Multi-Step Arithmetic Word Problems

A three-step problem has three places to go wrong: a wrong operation, a wrong order, or a right computation that answers the wrong question. That last one is the silent killer. You can do every step correctly and still pick the wrong number to circle, because the problem never asked for 'the total' — it asked for the change, or the difference, or the time including stops. A hard equation fails loudly, with a number that clearly doesn't work. A word problem fails quietly, with a number that looks perfectly reasonable and is simply not what was asked.

Before computing, underline or restate the actual target in your own words: 'I need the change from 50,' not 'I need the cost.' Then list the steps in the order the situation actually happens — discount before tax, driving time before adding stop time — and check after each one whether that step's result is the final answer or just an ingredient. Many problems are built so the natural last computation (the total cost, the driving time alone) is one step short of or one step past what's wanted.

This sits right next to rate and percent problems because those are the ingredients, not the topic itself. A discount-then-tax problem is just two percent calculations chained together; a drive-with-stops problem is just distance-over-speed plus added minutes. The new skill here is sequencing and target-checking, which is also exactly what two-worker rate problems demand: you compute each worker's rate, combine them, and still have to ask what quantity the question actually wants from that combined rate.