Are there any situations - not related to school ! - where children might need, do, and perhaps even discover, arithmetic ? Let us assume that the child has acquired rudimentary number language and associated experience. How rudimentary ? Perhaps a few number words, say, from "one" to "ten", the associated finger gestures, and the idea of a normal sequence.
Suppose you are going to sit down for your family dinner. You might ask your young ones whether they could help, may be get the dinner plates (unbreakable ones ! ) from the pantry closet or the dishwasher. Most probably, the first time they do it, they may not resort to counting and so bring too few or too many plates to the table. In that case, you could show them how counting, using the mumbo-jumbo words that they have heard from you before, could help. Perhaps, you could count out all the family members seated at the table and then count out the plates already brought out by the child. The next time, you could show how you would take them out yourself by counting aloud, even saying, this one is for you, then this one for your brother, then this one for Mom, and finally this one for Dad. And the next time count out aloud your family when they are not there, say, sister, one, brother , two, Dad, three, and Mom, four. There, that is all of us. Then follow this out by taking out the plates one by one, saying, this is one, then saying one more - oops !, saying this is two, and so on.
After the plates have been laid out, point out a one-to-one correspondence between the plates and the seated family members. You could also introduce the difference between the cardinal and ordinal aspects of numbers - take out a plate and say "one" and also "first", then take out one more, saying "this is one more", and yes, "a second one", and "now we have two", and so on. You got the idea ? But doing it with the children will require a lot of your patience and perhaps self-control by the older ones who already know all this.
Yes, next go on to the knives, forks, spoons - soup spoons, dessert spoons. What if you require "two" dessert spoons for each member ? So you take out two, and two, and two, and two, so that is twos four times. But hey, they are eight in all. So twos four times make eight. And eight distributed into four - assigning two for each family member - result in two for each. Yes, eight divided by - better, divided among - four results in twos !
What about planning a birthday party ? Plenty of counting, multiplying, dividing to do, before, during, and after the party.
One could introduce the measurement aspect of numbers. Pouring out milk or juice or water into cups or glasses. How may cups can be filled with this carton of juice ? Look, it says "one litre" on the carton, and "100 cc" on the cup or glass. We need pieces of string for playing some game. How long each piece ? Oh, about this long ? But look, there is a "reference" piece of length here, a marked scale or ruler.
What about counting beyond the fingers of your two hands ? Why ? How ?
