I know that made math teachers cringe. LOL. Admit it. But it’s not wrong. If you see students start out at that first step, by dividing through with 2, and you STOP THEM…they think they aren’t allowed to do that.
The truth is, they are!! It’s totally legal! No foul made! No correction necessary!
What’s bothering you is that it’s not efficient. You might even be bothered by the fact that they are creating a fraction they have to deal with unnecessarily. You might be reasoning with yourself that this child is horrible at fractions so he shouldn’t be allowed to create ones he isn’t going to be able to solve.
OMG, can you just stop your brain for a moment?
This child, who may be awful at fractions—which, in my experience, about 80% of adults are too—needs fraction practice and has just made his own fraction problem. Huzzah!! We don’t need to force him into drills. He’s willing to do it himself! More importantly, look how much practice he’s imbedded in this one problem! We categorize these in “Two-Step Equations” and, boy, does that drive me insane. Way to set them up for failure before he’s even started. Why would we ever discourage a child who wants to practice more?
In this example, the child followed all the rules and meandered his way to the correct answer. This should be celebrated. If he doesn’t follow a rule along the way, the rule should be corrected. Ideally, the rule should be corrected with materials…not with you…but I’m getting ahead of myself (see next section).
Slowly, over time, the young child learns where that post is by missing it. Slowly, over time, this child will learn to take shorter paths by practicing them. You can elicit this change by asking for a different way to solve the problems. Make sure to ask this of all children as though it is a game. Because…well…it is!