Addition boils down piles of 10's
There are just a five single digit combinations that add up to 10.
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
These combinations are important for children to know because you can quickly add up huge stacks of numbers very quickly by breaking it down into combinations of 10.
Let's add this stack of numbers;
145786
234568
456893
245985
345677
+ 985414
867122
It looks frightening as a full stack of numbers but Lets look at it line by line. Starting from the 1’s place. The first row is:
6
8
3
5
7
+ 4
2
In this row how many combinations of 10 can you find?
6
8
3
5
7
+ 4
2
There are three combinations of 10 in this stack with one lone 5 left over.
Cross out the combinations of 10, keeping track of each 10.
5 lll
+ 4
5
Each combination of 10 reveals a number that belongs in the 10’s spot. It’s usually called carrying over but I think it can be better understood as 10’s that belong in the 10’s spot.
By eliminating the 10’s there is only 5 that remain in the 1’s spot.
Next let’s look at the 10’s spot.
3
86
68
93
85
77
+ 14
22
5
Notice I have added the three on top. This is the three 10’s that were in the 1’s spot but belong in the 10’s spot.
3
8
6
9
8
7
+ 1
2
In this row there is a left-over combination that when added together equals more than 10 add this number together.
8 + 6 = 14
Now take the 10 and add it to the others and leave the 4 in it’s place.
3
8
6
9
8
7
+ 1
2
4
In the next row there are only two combinations of 10. But lets look at the 7, 8 and 5. In order to make combinations of 10, the 7 wants a 3 and the 8 wants a 2. Since 2 + 3 = 5 we can easily find two more 10 combinations in this row.
4
7
5
8
9
6
+ 4
1
4
The next row there are 3 sets of 10’s with 7 and 4 left over 7 + 4 = 11 add a 10 to the list leaving one in the row.
4
4
5
4
6
5
5
+ 5
7
1
Check out the next row:
4
4
3
5
4
4
+ 8
6
This row is a bit more complicated but still simple once you get the hang of thinking in 10’s. First pick out the simple ten combination. there are many combinations that add up to 8. The 8 wants a 2 and there are two 2’s in a four 2 + 2 = 4. Look at how many numbers can be eliminated still thinking in 10’s. 5 + 3 = 8 and 4 + 4 = 8 then adding 2’s in 4 makes more two tens.
4
4
3
5
4
4
+ 8
6
It takes time to get the hang of it but when you do it saves a whole lot of time and energy!
Happy Adding!
3 4 4 4 3
1 4 5 7 8 6
2 3 4 5 6 8
4 5 6 8 9 3
2 4 5 9 8 5
3 4 5 6 7 7
+ 9 8 5 4 1 4
8 6 7 1 2 2
3 2 8 1 4 4 5
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