Chapter 6.3, Problem 24P

* A student calculates $6998÷7$ as follows, and concludes that $6998÷7=1000-1,$ remainder 5, which is 999, remainder 5:
$\begin{array}{l}-1\\ 7\begin{array}{c}\hfill 1000\\ \hfill \overline{)6998}\end{array}\\ \underset{\_}{-7000}\\ -2\\ \underset{\_}{-\left(-7\right)}\\ 5\end{array}$
Even though it is not conventional to use negative numbers in a scaffold, explain why the student's method corresponds to legitimate reasoning. Write a simple word problem for $6998÷7$ , and use your problem to discuss the reasoning that corresponds to the scaffold.