Pure tone. This is a difficult matter to deal with. It is more largely a gift than an acquirement, and any drilling in it often produces stilted and artificial results. The greatest aid to the pupils is the example of the teacher. The voice of the teacher should be quiet, clear and pleasant; class instruction and reading to the pupils should present good models for ear training and worthy imitation. The pupils of the class who excel in this particular should be permitted to read aloud selections to which the other pupils listen. This encouragement to give pleasure to others is an incentive which appeals to all the pupils and helps them to do their best. It is a means of carrying out the social aim of the school.

Power to read new words and to pronounce them correctly.—Dr. McMurry has summed up the matter so well that I cannot do better than to quote him. He says: "Pupils should be encouraged constantly to help themselves in interpreting new words:

(1) By looking through the new sentence and making it out, if possible, for themselves before any one reads it aloud.

(2) By analyzing a new word into its sounds, and then combining them to get its pronunciation.

(3) By interpreting a new word from its context or by the first sound or syllable.

(4) By using the new powers of the letters as fast as they are learned in interpreting new words.

(5) By trying the different sounds of a letter to a new word to see which seems to fit best.

(6) By seeing that every child reads the sentences in the new lesson for himself."

Many of the new words will occur in connection with the picture at the head of the lesson. Place these on the board as they come up. Weave them into conversation and the pupils will not find them difficult. Where necessary the words should be briefly explained.

Correct pronunciation depends upon the proper sounding of the vowels. If mistake is made in pronouncing, point out the exact word, and the syllable in the word in which the mistake has been made.

In this sketch I have tried to bear in mind what to appeal to, and what to build upon; and have endeavored to make each exercise carry out some law underlying processes in teaching, and have tried to indicate the spirit, motive and disposition with which the work is done so as to contribute to the building of character.

BY ADELLE PARSONS, Tremont Grammar School, Rochester, N. Y.

The notion of a fraction includes three phases which must be taught before a pupil has a satisfactory idea of a fraction. These phases are: (1) One or more of the equal parts of a single thing; (2)One or more of the equal groups of a group of things; (3) The indicated quotient of one number divided by another. All three ideas should not be presented when the fraction is first introduced into school work. Fractions should be taught first as equal parts of a single thing, and this definition should control the method of teaching for Grade 2A. Then, the second definition should be employed in Grade 2B to enlarge the pupil's concept, and fractions should be considered both as equal parts of units and as equal parts of groups of units. In the third or fourth school year the third idea should be given in connection with the improper fraction. It is the object of this article to present a method of teaching fractions in harmony with the definitions above outlined.

To teach one-half of a unit.-Give to the pupils paper circles with centers plainly marked or hold such a circle in view of the class. Fold the circle through the center and open it out again. Question in this manner: Into how many parts does the fold divide the circle? How do the parts compare in size as shown by folding? Take a paper square and fold through a diagonal. Ask questions similar to those for the circle. State that each of the two equal parts in case of the circle is one-half of the circle, and that each of the two equal parts of the square is one-half of the square.

Applications.

1. Jennie and Clara divided an apple equally between them. What part of the apple did each have?

2. Charles and Myron divided a pop corn ball equally between them; what part of the ball did each have?

3. Ralph divided an orange into halves; into how many parts did he divide it? How did the parts compare in size?

4. Draw a circle and mark it as in the picture. (A) Draw a line to divide this apple into halves.

5. Draw a square and divide it into halves.

(B)

6. Draw a circle and a line through its center. Shade with a pencil or color with a brush one-half of the circle.

7. Draw a rectangle and draw a line from any corner to the opposite one; shade with pencil or color with a brush one-half of the rectangle.

To teach fourths of a unit.-The teacher holds a paper circle with the center mark before the class, or better, the pupils are given paper circles. The circle is folded through the center so that the first crease lies on itself. The circle is again opened out. Question in this manner: Into how many parts is the circle divided by the creases? By noticing how the parts lie as the circle is folded tell how they compare in size. Into how many equal parts is the circle divided? Fold a paper square through each diagonal.

Ask questions similar to those for the circle. State that each of the four equal parts of the circle is one-fourth of the circle, and that each of the four equal parts of the square is one-fourth of the square. How many fourths are there in a whole circle? In a whole square? Fold one side of a square to the opposite side. Open out the paper. Fold the other sides together and open out the paper. (C) Into how many equal parts do the creases divide the square? How do the parts compare in size? Each part is how much of the whole square?

Applications.

1. Four boys shared an apple equally; each had what part of the apple?

2. Lucy cut a pie as shown in the picture (D); how many pieces did she make?

3. Mary cut a cake into fourths; how many pieces did she make? 4. Four girls made a square garden in the sand and divided it so that each had an equal part. What part did each have? Make a drawing and divide it to show the part each girl had.

5. George picked a 4-quart pail full of berries, and the gardener gave him one-fourth of them for picking; how many quarts did George have? 6. Evelyn drew a line each way across the middle of her tablet (E) to make spaces in which to write problems; how many spaces did she make? How did they compare in size? Each was what part of the whole page? 7. A window sash contains four window panes. Each pane is what part of the whole surface?

8. Frank lives four blocks from the school; each block is what part of the distance to Frank's home?

To teach the relation of halves and fourths.-Fold the square again through the center lines. Into how many parts do the creases divide the square? Each is what part of the square? Fold the square over one of the creases. This surface is what part of the whole square? How many fourths of the square are there in it? How many fourths of the square are there in one-half of it?

Fold the circle into halves and fourths. Find as in the case of the circle the number of fourths in a half. Fold a rectangular piece of paper so as to show that two fourths equal one-half. Fold a square through its opposite corners and show that one-half contains two fourths.

Applications.

1. Four boys shared a pie equally; what part of the whole pie did two of them have?

2. Roy picked a 4-quart basket full of cherries and sold one-half of them; how many quarts did he sell?

3. Lucy divided an orange into fourths, or quarters, and gave Henry one-half of the orange; how many quarters did she give him?

4. Two panes in a 4-pane window sash are what part of the whole surface?

5. John lives four blocks from school; two blocks are what part of this distance?

6. When John is half way to school, how many blocks has he come? How many has he yet to come?

7. Draw a square and connect its opposite corners. Shade or color one-fourth of the square. Another fourth. What part of the whole square is now shaded? What part is not shaded?

8. Draw a square, and proceed as in previous exercise, but use mid lines instead of diagonals for the division lines.

9. Draw a square; divide it into fourths. Shade one of them. Two of them. Three of them.

10. Fold a circle and paint out three-fourths of it.

11. Three quarts of berries are what part of a 4-quart pail full? To teach thirds of a unit.-Give the pupils strips of paper 6 in. long and 2 in. wide marked, as shown in the figure (F), or fold such a piece of paper before the class. Fold one end through the nearest dot. Open out and do the same with the other end. Into how many parts do the creases divide the rectangle or oblong? How do the parts compare in size? (Find answer by folding).

The teacher holds a yard stick before the class and marks it off in feet by use of a foot rule. Into how many parts is the yard divided? How do the parts compare in size? Each part is called one-third of a yard. One foot is what part of a yard? Two feet are how many thirds of a yard? Each division of the rectangle was what part of the whole rectangle? Two divisions were what part of the whole rectangle?

Application.

1. Mary's mother gave her one foot of cloth cut from a yard. What part of a yard did she give her? What part of a yard was left?

2. Carl had a stamp book with three leaves; when he had filled one of them what part of the book had he filled?

3. Ruth spilled one quart of milk from a three-quart pail full; what part of the whole did she spill? What part was left in the pail?

4. A pie was divided as shown in the picture (G). One part was gone and Peter took half of the rest; what part of the pie did he get? How much of the pie remained?

5. How many lobes has the clover leaf in the picture? (H) What part of the leaf is one of them? If one is taken away what part of the leaf is left?

To teach sixths of a unit.-Use strips of paper as in the case of thirds; fold in the same way; then fold lengthwise through the middle (I). Compare the parts by folding. How many equal parts are there in the rectangle? Draw a hexagon on the blackboard and divide it as shown here. (J). How many equal parts are there in the figure? One of the six equal parts of the figure is called one-sixth of it. Two of them are two-sixths of the figure. What are three of them called? Four of them? Five of them? What part of the folded rectangle is each division?