Primary mathematics/Adding numbers

Adding two single digit numbers
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, 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 you two blocks, now have the children count how many blocks you 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.

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 combitations to remember, though this can confuse some children.

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

45 +37 === 82 ===  1

With the 1 underneath representing a carried digit.

It is possible to do addition left to right:

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

(adding the tens first).

Children taught this way will usually work out for themselves the shorter way of writing it out.