grassy hill, mount the paper on cardboard; paste Jack and Jill either going up the hill or falling down. . "Old Woman in the Shoe."

To dramatize: Select a little girl for old woman, the other children in the school being her children. Give them permission to run away from the house. of old woman and do anything they wish until they are caught and seated. Repeat (all of the children):

"There was an old woman Who lived in a shoe; She had so many children She didn't know what to do. She gave them some soup, A piece of white bread, And sung them a song, And put them to bed." During this time the old woman is giving the children bread and soup, then she sings them a song (one she has learned at school), while she is singing the children lay their heads on the desk, each playing he is asleep.

Poster Material: Gray cardboard, 7x9; shoe cut from black or brown paper (or colored with chalk); several very small sunbonnet babies; green chalk.

Plan: With the chalk represent the ground. Mount the shoe with the sunbonnet babies around it.

"Little Bo Peep."

To Dramatize: Choose Little Bo Peep and a number of children for sheep. Let Bo Peep be seated on a chair and all of the children playing sheep be on their

hands and knees around her. When she
falls asleep, all of the sheep hide, crying,
ba! ba! She awakens and goes in search
of them, when they are all brought back
to the fold (her chair) she gives them
imaginary salt and meal. The rhyme-
"Little Bo Peep is fast asleep,
Away her sheep are running
Over the hills and through the field,.
So early in the morning.

Little Bo Peep has found her sheep,
And lovingly she'll keep them.

Now they're at home no more to roam,
And lovingly she'll feed them."
Can be sung to the following key of G
time: def gagff, gfeefed, defga
gff, edebaa g.

All of the nursery rhymes can be used for poster work, and for play. The material used in making the posters can be made by the children before time for mounting it. This form of art work is being emphasized in the schools at present. It is good work because the same principles of art are as strictly practiced as they are in painting and drawing. And there is no more effective decoration than a border of posters representing the nursery rhymes. In making these the children have great pleasure.

Some one says, "The time it takes to play these games." I want you to think of the enthusiasm it puts into the children and teacher.

Again some one says, "The work in getting all of this material ready." It pays to do the work; try it.

A TEST OF DIVISIBILITY BY SEVEN. I. Seven is an exact divisor of any number of which the units figure doubled differs from the number represented by the remaining digit or digits by 0 or by a multiple of 7. Thus, in 14: twice 4 are 8; 1 from 8 leaves 7. In 21: twice 1 are 2; 2 from 2 leaves 0. In 28: twice 8 are 16; 2 from 16 leaves 14. In 35: twice 5 are 10; 3 from 10 leaves 7.

In 42: twice 2 are 4; 4 from 4 leaves 0. In 49: twice 9 are 18; 4 from 18 leaves 14. In 168: twice 8 are 16; 16 from 16 leaves 0. In 175: twice 5 are 10; 10 from 17 leaves 7. In 532: twice 2 are 4; 4 from 53 leaves 49. Corollary A. When the remainder after subtraction is 0, the original number is a multiple of 3, as well as of 7, therefore is a multiple of 21.

Corollary B. An even number which is a ́multiple of 3 must also be a multiple of 14, etc.

II. When the number to be treated is so large that the remainder found by subtracting the double unit from the rest of the number is too large to be judged by inspection, the same test may be applied to the remainder as to the original number. This process may be repeated until a remainder be found which is small enough to be factored by inspection.

For example, 22,134: twice 4 are 8; 8 subtracted from 2,213 leaves 2,205; twice 5 are 10; 10 from 220 leaves 210; 210 at once ap pears as a multiple of 7.

III. Demonstration. Multiplying the units figure by 2 and placing the product in the tens column, and ignoring the units figure in the subtraction is really multiplying the units figure by 21, which is a multiple of 7. The test then becomes merely the ascertaining of the difference between the number to be tested and a multiple of 7, and as the difference between multiples must be a multiple, the number tested is a multiple, if the difference found is a multiple of 7. The value of the test rests upon the facility with which the multiple of 21 is created, inasmuch as to multiply by 2 is a mental process much more surely within the mind of a child than dividing by 7.

Also it will be seen that other numbers having multiples of two digits of which the last is 1, may be readily tested as possible divisors by similar processes. Such numbers are 9, 13, and 17, having multiples 81, 91, and 51 respectively. Journal of Education.

THE LANGUAGE OF FRACTIONS.

A clear understanding of any language form depends more upon "suiting the action to the word and the word to the action," clean cut precise usage, than upon explanations and discourses about words. The main reliance of the teacher in teaching arithmetical language is the giving of questions one after another which differ only in the point to be taught so the pupil will have to judge and select the correct form of reply from the various answer forms which he has been taught to use.

.

The language used in fractions seldom conveys the meaning to the pupil which is intended. I think it is safe to say that the average pupil's notion of fractions is vague. Perhaps the majority of people prefer to use the decimal form of numbers even when the common fractional form, if well understood, is really simpler and shorter. As popularly thought of, a fraction means a ratio and nothing more. The idea that 3 is a real concrete number in the fraction, 3-5 of $25, is seldom thought of, and almost never dwelt upon and emphasized in teaching. The writer believes that the language of fractions should be so framed that the pupil's attention will be fixed upon the notion that a fraction is a concrete number instead of upon the idea that it is merely a ratio. A few forms are here submitted to illustrate the writer's meaning.

Problem: Form of an apple. Answer: We form of an apple by dividing the apple into 4 equal parts, and by counting off 3 of the parts for the number.

At the same time the explanation is given by the pupil, let him actually divide the apple, count off the three parts, and then tell what he has. When this process has been performed from ten to thirty times by different pupils in presence of the class, it will be time to direct their attention to the units involved. The number, 3 fourths-of-anapple is a fraction. The whole apple is the unit of the fraction, and the 1 fourth-of-anapple is the fractional unit. The number is 3 of the fractional units. It is 3 pieces of an apple. The word fourths helps us to determine the size of each piece. The word apple tells us more about the pieces, it reveals their qualities. When an extensive exercise has been given on these points, the class should be ready for the next step-a change in the fractional units, or "Reduction."

Problem: Change 2-3 of a potato to ninths of a potato. Answer: As there are 3 times as many ninths in a whole as there are thirds, to change 2 thirds-of-a-potato to ninths of a potato, we must divide each of the 2 thirds into 3 equal parts, and then we shall have 6 smaller pieces whose names are ninths, for 9 of such pieces make a whole potato.

As in the former model, let the act of di

viding be done by the pupil just as he gives the explanation. Have exercises of this kind continued until all points of the explanation are made clear and the language can be spoken habitually.

Problem: Change 6-10 of a circle to fifths of a circle. Answer: As there are one-half as many fifths in a whole as there are tenths, to change 6 tenths-of-a-circle to fifths-of-acircle, we must unite 2 of the tenths to form 1 fifth, and the 6 tenths will form 3 fifths, for 2 tenths is contained 3 times in 6 tenths.

The circle is a very convenient unit to divide, sub-divide, and in which to re-unite parts for it may be done by merely drawing and erasing lines.-Home and School Education.

(3) Buy an article for 25%, sell for 409. What part is gained? (Give result.). Ans. Buy an article for 40%, sell for 25%. What part is lost? . Ans.

(4) Find the cost of 12 pr. shoes at $3, at 40 per cent. and 10 per cent. off.

12 pr. shoes at $3=$36.

40 per cent. +10 per cent. = 50 per cent. 50 per cent. off off. $36-$18 = - $18. Cost.

SOLUTION 1.

Grades: (1) 0, (2) 0, (3) 12, (4) 0. Total grade 12%.

Mathematics is an exact science.

A solution is either right or wrong. There is no middle ground. In some other subjects an answer may be partly wrong, and yet deserve some credit. But this is not true in mathematics. In a problem like (1) an answer that is wrong by 1, is wrong, and should receive no more credit than if it were wrong 10. Effort may cause growth, but when the result is wrong the effort should be measured in increased brain power and not in an unearned per cent. J. P. O'Mara, Queensville.

SOLUTION 2.

Grades: (1) 124%. The answer is wrong, but the fractions are added correctly.

(2) 12%. Careless reading, but the interest is correctly found.

(3) 10%. Careless thinking.

(4) 2%. Found cost of shoes correctly.

W. M. Tucker, Goodland.

This query shows how widely teachers differ in their estimates of answers. In the near future another question of this sort will be proposed, and an effort will be made to have the grading done by a large number of teachers.

8. A man died February 14, 1888, aged 88 years 2 months and 14 days. When was he born?

88 years before February 14, 1888, was February 14, 1800. 2 months before February 14, 1800, was December 14, 1799. 14 days before December 14, 1799, was November 30, 1799. .. the man was born November 30, 1799.

Curtis G. Shake, Monroe City.

9. By the use of four 9's and whatever algebraic signs are necessary, express as many of the numbers from 1 to 20 as possible.

The answer to 9 is a composite of the answers furnished by Thomas Hallett, Ira E. Lee, Melvin Dowge, Stella Drake, Harold Parker, Arthur W. Parker, R. D. Minnich, Eudora A. Green.

QUERIES.

10. Express the numbers from 80 to 100 by the use of four nines and whatever algebraic signs are necessary.

11. An eight-gallon cask is full of brandy and a ten-gallon cask is full of water. How much must be transferred from one cask to the other that the mixture may be of equal strength?

12. An agent received $4,325 to invest in mess pork at $16.00 per barrel, after deducting his purchasing commission of 4%. If the charges for incidentals were $81.40, besides cartage of 75 per load of 8 barrels, how many barrels did he buy, and what unexpended balance does he place to the credit of his principal?

Query 10 is introduced because of the great interest shown in number 9. The only figure allowed in the solution is 9, and there must be just four of these for each number. Solutions to these queries should reach Robert J. Aley, Bloomington, not later than March 14. Some first-class problems for solution would be very acceptable.