How to Teach Part 16

SERIES A SUBTRACTION SCALE BY CLIFFORD WOODY

Name......................

When is your next birthday?......How old will you be?.....

Are you a boy or girl?.......In what grade are you?.......

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 8 6 2 9 4 11 13 59 78 7-4= 76 5 0 1 3 4 7 8 12 37 60 -- -- -- -- -- -- -- -- -- --

(12) (13) (14) (15) (16) (17) (18) (19) (20) 27 16 50 21 270 393 1000 567482 2 3/4-1= 3 9 25 9 190 178 537 106493 -- -- -- -- --- --- ---- ------

(21) (22) (23) (24) (25) (26) 10.00 3 1/2-1/2= 80836465 8 7/8 27 4yd. 1ft. 6in.

3.49 49178036 5 3/4 12 5/8 2yd. 2ft. 3in.

(27) (28) (29) (30) 5yd. 1ft. 4in. 10-6.25 75 3/4 9.8063-9.019= 2yd. 2ft. 8in. 52 1/4 -------------- ------

(31) (32) (33) (34) (35) 7.3-3.00081= 1912 6mo. 8da. 5/12-2/10= 6 1/8 3 7/8-1 5/8= 1910 7mo. 15da. 2 7/8 --------------- -----

SERIES A DIVISION SCALE BY CLIFFORD WOODY

Name...............................

When is your next birthday?....... How old will you be?......

Are you a boy or girl?.......... In what grade are you?......

(1) (2) (3) (4) (5) (6) __ ___ ___ __ ___ ___ 3)6 9)27 4)28 1)5 9)36 3)39

(7) (8) (9) (10) (11) (12) 4 2 = __ __ 6 __ = 30 ___ 2 2 = 9)0 1)1 2)13

(13) (14) (15) (16) (17) ______________ _____ 1/4 of 128= _____ 50 7 = 4)24 lbs. 8 oz. 8)5856 68)2108

(18) (19) (20) (21) (22) ______ 248 7 = _____ _____ ______ 13)65065 2.1)25.2 25)9750 2)13.50

(23) (24) (25) (26) ____ ________ _______ _____ 23)469 75)2250300 2400)504000 12)2.76

(27) (28) (29) (30) 7/8 of 624 = ______ 3 1/2 9 = 3/4 5 = .003).0936

(31) (32) (33) 5/4 3/5 = 9 5/8 3 3/4 = _____ 52)3756

(34) (35) (36) 62.50 1 1/4 = ______ ______________ 531)37722 9)69 lbs. 9 oz.

SERIES A MULTIPLICATION SCALE BY CLIFFORD WOODY

Name......................

When is your next birthday?...... How old will you be?.....

Are you a boy or girl?....... In what grade are you?.......

(1) (2) (3) (4) (5) (6) (7) 3 7 = 5 1 = 2 3 = 4 8 = 23 310 7 9 = 3 4 -- --- (8) (9) (10) (11) (12) (13) (14) (15) 50 254 623 1036 5096 8754 165 235 3 6 7 8 6 8 40 23 -- --- --- ---- ---- ---- --- ---

(16) (17) (18) (19) (20) (21) (22) 7898 145 24 9.6 287 24 8 53/4 9 206 234 4 .05 21/2 ---- --- --- --- --- --

(23) (24) (25) (26) (27) (28) (29) 11/4 8 = 16 7/8 3/4 = 9742 6.25 .0123 1/8 2 = 2 5/8 59 3.2 9.8 ------ ---- ---- ----- (30) (31) (32) (33) (34) 2.49 12 15 6 dollars 49 cents 2-1/2 3-1/2 = 1/2 1/2 = 36 -- -- 8 ---- 25 32 ------------------

(35) (36) (37) (38) (39) 9873/4 3ft. 5in. 21/4 41/2 11/2 = .0963 1/8 8ft. 91/2in.

25 5 .084 9 ---- --------- --------- ----------

A series of problems in reasoning in arithmetic which were given in twenty-six school systems by Dr. C.W. Stone furnish a valuable test in this field, as well as an opportunity for comparison with other schools in which these problems have been used.[22] A list of problems follows.

Solve as many of the following problems as you have time for; work them in order as numbered:

1. If you buy 2 tablets at 7 cents each and a book for 65 cents, how much change should you receive from a two-dollar bill?

2. John sold 4 Sat.u.r.day Evening Posts at 5 cents each. He kept 1/2 the money and with the other 1/2 he bought Sunday papers at 2 cents each. How many did he buy?

3. If James had 4 times as much money as George, he would have $16. How much money has George?

4. How many pencils can you buy for 50 cents at the rate of 2 for 5 cents?

5. The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 a pair. What was the total cost of uniforms and shoes for the nine?

6. In the schools of a certain city there are 2200 pupils; 1/2 are in the primary grades, 1/4 in the grammar grades, 1/8 in the High School, and the rest in the night school. How many pupils are there in the night school?

7. If 3-1/2 tons of coal cost $21, what will 5-1/2 tons cost?

8. A news dealer bought some magazines for $1. He sold them for $1.20, gaining 5 cents on each magazine. How many magazines were there?

9. A girl spent 1/8 of her money for car fare, and three times as much for clothes. Half of what she had left was 80 cents.

How much money did she have at first?

10. Two girls receive $2.10 for making b.u.t.tonholes. One makes 42, the other 28. How shall they divide the money?

11. Mr. Brown paid one third of the cost of a building; Mr.

Johnson paid 1/2 the cost. Mr. Johnson received $500 more annual rent than Mr. Brown. How much did each receive?

12. A freight train left Albany for New York at 6 o'clock. An express left on the same track at 8 o'clock. It went at the rate of 40 miles an hour. At what time of day will it overtake the freight train if the freight train stops after it has gone 56 miles?

A different type of measurement is accomplished by using Thorndike's scale for measuring the quality of handwriting.[23] A typical distribution of the scores which children receive on the handwriting scale reads as follows: For a fourth grade one child writes quality four, two quality six, five quality seven, seven quality eight, eight quality nine, three quality ten, two quality eleven, two quality twelve, one quality thirteen, one quality fourteen. In a table the distributions of scores in penmanship for a large number of papers selected at random show the following results:

============================================================ | GRADES SCORES +------+------+------+------+------+------+----- | 2 | 3 | 4 | 5 | 6 | 7 | 8 ------------+-------------+------+------+------+------+----- 0 | -- | -- | -- | -- | -- | -- | -- 1 | -- | -- | -- | -- | -- | -- | -- 2 | -- | -- | -- | -- | -- | -- | -- 3 | -- | -- | -- | -- | -- | -- | -- 4 | 5 | 2 | -- | -- | -- | -- | -- 5 | 22 | 2 | 3 | 3 | -- | 1 | -- 6 | 21 | 21 | 16 | 3 | 2 | -- | 1 7 | 29 | 44 | 24 | 12 | 1 | 3 | 3 8 | 28 | 86 | 42 | 56 | 20 | 15 | 7 9 | 42 | 41 | 55 | 61 | 25 | 29 | 11 10 | 7 | 8 | 20 | 16 | 9 | 11 | 1 11 | 29 | 13 | 21 | 17 | 32 | 25 | 23 12 | 5 | 2 | 15 | 15 | 44 | 12 | 21 13 | 7 | 2 | 2 | 6 | 17 | 19 | 9 14 | -- | -- | 3 | 4 | 10 | 16 | 9 15 | -- | -- | 1 | -- | 9 | 6 | 15 16 | 1 | -- | -- | 1 | 10 | 12 | 17 17 | -- | -- | -- | -- | 6 | 2 | 3 18 | -- | -- | -- | -- | 3 | 1 | -- ------------+------+------+------+------+------+------+----- Total papers| 196 | 221 | 202 | 194 | 188 | 152 | 124 ============================================================