In the previous worksheet, we saw that calculations in columns can be problematic and lead to errors. The "rule" that was provided is the common way that this is taught. But this is not the only way to think about doing this calculation in columns. We’re going to explore this in a different way.
Rather than working with digits, we will work with values. We will look at the calculation \(-53 + 27\) again, but rewriting the calculations using expanded form. From here, it is much easier to perform the calculation while avoiding errors.
Using the expanded form version of writing the calculation, calculation \(42 - 76\text{.}\)
2.
What this is showing is that the calculation can be performed if we focus on individual place values. Upon a deeper investigation, this would also reveal that the real issue comes down to the steps of "carrying the one" or "borrowing." The digit manipulations that one might normally do are incompatible with the algorithms for addition or subtraction in columns. Here are two of the most reasonable attempts at performing this calculation using the traditional algorithms.
As best as you can, try to explain the conceptual errors of each attempt.
