If I see things like 12 - 6 for Problem 4 or 10 for Problem 5, then I know that students are not thinking about using an unknown and are using their actual ages.

I ask students which value should come first in the expression, the 4 or the n. We could use the division symbol, or we could use the fraction bar. Many students struggle that these phrases are represented by n and not 12 — n, the way that the values appear in the phrase.

I stress that the order of the variable and the number matter for division and subtraction.

Problem 23 will confuse some students, because the expression will be 6 - I then show students the different ways to represent those expressions parentheses, dot, fraction bar, etc. I find that students enjoy sharing out these goals — it is a way for them to be held accountable by their teacher and peers.

Palmer has n dollars.

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