Decomposition

We use the "decomposition algorithm" to teach subtraction. Decomposing means breaking down. Initially children learn using concrete materials; physically changing one hundred into ten tens or a ten into ten ones. Only when they are secure with this method do we move on to written sums.

When we subtract 123 from 987, what we are really doing is subtracting each place value separately. We look at the problem

this way: or this way:

 
 
       987            9 hundreds   8 tens   7 ones
      -123           -1 hundred    2 tens   3 ones
       ____           ______________________________

That is pretty easy to solve. Three from seven leaves four ect.

 
But what about this one: 907 - 123. We write the sum like this;
907
-123
4 Three from seven leaves four
Now, two tens from zero we cannot take, so we "exchange":
907 WE exchange one of our hundreds for 10 tens. That works because 8 hundreds 10 tens and 7 ones is the same thing as 9 hundreds 0 tens and 7 ones.

8 10 7

 
-1   2 3  Now we can complete the sum in the usual way.
 

8 10 7

 

-1 2 3

 
7 8 4 Three from seven leaves four.
 
Two from ten leaves eight.

One from eight leaves seven.

We encourage the children to check their answer by adding;
123 + 784 = 907