Primary Mathematics
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## Adding two single digit numbers

Adding single digit numbers is done according to the table below. To add two single digit numbers, find one number in the first row and one number in the first column of the table. You will find the sum where that row and column intersect. These sums follow a regular pattern and are quite easy to remember with a little practice. Knowing these sums is the first step to mental arithmetic.

+ 0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 10 11
3 3 4 5 6 7 8 9 10 11 12
4 4 5 6 7 8 9 10 11 12 13
5 5 6 7 8 9 10 11 12 13 14
6 6 7 8 9 10 11 12 13 14 15
7 7 8 9 10 11 12 13 14 15 16
8 8 9 10 11 12 13 14 15 16 17
9 9 10 11 12 13 14 15 16 17 18

To add multiple digit numbers, use the following procedure.

1. Start at the right-most digit in each number.
2. Add the right-most digit of each number as though they were single digit numbers.
3. If the sum of those digits is 0 to 9, that is the right-most digit of the answer.
4. If the sum of those digits is 10 to 18, the right-most digit of this sum is the right-most digit of the answer.
5. Move one digit to the left in each of the two numbers you are adding.
6. Prepare to repeat the process with these digits, with one difference. If the sum on the previous round was 10 or more, you will add 1 to the sum of these digits. If the sum on the previous round was 0 to 9, you will not add one to these digits.
7. Repeat the process, moving left each time, remembering to add 1 if required, until there are no more digits to add. For each round, you will find the next digit to the left of the answer.

If you are using pen and paper, write the two numbers you are adding one below the other, aligning the right-most digits. Draw a line beneath the two numbers below which you will write the answer as you calculate it. As you calculate each digit of the answer, write it below the digits of the numbers above. For those rounds where the sum is 10 or more, write the "1" that you will add above the digits of the next round so that you won't forget it.

  26
+ 15
---
41


You now know how to add numbers of any size.

When teaching young students how to add you will need to use physical items to help them understand how addition works, use items that are similar to avoid confusing younger children. It is very important that they understand the number system before trying to add or subtract. The following is an example of how to show a child how to add.

I have two blocks, and Mary has two blocks. If Mary gives me two blocks how many blocks do I have?

First show that you do in fact have two blocks, then show that Mary (or whatever the name of the person is) also has two blocks. Have the children count the number of blocks you have and the number of blocks Mary has.

Have Mary give them two blocks, now have the children count how many blocks they have. You have four blocks and now Mary has zero blocks. Some children may be able to understand addition better if you teach subtraction at the same time, some may notice that Mary has zero blocks while others may not make this connection, this depends completely on each child.

This block example should be done multiple times until every student understands how to add two single digit numbers together, if some students have trouble understanding the concept have them hold the blocks and do the above block example with each other, help them count the blocks they have. You can later increase the number of blocks slightly to help encourage further counting.

When the basic concept of adding has been introduced via a physical method children should be encouraged to learn the combinations of single digit numbers - so that addition no longer relies on counting blocks (or fingers). Especially important for mental subtraction is to learn the combinations of numbers that add to give 10.

When these basics have been taught and before moving on to adding 2 digit numbers children must learn place notation (ie that 25=20+5). Once this is learnt children can progress to adding 2 (and more) digit numbers. It needs to be explained that when you have 10 in the units column you must 'carry' that over to be 1 in the 10s column. Note that this means that 25+97 is MUCH harder than 12+13.

Depending on the child it can be useful to do this in binary as there are far fewer number combinations to remember, though this can confuse some children.

Due to place notation addition is usually carried out right to left:

      1   1
45   45  45
+37  +37 +37
===  === ===
2  82



With the 1 above the addition representing a carried digit.

It is possible to do addition left to right:

 45
+37
====
70
12
====
82