ARITHMETIC 350 



is taught. It is important that articles in 

 . volumes be referred to, where such sug- 

 :ons appear, for under those titles are given 



many methods to be employed in teaching: 



FIRST YEAR 



Numerical Expression. Writing and reading 

 of Arabic numbers to 100 ; Roman numerals from 

 I to XII; the signs +, -, X, -^, =. 



Notation and Numeration. Count by 1's and 

 10's to 100 ; numbering groups of objects with- 

 out counting; addition, subtraction, multiplica- 

 tion and division with numbers to 10, using 

 objects for illustration. See NOTATION ; Addi- 

 tion, etc. 



Measuring. Teach ideas of size, form, direc- 

 tion. 



Fractions. Deal with halves, thirds, fourths; 

 with problems such as % of 2, 4, 6, 8, 10 ; % of 

 3, 6, 9 ; V of 4, 8, etc. 



Denominate Numbers. Familiarize pupils with 

 values of cent, nickel, dime, day, week, pint, 

 quart. Do not reach numbers above 10. 



Practical Applications. Keep everything within 

 the children's experience. Problems relating to 

 things in which they have an interest will bring 

 instant response. Two yards of silk mean less 

 than two dolls' dresses; two glass marbles pos- 

 sess more meaning than two bushels of potatoes. 



SECOND TEAR 



Oral and Written Expression. The reading 

 and writing of numbers below 1,000 and of all 

 language forms used to state the relations of 

 numbers expressed in the signs +, , X, -H, =, 

 $, < ; including Roman numerals to L, if the 

 reading lessons are so numbered ; simple work 

 involving the expression of dollars and cents ; the 

 reading and writing of time from the clock. 



Notation and Numeration. The addition and 

 subtraction of numbers not exceeding three 

 orders. See NOTATION. 



The building and learning of the multiplica- 

 tion tables from 1 to 5 inclusive ; aiding the work 

 in tables by counting by 2's, 3's, 4's and 5's. 



Simple combinations in multiplication and 

 division in connection with tables. The com- 

 paring of numbers. 



Fractions. Review fractions learned in the 

 first year and deal with %. 



Denominate Numbers. The learning of the 

 units in measure, time and money, such as inch, 

 foot, yard, pint, quart, peck, degrees of heat ; 

 fractions of hour and minute ; cent, nickel, dime, 

 quarter, half-dollar and dollar ; in all cases using 

 objective material such as coins, measures, the 

 clock and thermometer. See DENOMINATE 

 NUMBERS. 



Measuring. By means of foot-rule, yardstick 

 and other objects, have the pupils measure length 

 of blackboards, window-sills, paper or parts of 

 these objects. Simple work in area, using rectan- 

 gles and triangles of folded paper made by the 

 pupils. 



Practical Problems. At this age the pupils 

 have begun to develop the spirit of competition 

 with their classmates and a comparison of the 

 weight and height of the children in the room is 

 Interesting to them. 



ARITHMETIC 



In measuring Charles. Alice and Mary we 

 found that Charles was 4 ft. 2 in. tall, Alice was 

 3 ft. 5 in. tall aixl Mary was ;} ft. 8 in. tall. 

 Who was the shortest? How much tailor was 

 Charles than Mary? 



Have the children suggest original problems 

 like the above, which involve but one step. 



Problems are made much easier to the pupils 

 if they deal with familiar and interesting objects, 

 as the following, correlated with their nature 

 study. 



The rose bush we planted in the school yard 

 grew 1% inches last year, and in measuring it 

 this year, we find that it has grown 2% inches 

 higher. How much less did it grow last year 

 than this? 



Real Problems for Oral Work. I have six 

 apples and three bags. How shall I find how 

 many apples I should put into each bag? 



The picture near the clock is square. If we 

 know the length of one side of it, how can we 

 find the distance around it? Outline the picture 

 and explain. 



THIRD TEAR 



Oral and Written Expression. The reading 

 and writing of Arabic numerals to 10,000 and of 

 the Roman numerals to C ; the rapid reading and 

 writing of fractions and of sums of money ex- 

 pressed in dollars and cents. 



Notation and Numeration. The rapid addition 

 and subtraction of simple combinations. See 

 NOTATION. 



A review of the multiplication tables through 

 10 and the learning of the tables of 11 and 12 ; 

 practice in counting forwards and backwards by 

 2's, 3's, 4's and 5's. 



The thorough mastery of the multiplication 

 table to 10 X 10 and of division by numbers 

 through 10. The comparing of numbers and 

 quantities continued. See ADDITION ; SUBTRAC- 

 TION ; MULTIPLICATION ; DIVISION. 



Fractions. Addition work in the fractions %, 

 %, %, % and I/G. 



Denominate Numbers. Continue the work in 

 denominate numbers begun in the first and sec- 

 ond years with drill in changing denominate 

 numbers to the new smaller or larger units ; as 

 the number of quarts in 12 gallons; the number 

 of inches in 3 feet; the number of minutes in 

 2 hours, etc. 



Additional practice in reading time from the 

 clock. See DENOMINATE NUMBERS. 



Measuring. Continue the measurement of 

 familiar objects and the working of practical 

 problems in measurement. 



Practical Problems. Let the problems deal 

 with objects full of meaning and interest to the 

 children. 



Real problems in comparison such as : If 3 

 tops cost 6 cents, what is the cost of 6 tops? 

 Let the pupil compare 3 and 6 before proceeding 

 to the second step of the problem. Many such 

 comparisons may IK- made. 



Henry and John kept a lemonade stand in 

 their front yard. They made 3 gallons, but in 

 pouring it into the pitcher, spilled 1 quart. They 

 sold it at 6 cents a quart ; how much money did 

 they receive? The lemonade cost them 1 cent a 

 half-pint glass; what was their gain? 



