Very young children, learning to count, haven’t yet associated the spoken number with a written one. They also haven’t made the connection between numeral and number of objects.
You may find a child counting 1, 2, 3, 4, 5… while looking at three items. This is to be expected as really understanding a number is a process.
A preschool child will associate number with the numeral.
A first grader will begin learning “fact families” to add the numbers or items of things, together. One way to solidify this skill and help a child to internalize the number, understanding it fully, is to play a guessing game with items in a fact family. I put together an easy game when my own children were small, called “Math Beans.” (It works well with M&M’s too.)
Let’s say you want to teach a combination of facts for the number 7. Take 7 beans (or M&M’s or other item of interest to your child that you can easily hide in your hand). Ask them first, to count the beans.
Once counted, put the beans behind your back and take some of them out of one hand, putting them in the other hand. Bring out both hands and show them what is in one, leaving the other hand closed. Ask them to figure out how many “beans” are in the closed hand. This is a fun game, and after playing with the 7 beans, using several combinations – they should begin to answer more quickly, or know immediately. Once they have mastered all the facts of 7, show them what these facts look like on paper.
7 + 0 = 7
6 + 1 = 7
5 + 2 = 7
4 + 3 = 7
3 + 4 = 7
2 + 5 = 7
1 + 6 = 7
and 0 + 7 = 7.
This would also be a good time to explain the Commutative Law for Addition (though you don’t need to name it yet). It doesn’t matter what order you add the numbers.
2 + 5 will give you the same number of beans as 5 + 2.
By playing interactive math games with your children, they will not only master the material, but enjoy doing it. Learning that is enjoyed is remembered.