V

EXERCISES WITH NUMBERS

Multiples, Prime Numbers, Factoring

When the child, by the aid of all this material, has had a chance to grasp the fundamental ideas relating to the four operations and has passed on to the execution of them in the abstract, he is ready to continue on the numerical processes which will lead to a more profound study preparatory to the more complex problems that await him in the secondary schools.

These studies are, however, a means of helping him to remember the things he already knows and to enlarge upon them. They come to him as a pastime, as an agreeable manner of thinking over either in school or at home the ideas which he already has gained.

One of the first exercises is that of continuing the multiplication of each number by the series of 1 to 10 which was begun by the exercises on the multiplication tables. This should be done in the abstract: that is, without recourse to the material. Let us, however, set some limit—we will stop when each product has reached 100. In order that these series of exercises may each be in one column the first exercises will stop with 50 and another can be used for the numbers from 51 to 100.

The two following tables (A and B) are the result. These are prepared in this manner in our material so that the child may compare his work with them.

TABLE A

2× 1= 23× 1= 34× 1= 45× 1= 56× 1= 67× 1= 78× 1= 89× 1= 910× 1=10
2× 2= 43× 2= 64× 2= 85× 2=106× 2=127× 2=148× 2=169× 2=1810× 2=20
2× 3= 63× 3= 94× 3=125× 3=156× 3=187× 3=218× 3=249× 3=2710× 3=30
2× 4= 83× 4=124× 4=165× 4=206× 4=247× 4=288× 4=329× 4=3610× 4=40
2× 5=103× 5=154× 5=205× 5=256× 5=307× 5=358× 5=409× 5=4510× 5=50
2× 6=123× 6=184× 6=245× 6=306× 6=367× 6=428× 6=48
2× 7=143× 7=214× 7=285× 7=356× 7=427× 7=49
2× 8=163× 8=244× 8=325× 8=406× 8=48
2× 9=183× 9=274× 9=365× 9=45
2×10=203×10=304×10=405×10=50
2×11=223×11=334×11=44
2×12=243×12=364×12=48
2×13=263×13=39
2×14=283×14=42
2×15=303×15=45
2×16=323×16=48
2×17=34
2×18=36
2×19=38
2×20=40
2×21=42
2×22=44
2×23=46
2×24=48
2×25=50