COMBINATIONS OF NUMBERS
We now come to the method of teaching the combinations in Addition and Subtraction.
We can count books, tables, and houses and say that we have counted so many things but we do not add books, tables, and houses. We add books and books, tables and tables, houses and houses.
We count by ones. When we add three beads and two beads we are counting by ones, for it means that we are adding three ones of beads and two ones of beads, making five beads in all.
From 1 to 9 we use only one figure to tell how many we mean. When we wish to say in writing that we have ten of anything we write a 0 after the 1 and have 10, ten.
1. Add 1 to every number up to 10; later to 20.
2. Subtract 1 from every number up to 10; later to 20.
3. Add:
+2 +3 +4 +5 +6 +7 +8 +9 +10
+2 +3 +4 +5 +6 +7 +8 +9 +10
Here the addends are equal and easily added. The figures should be placed as above and not 2 + 2, 3 + 3, etc., because the vertical form is the natural one which the child will use all through life. It does not look so formal and represents better what he really does with the objects.
4. Add:
+1 +2 +3 +4 +5 +6 +7 +8 +19
+2 +3 +4 +5 +6 +7 +8 +9 +10
Here one addend exceeds the other by 1.
5. Subtract:
-2 -3 -4 -5 -6 -7 -8 -9 -10
-1 -2 -3 -4 -5 -6 -7 -8 1-9
Here the minuend is one greater in each case.
6. Teach the parts of 10.
+5 +2 +3 +4 +9
+5 +8 +7 +6 +1
7. In adding 9 to numbers have the child think of 9 as 10,
thus 9+6 = 10+5 and 9+8 = 10+7
8. Teach the corresponding subtractions.
9. Add 8 to each number up to 10.
10. Teach the corresponding subtractions.
11. Add 7, 6, and 5 to each number up to 10.
12. Teach the corresponding subtractions.
13. Review and give combinations not taught above.
Objects should be grouped by tens and units, in showing numbers above ten. Ten should be the basis of all our reckoning, and if the children know ten, and the numbers which precede it, they can soon be taught the rest. Little children should not have “sums” given them to do on their slates, for “sums” are made up of abstract figures, and children of tender years cannot grasp the abstract.
Number to One Hundred.—When the children are conversant with numbers up to ten, it is very easy to teach them one hundred.