# Math textbook stupidity **URL:** \ **Category:** Factual Questions\ **Created:** [December 16, 2004, 5:29pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179 "2004-12-16T17:29:03Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [December 16, 2004, 5:29pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/1 "2004-12-16T17:29:03Z")
My son is in 7th grade. I was checking his math homework the other day, and came upon this question: The temperature yesterday was -5 degrees C. Today, the temperature is -20 degrees C. How many times colder is it today than it was yesterday? **AAAAAAARRRRGH!** I sent a note with the homework to the teacher saying (in essence), my son’s answer to this question was 4. That’s probably what the textbook publisher was looking for. But it’s _wrong_! Completely and utterly wrong! For the concept “four times as hot” (or cold) to have any meaning, it must take energy levels into consideration. If the temperatures had been listed in degrees Kelvin, I probably wouldn’t have said anything, but -20C is simply not four times as cold as -5C. Okay–I posted this in GQ instead of the Pit for a reason. Can any of you come up with any justification for this question, or am I right that it’s simply meaningless drivel that some poor physics teacher is going to have to “un-teach” sometime down the road? (I know—can you spell “anal retentive”?) ---
**Author:** ![robcaro](https://avatars.discourse-cdn.com/v4/letter/r/df705f/32.png) [@robcaro](https://boards.straightdope.com/u/robcaro)\ **Post date:** [December 16, 2004, 5:39pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/2 "2004-12-16T17:39:21Z")
And what was your answer? My calculator says that the answer is 4. ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [December 16, 2004, 5:43pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/3 "2004-12-16T17:43:22Z")
Yes, it’s a stupid question, because it depends on the temperature scale. In Fahrenheit, the two would be +23 and -4. How many times colder is -4 than +23? In Kelvin, the two would be +268 and +253. How many times colder is +253 than +268? ---
**Author:** ![Inigo\_Montoya](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inigo_montoya/32/124_2.png) [@Inigo\_Montoya](https://boards.straightdope.com/u/Inigo_Montoya)\ **Post date:** [December 16, 2004, 5:43pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/4 "2004-12-16T17:43:40Z")
I know Montana is right next to Canada, but its still in the US, right? Why is a 'merkin textbook discussing Celcius? That’d be my answer. -5 x 4 is -20 The publisher was probably just thinking “how many points away from zero is that?” Yeah, the relative energy involved is not the same thing…let’s just hope the same kind of assumptions are not made in Biology class. ---
**Author:** ![asterion](https://avatars.discourse-cdn.com/v4/letter/a/4da419/32.png) [@asterion](https://boards.straightdope.com/u/asterion)\ **Post date:** [December 16, 2004, 5:44pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/5 "2004-12-16T17:44:57Z")
Lessee. Convert to Kelvin for an absolute zero scale, so we’ve got 268 K and 253 K. Assuming you do 253/268 (what I’m assuming is that you did 20/5), that comes out to 0.944029851 plus some more digits if you want to take it out even more absurdly far. That’s a temperature change of what, six percent? ---
**Author:** ![Nametag](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nametag/32/406_2.png) [@Nametag](https://boards.straightdope.com/u/Nametag)\ **Post date:** [December 16, 2004, 5:57pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/6 "2004-12-16T17:57:21Z")
> [@InvisibleWombat](#): > > My son is in 7th grade. I was checking his math homework the other day, and came upon this question: > > The temperature yesterday was -5 degrees C. Today, the temperature is -20 degrees C. How many times colder is it today than it was yesterday? > > **AAAAAAARRRRGH!** Richard Feynman had the same reaction while reviewing textbooks – his example was asking students to calculate the average temperature of a bunch of stars. Math textbooks are written under pressure to include word problems from which students have to extract the necessary information. They don’t seem to mind if the situation is impossible, or the problem makes no physical sense. Feynman’s wife likened it to living over a volcano – he worked in the basement, and would periodically erupt. ---
**Author:** ![mks57](https://avatars.discourse-cdn.com/v4/letter/m/b9bd4f/32.png) [@mks57](https://boards.straightdope.com/u/mks57)\ **Post date:** [December 16, 2004, 5:58pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/7 "2004-12-16T17:58:45Z")
> [@robcaro](#): > > And what was your answer? My calculator says that the answer is 4. It’s a meaningless question. As posed, it has no answer. Temperature measurements can’t be treated like other common measurements, unless you use an absolute scale like Kelvin or Rankine. ---
**Author:** ![vetbridge](https://avatars.discourse-cdn.com/v4/letter/v/b5e925/32.png) [@vetbridge](https://boards.straightdope.com/u/vetbridge)\ **Post date:** [December 16, 2004, 6:09pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/8 "2004-12-16T18:09:05Z")
It’s not the heat, it’s the humidity. ---
**Author:** ![Tyrrell\_McAllister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tyrrell_mcallister/32/16772_2.png) [@Tyrrell\_McAllister](https://boards.straightdope.com/u/Tyrrell_McAllister)\ **Post date:** [December 16, 2004, 6:10pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/9 "2004-12-16T18:10:10Z")
> [@robcaro](#): > > And what was your answer? My calculator says that the answer is 4. Suppose I said, “Jack is 5 inches shorter than 6 feet, and Jill is 20 inches shorter than 6 feet. How many times shorter is Jill than Jack?” Do you think it makes sense to say that Jill is four times shorter than Jack? ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [December 16, 2004, 6:11pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/10 "2004-12-16T18:11:59Z")
Yeah, it’s stupid, but if you have a scale with a zero point on it, people are going to do this sort of thing, whatever the underlying physical motivation of the scale. They really mean “By what factor is today’s temperature further below zero on the Celsius scale than yesterday?”. In casual use, the arbitrary zero point winds up separating “hot” from “cold” in people’s minds, meaningless as that might be. The textbook still shouldn’t reinforce it, and I’d say it’s a bad question. I’m curious about something else - it’s a word problem to motivate an exercise in simple arithmetic, making sure the student knows how to handle negative numbers. 7th grade? It’s seems more like an elementary school level problem, doesn’t it? ---
**Author:** ![Tyrrell\_McAllister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tyrrell_mcallister/32/16772_2.png) [@Tyrrell\_McAllister](https://boards.straightdope.com/u/Tyrrell_McAllister)\ **Post date:** [December 16, 2004, 6:27pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/11 "2004-12-16T18:27:26Z")
> [@yabob](#): > > I’m curious about something else - it’s a word problem to motivate an exercise in simple arithmetic, making sure the student knows how to handle negative numbers. 7th grade? It’s seems more like an elementary school level problem, doesn’t it? I expect that the point is not to re-enforce basic arithmetic skills, but rather to learn how to apply those skills to real-life situations. This makes it all the more tragic that it is incorrect to apply those skills in the manner that the textbook expects. ---
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [December 16, 2004, 6:38pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/12 "2004-12-16T18:38:28Z")
> [@yabob](#): > > I’m curious about something else - it’s a word problem to motivate an exercise in simple arithmetic, making sure the student knows how to handle negative numbers. 7th grade? It’s seems more like an elementary school level problem, doesn’t it? At the end of each section, they have word problems tying what they’re doing to what they’ve already learned. Right now, they’re working on operations involving negative and positive fractions. Seems to me I got that stuff in 4th grade or so, but I can’t remember… ---
**Author:** ![asterion](https://avatars.discourse-cdn.com/v4/letter/a/4da419/32.png) [@asterion](https://boards.straightdope.com/u/asterion)\ **Post date:** [December 16, 2004, 6:44pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/13 "2004-12-16T18:44:46Z")
Now that I think about it, shouldn’t it be 1.06 times colder? In Kelvin, of course. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [December 16, 2004, 7:03pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/14 "2004-12-16T19:03:54Z")
> [@Tyrrell McAllister](#): > > Suppose I said, “Jack is 5 inches shorter than 6 feet, and Jill is 20 inches shorter than 6 feet. How many times shorter is Jill than Jack?” > > Do you think it makes sense to say that Jill is four times shorter than Jack? Or better yet, in keeping with the spirit of the question, try different numbers to see how much sense this makes: **The temperature yesterday was 0 degrees C. Today, the temperature is -20 degrees C. How many times colder is it today than it was yesterday?** -20/0 = undefined. **The temperature yesterday was 5 degrees C. Today, the temperature is -20 degrees C. How many times colder is it today than it was yesterday?** -20/5 = -4. So it’s -4 times colder than it was yesterday or 4 times _hotter_ than it was yesterday. WTF? **The temperature yesterday was 100 degrees C. Today, the temperature is 0 degrees C. How many times colder is it today than it was yesterday?** 0/100 = 0. Today it’s 0 times as cold as yesterday. Huh? The question makes no sense. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [December 16, 2004, 7:12pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/15 "2004-12-16T19:12:30Z")
> [@Tyrrell McAllister](#): > > Suppose I said, “Jack is 5 inches shorter than 6 feet, and Jill is 20 inches shorter than 6 feet. How many times shorter is Jill than Jack?” > > Do you think it makes sense to say that Jill is four times shorter than Jack? Well, it could be said that Jill is four times shorter than 6ft than Jack is shorter than 6ft. If they were 6 foot yesterday and Jill had been hit by four times as many mallets as Jack since it’d even make sense. But ‘colder’ is still stupid because it encourages sloppy thinking, never does make sense, and is AT BEST very ambiguous and misleading, and IN ALL EXAMPLES I’VE EVER SEEN flat out wrong. > [@asterion](#): > > Now that I think about it, shouldn’t it be 1.06 times colder? In Kelvin, of course. Nitpick: the scale doesn’t matter (so long as it starts at 0). ---
**Author:** ![Tyrrell\_McAllister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tyrrell_mcallister/32/16772_2.png) [@Tyrrell\_McAllister](https://boards.straightdope.com/u/Tyrrell_McAllister)\ **Post date:** [December 16, 2004, 7:29pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/16 "2004-12-16T19:29:51Z")
> [@Shade](#): > > Well, it could be said that Jill is four times shorter than 6ft than Jack is shorter than 6ft. yesbut (1) that isn’t what was asked, and (2) it could also be said that -20 degrees C is four times colder than 0 degrees C than -5 degrees C is. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [December 16, 2004, 7:30pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/17 "2004-12-16T19:30:01Z")
> [@InvisibleWombat](#): > > Okay–I posted this in GQ instead of the Pit for a reason. Can any of you come up with any justification for this question, or am I right that it’s simply meaningless drivel that some poor physics teacher is going to have to “un-teach” sometime down the road? Yes: drivel. What’s the title and publisher of the book? ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [December 16, 2004, 7:32pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/18 "2004-12-16T19:32:59Z")
> [@yabob](#): > > Yeah, it’s stupid, but if you have a scale with a zero point on it, people are going to do this sort of thing For those who care about this sort of thing, it’s a distinction between the _vector_ space **R** and the _affine_ space **R** , which most calculus books also screw up. The distinction is only clearly drawn post-calculus in most people’s experience. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [December 16, 2004, 8:51pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/19 "2004-12-16T20:51:12Z")
Here’s a gem from my nephew’s junior high school science textbook (about 8 years ago): Underneath a large photo of an astronaut doing a tethered spacewalk from the Shuttle was this caption: “As you get further from the center of the earth, the earth’s gravity decreases until, in outer space, you are weightless!” The mind boggles. ---
**Author:** ![spingears](https://avatars.discourse-cdn.com/v4/letter/s/ebca7d/32.png) [@spingears](https://boards.straightdope.com/u/spingears)\ **Post date:** [December 16, 2004, 9:02pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/20 "2004-12-16T21:02:45Z")
WAG? The textbook publishers have to have “reasons” to revise and update textbooks every year or so and hence include stupid questions to justify the updates? The aurthor(s) were brought up in government schools & universities? [Next page](https://boards.straightdope.com/t/math-textbook-stupidity/280179.md?page=2)