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Prologue 1

ELEMENTARY ADDITION

Sums less than 10

Composing 10 itself

Sums between 10 and 20

Doubling

Zero

Practice problems


ADDITION is the problem of naming the one number that results from joining together two or more numbers.


The addition sign is this:  + , which we read "plus."  The solution to the problem -- the result of adding -- we call the sum; and the numbers that we are adding we call the terms of the sum.  And so when we add 3 + 6, the terms are 3 and 6; their sum is 9.  We also call '3 + 6' a sum -- even if we do not name the answer


We can only add quantities of the same kind, that is, which have the same name.

3 girls + 6 girls = 9 girls.

We cannot add  3 girls + 6 boys -- at least not until we call them "children."

Skill in addition begins with knowing sums that are less than 10.

3 + 6 = 9,  4 + 2 = 6,  5 + 3 = 8,

and so on.  First, though, an elementary fact of addition is that the order in which we add does not matter.  For if you know that 3 + 6 = 9,

then you would also know that 6 + 3 = 9.

The order does not matter.  That will be true for any number of terms.

2 + 3 + 4 = 3 + 2 + 4 = 4 + 3 + 2 = 9.

Now practice these sums that are less than 10.

To see the answer, pass your mouse over the colored area.
To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!


  7 + 2 = 9   3 + 4 = 7   2 + 3 = 5   5 + 2 = 7   1 + 5 = 6
 
  6 + 3 = 9   4 + 2 = 6   3 + 5 = 8   1 + 3 = 4   2 + 4 = 6
 
  1 + 7 = 8   2 + 5 = 7   1 + 8 = 9   4 + 5 = 9   3 + 2 = 5
 
  2 + 6 = 8   1 + 6 = 7   2 + 7 = 9   5 + 3 = 8   4 + 4 = 8
 
  5 + 4 = 9   3 + 6 = 9   1 + 4 = 5   4 + 3 = 7   6 + 2 = 8

Composing 10 itself

It is useful to know all the ways of "composing" -- that is, making -- 10.

  2 + 8 = 10     6 + 4 = 10     1 + 9 = 10  
 
  4 + 6 = 10     9 + 1 = 10     7 + 3 = 10
 
  8 + 2 = 10     3 + 7 = 10     5 + 5 = 10

Sums between 10 and 20

Finally, the student must know sums such as  9 + 6 = 15 ,  8 + 5 = 13, and so on.  To become familiar with them, you can first compose 10 by regrouping.  But eventually, you must know them.

Example 1.   9 + 6.

On splitting 6 into 1 + 5,

9 + 6 = 9 + 1 + 5 = 10 + 5 = 15.

Say, "9 + 1 is 10, plus 5 is 15."

That is, regroup 1 with 9 to compose 10.

Example 2.   5 + 7.

"5 + 5 is 10, plus 2 is 12."

Example 3.     3 + 8.

"8 + 2 is 10, plus 1 is 11."

Doubling

It will help to know the sum of a number added to itself.

5 + 5 = 10

6 + 6 = 12

7 + 7 = 14

8 + 8 = 16

9 + 9 = 18

Now, once you know that

6 + 6 = 12,

then you could know that

6 + 7 = 13,

and

6 + 5 = 11.

7 + 7 = 14

7 + 8 = 15

7 + 6 = 13

8 + 8 = 16

8 + 9 = 17

8 + 7 = 15

9 + 9 = 18

9 + 8 = 17

Zero

0 is a number. It can answer the question How much? or How many?
0 is best introduced by subtraction.

Say, for example, that you have 2 dollars.  If you spend those 2 dollars, you now have 0 dollars.

2 dollars − 2 dollars = 0 dollars.

That is,

2 − 2 = 0

for any unit:  dollars, apples, chairs, etc.

Here is a basic fact about 0:  If you add it to any number, that number does not change.

5 + 0 = 5.

0 + 6 = 6.

0 means no units.

There is a subtle difference between 0 units and nothing. Say that you have an account at the First National Bank and that your balance is $10.  If you now withdraw $10, your balance is 0 dollars. But say that you have no account at that bank. Then you do not have a balance of 0 dollars there -- you have nothing!

That is the difference between 0 and nothing.


*        *        *

Practice the following until you remember each one.


8 + 5 = 13   3 + 9 = 12   5 + 9 = 14   6 + 8 = 14   7 + 9 = 16
 
9 + 6 = 15   7 + 6 = 13   8 + 6 = 14   6 + 5 = 11   8 + 4 = 12
 
3 + 8 = 11   5 + 8 = 13   9 + 4 = 13   7 + 4 = 11   6 + 6 = 12
 
4 + 9 = 13   4 + 8 = 12   6 + 9 = 15   8 + 9 = 17   4 + 7 = 11
 
5 + 7 = 12   6 + 7 = 13   9 + 3 = 12   9 + 2 = 11   7 + 7 = 14
 
7 + 8 = 15   9 + 5 = 14   9 + 8 = 17   7 + 5 = 12   2 + 9 = 11
 
9 + 7 = 16   8 + 7 = 15   5 + 6 = 11   8 + 3 = 11   8 + 8 = 16
 
9 + 0 = 9   8 + 0 = 8   0 + 6 = 6   0 + 3 = 3   0 + 0 = 0

The multiplication table


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