Transitioning to Abstract Thinking

In 8th grade, we're learning how to solve one and two step equations. The students are fairly good with the solving, though some are still rusty with their adding and subtracting integer skills. As an extension of the one and two step equations solving, we did word problems. They're nothing special; I just pulled them straight from the book. But what I've noticed is that students know how to solve them, but they have trouble seeing how to write the problem as an equation. I don't fault them for this - it's a big leap conceptually. And we haven't even done any work on what equations really mean. My struggle is that I don't know how to help them on their journey from knowing how to answer the problem to knowing how to write the problem as an equation. They're focused on the answer, so the extra step of writing it as an equation seems like a burden.

Here are some examples of their work:

 

I showed a couple of students how to work backwards from their solution to writing an equation. For example, if they know that to get the answer they need to subtract 5 and then divide by 2, I said that the equation will have the opposite - it will have addition and multiplication. That was enough to help a couple of them figure out how to write the equation. I know there's an inverse relationship between the solving and the equation, but I don't know how to teach it without confusing the heck out of some of them. The few that I showed this to, I showed during the quiz, actually. (I know many might disagree, but I often use assessment time as teaching time. I have their full attention then and they get the one-on-one instruction that many of them need.)

Now that I've graded their quizzes, I know they still need work on this. Tomorrow they're going to go through and correct their mistakes, and it might be a good time to show them the relationship between their intuitive steps for solving a problem and the written expression of the equation.