Write, read, and evaluate expressions in which letters stand for numbers.
Suppose we have two types of measuring tools. The first, measures 1 cm, and the second measures \(x\) cm. Now suppose there is some length we wish to measure, and it just so happens that the length is not a whole number. We find that by placing some number of \(x\) cm lengths, and some number of \(1\) cm lengths, that we reach a more precise measurement. Teaching measurement with an unknown unit of length would be interesting, because it frames variables somewhat concretely, as an unknown unit of measure. We could provide problems which give results of \(ax + b\) and \(ax - b,\) where \(a\) and \(b\) are whole numbers.