each作为形容词,修饰单数名词,接单数动词.作为代词,单独使用,接单数动词；放在复数名词和代词后作同位语,接复数动词.each of them后可接单数或复数动词.如：
Each man carries his own bag.（修饰单数名词）各人背自己的包.
We each have our own office.(作We的同位语)我们各有各的办公室.
Each carries his own bag.(代词)各人背自己的包.
Each of them are/is here.(代词)他们每个人都在这儿.
本题中the children是复数,所以用have