Quandaries
and Queries 

Question: Assume a child does not know what multiplication and division are. Assume the child knows how to count from 0 to 10 How do you explain that 2, 4, 6, 8 and 10 are even numbers And 1, 3, 5, 7 and 9 are odd numbers And these three facts?
Can all of these be reasoned out, without using the concepts of multiplication or division? name: Martin 

Hi Martin, I taught primary grades for many years. I taught about even and odd numbers by talking about sharing. As an example, if you and your granddaughter are sitting at the table sharing some candies or cookies, what are the numbers of cookies such that when you share them equally, there are none left (one for you, one for me, ......). The numbers which give a left over are the odd ones. By writing the numbers down and as the child increases her knowledge of numbers, she can "discover" a pattern (0, 2, 4, 6, 8) (1, 3, 5, 7, 9) in the last digit. Having "discovered" these things, she may, at a later time, also "discover" the other facts. If she knows that 4 cookies are even because there are none left over when she share with you, and 6 cookies are even, what do you think happens when we put these 2 groups of cookies together. She may add and come up with 10, which she knows by then is even. But she may also think that if 4 cookies are shared and none are left over, then 6 cookies are shared, and none are left over, then (without knowing the answer '10') she may deduce that grouping these cookies would also make an even number. By similar reasoning, she may also come to "discover" the other 2 facts. I use the word "discover" to indicate guided discovery. Also take into consideration that there is a lot of discovery involved in all of this and depending on the child may take more or less time than you think. I hope this was of some help. Good luck, this is the kind of voyage we wish every child could take in each classroom! Let us know how it worked out! Diane 

