We here at the MathMistakes world headquarters got today’s mistake via email submission:

Question: If you are driving 60 km/h, how far would you go in 20 minutes?

Student’s answer: 1200 km

Since we don’t have much to work with, in terms of diagnosing the students’ error, let’s do two things in the comments today. First, leave a note if you have about the specific question and student answer. Second, let’s use the comments as a place to discuss strategies for helping students form an intuition for rates.

## 5 replies on “Rates”

It is clear that the student has made a mistake of assuming that he can use the come,a distance = speed x time.

What he has not realised is that there is a mismatch of units. In order t help the student you would have to point out that currently the person is traveling a certain distance every hour. Has the traveller travelled for a whole hour, he has not had the chance to travel 60km yet. The answer would have t be smaller, what could you do from there

I think that using the various models for rates (that CCSS standards specifically state) — such as double number lines and ratio tables — can help students make sense of problems like this. With a double number line, for example, putting miles on one line and hours on the other, I think that the use of different units would become apparent quickly. If you take this problem and expand to look at what other times/distances could be traveled at the same rate of speed, you’re building that proportional reasoning that may make misconceptions like this one less likely to happen.

I try to have my kids estimate their answers first before doing the arithmetic. I would ask, “If your rate or speed is 60 km per hour, then how far did you travel in half an hour?” Then, “How many minutes are in half an hour?” I just left a comment on the latest post (solving equations with fractions) about reasonableness of an answer. It’s so important for us to teach kids to check their answers as the last step. Many kids are perfectly happy with boxing up a ridiculously incorrect answer!

Move to a different domain and illustrate with an example he can relate to more easily. For example, you can eat 60 apples an hour, eating at a steady pace. How many can you eat in 20 minutes? He’d realize it would be less than 60, and start looking at the units on his own. If he didn’t, I’d ask him to pay attention to the units.

The student might have simply misread the problem as “how far would you go in 20 hours?”