Being flexible about division

<p dir="ltr">I recently saw a child trying to work out 45 divided by 5. They wrote: 5/<del>4</del> ⁴5 saying, “Five into four is zero, remainder four. Five into forty-five is …” – and they didn’t know. Indeed, if they had known this, then perhaps they wouldn’t have been using this short-division method. The method was just returning them to the same question that they started with. The method is supposed to help you with large numbers by breaking up the number into separate digits, so why doesn’t it work here? This problem always arises whenever a (single-digit) divisor is greater than the leading digit of the (two-digit) dividend (Figure 1). Applying the method merely reproduces the original division. It seems as though you have to go about it some other way, such as skip-counting up in 5s from 0 to 45, or doubling 45 and dividing by 10. (cont.)