4timesless I’ve seen a few instances where instead of writing “you’ll use 1/4 the amount” the ad states “4 times less.” This practice may be getting more common, but it’s bad math and ambiguous English. Say, for example, I have 4 slices of pizza. You have one. When using addition or subtraction for a comparison, I have 3 more slices than you, and surly, you have 3 fewer. Multiplying doesn’t work the same, I have 4 times the pizza you do, and you have one fourth as many as I. To say you have four times fewer makes no sense.

Do you have any similar examples? Send them in. Just hit “submit an example” above.

boardcuts I saw this online a couple years ago, and saved the image. It was posted on Stack Exchange as
A “simple” 3rd grade problem…or is it? by the member with username Enigma.
What’s disturbing here is that the student got the question right. And I suspect many, or most of the students produced the same wrong answer the teacher expected. Do you see the issue?

If I were the student…. pause, I am 50+, but I remember grade school vividly. The school I went to did not have teachers for single subjects. Up till 8th grade, it was one teacher all day. Math was my passion, but not hers. I learned how to politely point out errors, made by either teacher or the published materials we used. Now, the clarifying moment  would come by asking the teacher to continue the chart she produced. “5=1 pieces”? No, you don’t cut for 5 minutes for 1 piece. It’s there at 0 time.

  • 0 min = 1 piece
  • 10 min = 2 pieces
  • 20 min = 3 pieces

The source of this misunderstanding is twofold, the 10 minutes is one cut, it’s the same time to go from 5 pieces to 6. Second, the teacher should not have insisted, but should have used further analysis as I did to better understand the relationship between variables.


This was the text that came in an email I received today. It falls into the category of minor mistakes, but big enough to catch my eye. 10 apps at $10 is $100, 80% off is $20, anything lower is “more than” 80% off, not “nearly”.  Not a big deal, but a copy editor should catch this.

I spend 2 days a week working for the math department at a local high school. One day, I was working with a student who was using the equation for a falling object, h=16t^2, and she was calculating the time for a rock to fall off a very tall building. The student used her calculator and the answer was 884 seconds. Hmmm. I asked her if she was certain of her answer. She pointed to the calculator, and there’s the number. Calculators are never wrong.

I asked, “how many seconds in a minute?” 60, of course. How many 60s in 884? No calculator, just round it, 60 into 900 is 6 into 90, or 15. 15 minutes. It hadn’t sunk in yet. So I keep pushing. “You see your friend wave, at the top of the Empire State Building. She drops a baseball. You go into a Starbucks, buy a coffee, stop in the restroom, and come back 14 minutes later, to see the baseball still falling? She responded, “Ok, now you’re making fun of me.” Perhaps, but at the moment for me was the disconnect between the word problem and the numbers. I think there’s a skill worth teaching, estimating the expected answer in a way that would help prevent such gross errors. The correct answer was 8.84 seconds for a 1250 ft tall building. I’d hope a student would be able to take a moment and say she expects a range between say, 5 and 15 seconds.

John Quiggin has a blog with the tag line “Commentary on Australian & world events from a social-democratic perspective,” offering intelligent discussion on a mix of political and economic topics. This particular article, Two Billion Examples of Innumeracy, discusses the notion that 2 billion people would be watching the British Royal Wedding. It doesn’t take too much logic to look at the world population and realize that 2 billion is an absurd number. Over 1/4 of the world is living without electricity, and when you continue looking at the facts, it comes down to some sub 500 million number. One web site put the final number at 300 million or so. In line with John’s estimate of 250M as a high end number.

What’s important here isn’t getting the number accurate to 1% or even 10%. It’s being off by a factor of 7 that’s so unsettling. Estimating large numbers with a 50% accuracy has its place, and this is one example of the media getting it so wrong.