of fruit? How many cans are there in two-sixths of twelve cans? How many in three-sixths? In four-sixths? In five-sixths? 2. By reference to the box of cans how many sixths are there in onethird of twelve? In two-thirds of twelve? 3. Six badges 4 in. long can be cut from 24 in. of ribbon; each badge is what part of the whole piece of ribbon? Four is what part of 24? 4. Five-sixths of the braid on a spool is wound off; what part remains on the spool? The length of the braid remaining on the spool is 2 yards; how many yards were there in all? 5. Show by reference to a foot rule that one-half of 4 is one-sixth of 12. Besides many applications of this type there should be much miscellaneous drill like the following: The third, or ratio, idea of the fraction, may be introduced into the work of the third school year. This naturally grows out of inexact division. It is customary to write the divisor under the remainder to indicate that there is a part of the dividend still undivided. For example, in dividing 26 by 5 we have 26 51-5, in which 1-5 indicates that there is one still undivided by 5. Thus, the bar used to indicate a fraction also indicates division, and we may write 164 in this way, 16-4. Consequently, 16-44. The improper fraction and its reduction may now be introduced, with appropriate applications. 20th. Review Review Prac. exam. Hour-day Prac. exam. Week-month Prac. exam. Year, Rev. Time Table Prac. exam. Prac. use Prac. use Div. by 3. Mult. by 4. Div. by 4. Prac. subt., hundreds. Mult, by 5. Div. by 5. Subt. borrowing 2d place. Cost of one. Borrowing both places. Problems, 4 rules. Problems, 4 rules. Div. 2nd case. Numeration and notation every day-inc. 100's. Writing each day the current date. From the addition table develop the multiplication table, thus: A horse cost $97; cost of two horses? A yard of lace cost $21; cost of two yards? There were 63 children in one class; how many in two |
