Math Word Problems and Stress Management

My 13yo girl is good at math, though she is quick to get discouraged. There’s something about the “hard” sciences that brings that out in a lot of people, students and parents alike. My theory is that it’s to do with the right or wrong nature of the work. History is open to interpretation, composition is strongly influenced by your imagination and writing style and physical education, well, if you can throw a ball…

But math is hard and lots of kids get flustered trying to solve problems. Parents often being poor at math and therefore unable to help or explain doesn’t help matters much either, but the reality is that if a math teacher does the classic “teach to the middle” strategy, the bright kids can be kept busy with extra credit problems but the kids who aren’t keeping up just fall further and further behind. Eventually too many kids just give up and an unfortunate preponderance of them are girls. Interestingly, the National Institutes of Health report that “women earn 45% of the undergraduate degrees in mathematics but women make up only 17% of university faculty in mathematics”.

Perhaps more surprisingly, the same research reports that “the stereotypes about female inferiority in mathematics stand in distinct contrast to the scientific data on actual performance” so I need to be careful with my comments about math ability and gender. Regardless, all of my children have wrestled with mathematics, and my youngest is definitely hot and cold with the subject.

And sometimes she’s very cold indeed, like when she read this problem on a recent worksheet:

math word problem, rates

To be honest, I would have likely been intimidated when I saw this problem if I was in middle school. K- certainly tried to understand it by herself, got flustered, and refused to go further. Here’s how it went:

Her: I don’t get it. Can you explain it to me?

Me: Okay. Let’s sketch out what’s going on in this problem.

Her: I already did that and it’s useless.

At this point I ignored her protests and just pulled out an envelope to start drawing the facts and information presented in the problem. Here’s what that envelope ended up being, a literal “back of the envelope” solution:

word problem solved on back of envelope

The critical concept to understand with all these type of problems is the formula:

rate x time = distance

With that, I told her, you can solve for any one of the variables by knowing the other two. I then just kept sketching and asking her questions…

Me: What’s the difference in speed between the police car and the bad guy?

Her: 15mph

Me: Is it true that the bad guy is the further ahead he’ll be until caught when the cop just crosses the bridge?

Her: Yeaahhhhh

Me: So how far ahead is the bad guy at that moment if he’s going 60mph and has had a what head start?

Her: 12 minute head start. At 60mph that means he’d have gone 12 miles.

Me: Right! So isn’t this question really about “how long does it take to go 12 miles at 15 miles per hour”?

Her: (with dawning comprehension) Oohhh, yeah, okay.

Me: And using our original formula, that time is from the formula rate x time = distance, or, in this case time = distance / rate.

Her: (calculating) I get 0.80.

Me: 0.8 what?

Her: Um… 0.8 hour. How do I convert that to minutes?

Me: How do you convert 80 / 100 to something / 60? What about four-fifths of an hour?

Her: (calculating) 48 minutes!

We carried on in this vein and as we proceeded I could see that each correct answer removed a brick from the heavy backpack of her anxiety and concern about math. By the end she was prompting me with ideas about how to solve specific parts of the problem and I was simply reminding her my rule of thumb with all math problems: ballpark the answer so you can reality check what you calculate.

Teaching a hard science is difficult because you can’t really sugar coat the reality of formulas, calculations and mathematics. But being able to listen to your child, be candid about whether you are good at these problems or they intimidate you too, and then calmly going through the steps needed to solve a math word problem like this can be darn satisfying for all involved.

Now, you do the math and you tell me, how far and at what time does the cop catch up with the bad guy?

3 comments on “Math Word Problems and Stress Management

  1. I love your post. I am having similar issues with my 8 year old kid, but they are about division and multiplying 2 large numbers.

    So… Hmmm… You already gave the answer. I’m showing my work.

    i converted mph to mpm (robber goes 1 mpm, cop goes 1.25 mpm)

    12 +x minutes=5/4(x)minutes
    = 4(12 +x)=4(5x/4)=
    48 +4x=5x
    48 +4x -4x =5x-4x
    48 minutes from 9:49=10:37 pm
    So it’s 60 miles from the bridge (because at 10:37 both cars would have gone 60 miles)

    I feel like there is a more elegant way to solve this problem, but I don’t know what it is.

    • Yeah, I thought about us switching to miles/minute but since switching units seems to be a classic challenge with these sort of problems, I now try to avoid doing so as much as possible and instead converting things to a shared and consistent unit. We have mph as our rate, so we just stuck with that. Plus then it’s not so easy to forget to convert back!

  2. At the point when they meet, they will have travelled the same distance.
    Robber has 12/60 hrs extra time, though.
    Cop: 75mph times H hrs = __ miles
    Robber: 60mph times H hrs plus 1/5hr times 60mph = __ miles
    75H=60H+(1/5 * 60) hrs
    75H=60H+12 (subtract 60H from both sides)
    H=12/15 hrs — (normalize) –> 4/5 hrs or 0.8hrs or 48min
    Plug H hours back into both equations to verify that they match.
    0.8hr * 75mph = (calculator) 60miles
    0.8h * 60mph + 1/5hr * 60mph = 48miles + 12miles = 60miles

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