Mathematics help: Strategies for word problems

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I am a continuing graduate in the math department at U. Texas at Austin. I have always struggled with word problems in mathematics. The more difficult/specific the sub-field, the more pronounced the trouble isolating the relevant information. If a colleague or professor links the figures to the equations for me, I have no issues with the computations, but I am having a lot of trouble setting up the needed information on my own.

Does anyone have any tips for approaching word problems in mathematics? General thoughts on approaching mathematics and physics are interesting to me and appreciated. Thank you.

Well, I don't know how to help you, but I do know that Aspies have difficulty with word problems because it requires you to integrate both verbal and visual-spatial intelligence. I am a verbal person and I always hated them but I am one of the few Aspies who is terrible at math ever since I needed to learn to multiply.

I have trouble task-switching as well, that is; I am able to think in terms of numbers and equations or to think about things linguistically, but I experience difficulty switching from one mode of thought to another in a small span of time. Is that common to you as well?

This is off topic here, you can disregard if you like: Number sense and verbal ability in human brains are electorally co-determinant (The Math Gene, Devlin), so you're not likely terrible at math. You were probably taught poorly and/or you do not have an interest in it. That's more reasonable than an actual lack of mathematical ability, and either or both would be understandable for an Aspie. I generally don't like people to say they are bad at things.

All I know is that my Verbal IQ is in the 90th percentile and my Visual IQ is in the 40th. The neuropsychologist who examined me said "avoid math" and "take the easiest math you can." She also said I was probably bad at painting, which I am. She actually made me feel a little negative because she made me feel like I'll never drive.

What is a word problem in maths, what I found was that university level maths was just like a gaint spelling bee of random text and greek symbols. As I need pattern in something to be able to recall it later I had a hard time with the maths in my subject.

I never had any problem with math - not regular calculations, not verbal questions (as long as I had them in a written form. I suck at listening). Since I was a child I was making my own math problems to resolve all the time. Stuffs like "How much degree colder must it be for puddles turn into ice?" were on my mind when I was 5 year old. I learned it by myself, just looking at the thermometer behind window everyday - I couldn't read yet (except numbers) but I already could use the thermometer and think out real examples. I was fascinated by math. I could count to 100 at age of 3 and I knew all numbers to 1 000 000 and had the knowledge about Infinity at age 6.

I don't really know how it is when you can't understand the math problem but I guess I can give you some tips that make it easier to resolve. I was using those at physics lessons - the examples were much harder to imagine than simple math, and I never knew the physics formulas so I had to make them by myself from the data available - and I succeed!

I will use a lame example, I know usually the questions are much harder but the method is the same.
Example: "You got two apples and there is four children on the playground. How many would each child get if you give them the apples?"

Short version:
- Read the math problem description backwards (last sentence goes 1st, it tells you what exackly you need to look for) and ask yourself how it translates to math (identify subjects, amounts and operators from the words).

Long version:
1. Read the example once so you get a basic idea whats going on.
2. Reread last sentence (the "?" one, some examples give you some additional tips as last sentence but they are not that important,the "?" sentence is the key).
3. Identify the subjects you need. The "?" sentence gives all tips. (apples, child)
4. Identify the amounts of identified subjects. (2 apples, 4 children) You got your data.
5. Identify what you do. (You want to know how many apples each children gets so you want to share apples between the children) You got your operator.
6. Translate it to math. (amount of apples shared by amount of children)
7. Do the math. (2/4=0,5)
8. Reread "?" sentence again to remind yourself what they ask you for.
9. Translate math to text.. (Every child gets a half of an apple)
10. Does your answer make sense?
- Yes.
Great, problem solved, write the answer down.
- No.
Repeat from step 5 or 6 or rethink steps 8-9, you probably made a mistake there.

Kiriae, your advice was extremely helpful. I just tried the reading backwards approach with good results. Got any advice for approaching interpreting curvilinear graphs? I get frustrated thinking about moving things as pictures, so a good example would be total distance traveled or multivariable derivative visuals.

For example: Basic total distance traveled the derivative of position for velocity. How should I think about that in a way that is useful toward solving the problem? Does that make sense.

Sorry. English is not my national language so I have trouble interpreting advanced English words ("Basic total distance traveled the derivative of position for velocity"? )

But I can give you an example of interpreting the total distance traveled graph and the other one.

Total distance traveled graph <image I found>
- To read "How long distance the thing traveled within 6 seconds?" you point 6 seconds on the time line, move your finger up to the curve than move your finger left till you hit the distance line. Read the amount(9 meters).

- To read "How long did it take to travel 10 meters?" you do the same but start at distance line (point 10 meters), move to curve and go down till you hit the time line. Read amount (6,5seconds)

- Make sure you read the scale right. In this specific image 1 second = 2 squares.

- To check if the thing travels same speed all the time you compare three or more points that differ by a interval (example: 2 seconds).

2 seconds = 1 meter
+ interval 2s
4 seconds = 4 meters, increase from 2seconds = 4-1=3 meters)
+ interval 2s
6 seconds = 9 meters, increase from 4 seconds = 9-4 =5 meters)

As you can see between 4th and 6th second the distance increased by more than between 2nd and 4th second, so the speed increases with time.

You can see it in the curve shape. It goes up slowly at start but gets more and more abrupt (is it right word?) as the time passes.
If the curve wasn't going up all the time you might need to compare more than 3 points.

Multivariable derivative visuals
After googling it I got a little scared since I never had to work on anything like that (my math adventure finished in high school stage). 3d graph...
But after looking at this <picture> I quess I get how to deal with it. However it is not easy to imagine in practice. It requires a lot of visual thinking.

- You need to imagine a 2d graph cutting the picture along a specific amount.

- You deal with the created image as if it was a regular 2d graph. You will get the results for amount you cut the image for.

- To read it you must clap the 2d graph created on the scale on the back(z) and bottom(x), it might be easier if you use a liner and a setsquare (the parallel check trick they teach in elementary/middle school ). The amount of z will be parallel to x line and you can read it on the scale on right side (you might want to copy the numbers from back of picture there) or the scale on the back of image (but it is easy to make a mistake this way) and amount of x will be parallel to z line (and you read it following/paralleling the dots going to x line on bottom).

For example in this case for y=1 the maximum amount of z is 8 (for x =0) and the minimum amount of z is 4 (for x= 2 and x=-2) and the further from x=0 the amount of z decreases faster (can be seen in the line shape).

I hope it makes sense.

I draw everything out as I go. Helps me to convert it from words to pictures. It helps a lot. Good luck!

Rewrite them to be relevant to your special interests. I often can't focus on any that have to do with money or people, so I cross out what's being sold and the people's names and make them items and characters from my favorite shows and video games. "Jennifer and Joe sell candles for $5 each" becomes "The Weasley Twins sell Dungbombs for $5 a bag," etc.

Whatever method you use to obtain the correct answer is correct in my book.

I use what I call "shortening the word problem". That means removing the "clutter words" in the word problem as much as I can, until I have only what's needed to construct a neat equation. For example, you have the original word problem (for an equation system) that goes something like this:
A bookstore had an inventory of 8 bestsellers and 24 classics. One person purchased 12 classics and 3 bestsellers for $84. Another person purchased 12 classics and 5 bestsellers for $100. What is the price of 1 bestseller and 1 classic?

Now, review the word problem. Do you see any extra information that is irrelevant? Anything at all? Think about it: the word problem asks you for the price is 1 bestseller and 1 classic. You are asked for prices. Is the original inventory relevant? No! Get rid of that information, so it doesn't confuse you. Simplify the wording while you're at it. This leaves:
One person bought 12 classics and 3 bestsellers for $84. Another person bought 12 classics and 5 bestsellers for $100. How much is 1 bestseller and 1 classic?

Easier, right? But is it relevant who bought these bestsellers and these classics? It's math. What matters is the numbers. So get rid of the people in the word problem, leaving only the numbers, or in this case, prices. Now, what you have is:
12 classics and 3 bestsellers cost $84
12 classics and 5 bestsellers cost $100

Now, it almost looks like a real equation system. Convert it into one. Change the classics and bestsellers into X and Y.
12x + 3y = 83
12x + 5y = 100

When you solve for X and Y (impossible to do an equation neatly in plain text), you find that x = 5 and y = 8. So, we solved the word problem:
A bestseller costs $8, and a classic costs $5. (Must be a really cheap bookstore, but pretend it's an old textbook you're looking at.)

This method is not my own work. It comes from a foreign-language children's book that a buddy translated for me.

Thanks newtonegg. A little off topic, but I was horrible in math. In high school I took Algebra 1 three times and D- was as high as I got. Strangely, recently I bought several math books and blew through Algebra in about a month of solid work. Math is not the problem. Bad teachers and bad family life is the problem.

About all I know about word problems (I'm bad at them too) is that you can only get certain formulas from certain "boilerplates" that is to say organised paragraphs. Not much help with advanced mathematics here, but I could tell if it is a proportion problem with one variable missing, for instance whether the "story" is about apples and oranges or tacos and buritos.

The first thing I try to do is get rid of words that try to divert or confuse you. I mean who cares if Jenny and Tom are running a race?
Its just X and Y.

Its like parsing a sentance. What's the subject, object, verb, coordinating conjunction. What does the pattern look like? Type A problem is type A formula, type B problem is type B formula.

Oh well that's as advanced as I ever got.