Day 160: Parentheses

Throughout the year, I have felt uneasy teaching students to work with problems involving parentheses. If I gave students something like:

Solve: 3(x + 4) – 8 = 16

A large number of students would subtract 4 at the incorrect time in the problem. Over the last two years of teaching I haven’t come across a way to address this problem… Until today.

We were working with solving quadratics by square roots. After a bit of scaffolding, I posed students with this problem.

Quite a few of them wanted to subtract 13 first. I put on the breaks and asked them “If we knew what x was, say 5, how would you simplify the expression?”

We wrote a list of the order to simplify things:

2. Square that number (Exponents)
3. Divide by 2

We then talked about how solving equations starts at the bottom of this list and uses inverse operations to undo whatever is happening. So to solve for x:

1. Multiply by 2
2. Square root
3. Subtract 13

They seemed to catch on after this point. It seems like a simple strategy, but I had never really thought it this way. I always talked about solving equations as a process of working your way from the outside in.