SUBTRACTION 



5607 



SUBTRACTION 



Here we clearly have the problem, 9 5 n, 

 or, "When 5 is taken out of 9, how many are 

 left?" This is not the problem of the difference 

 between 9 and 5, like problem 1, and it is seen 

 thus: 



000000: O.-QQ 



FIG. 2 



Concrete Work. As in addition (see ADDI- 

 TION), much concrete work should be done in 

 building up groups and taking them apart to 

 make subtraction clear; for example, a group 

 of 12 pennies may be separated in various 

 ways: 12=5+7, 12-5=7, 12-7=5. This 

 formal way of writing it must be introduced 

 slowly and carefully, with much oral work pre- 

 ceding it and accompanying it. Below are sug- 

 gestions for concrete material: 



1. Groups of pennies, nickels, dimes. 



2. Groups of inch cubes, of cardboard squares. 



3. Compare various objects as to length, 

 width and height by measuring with foot rule 

 or yard rule. 



4. Compare heights of children. 



5. How much farther can John jump than 

 Dan? Measure in inches and subtract. 



6. Compare weights of articles. 



7. Compare costs of various articles, using 

 money. 



8. Have foot rule, yard rule, scales, money, 

 pennies, nickels, dimes, dollars (real money), 

 cubic blocks, etc. 



Home Help. At home mother or father may 

 do much to help at this point, for the freedom 

 of movement and variety of material, and op- 

 portunity for measuring and grouping and thus 

 getting material for comparison by subtraction, 

 are much greater at home than in the ordinary 

 schoolroom. (For further suggestion as to 



home help, see 



ADDITION.) 



Suggestions for 

 Rapid Work. 1. 

 Cards like the 

 illustration may 

 be held up before 

 the class by the 

 teacher for an in- 

 stant, and the 

 children may 

 write each 

 answer. When a 

 number of cards have been shown in this way, 

 the answers may be given, and each child may 

 know where he has made an error. In checking 



16 

 -9 



FIG. 3 



in this way, the teacher finds which combina- 

 tions give greatest difficulty. The class may 

 take sides in this, seeing which side has the 

 greater number correct. This may be done 

 orally as a rival game or just as a quick review. 



11 



-3 



12 



7 



21 

 3 



22 



-7 



32 



7 



41 

 3 



42 



-7 



A set of 'cards like the above may be passed 

 to the class and exchanged among the children; 

 the answers may be given orally, or written on 

 the blackboard or on paper, but not on the 

 card. Thus the same cards may serve many 

 classes. 



12 



-5 

 6 



29] 

 18 

 15 

 17 

 9 



11 

 21 

 12 

 22 

 27 



7 



Placing lists of this kind 'upon the black- 

 board gives opportunity for comprehensive re- 

 view, and for repeated review of any difficult 

 subtraction. The lists may be long or short 

 and the subtrahend may be changed many 

 times. 



4. n n n n n n n 



8 9 7 5 6 4 6 



15 9 3 9 7 9 



The problems are on the blackboard; the 

 child goes quickly to the board, erases n and 

 puts the minuend number in its place. 



5. 12 16 13 23 

 n n n n 



12 12 

 n n 



7 7 4 14 9 5 



The child goes to the board, erases n and 

 puts the subtrahend number in its place. 



6. Under ADDITION many suggestions will be 

 found that may be changed so as to serve the 

 purpose of the teacher in subtraction (see AD- 

 DITION). 



Subtraction of Numbers of Two or More 

 Digits, (a) Use dimes and pennies and the 

 first step is very simple. The child has 2 dimes 

 and 7 pennies. He spends 9 pennies. What 

 has. he left? 



dimes 



2 



pennies 



7 



dimes 

 1 



pennies 

 17 



Have a stack of pennies so that he may 

 change his dime for pennies. 



