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Need help with input / output tables
Old 08-24-2012, 11:00 AM
 
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I'm hoping one of you math teachers can help me out... Last year in 7th grade pre-Algebra, my son struggled with data tables ( or are they called input / output tables ? ) and now they're showing up again in Algebra. He understands how they work, and the x / y relationship, but has a really hard time trying to write a formula to represent the relationship. And unfortunately, I'm not strong enough in math to help him with this particular type of problem. Here is an example of one :

Number of Hours______Distance Traveled
1 ______________________55 mi.
3 ______________________165 mi.
5 ______________________275 mi.

I can see that y goes up by 110, every time x goes up by 2, but how do you figure out what the formula is ? How do you figure out what coefficient needs to be with x and what integer to add or subtract ?


Several months ago, someone posted a "trick" or something here on ProTeacher --- though not necessarily on this board ---to figure out the formula for such tables, but I can't find it now. I really should have bookmarked it!

Can anyone help me out? Do you know the trick ?

Thanks in advance!



Last edited by Mme Escargot; 08-24-2012 at 12:07 PM..
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Never mind !
Old 08-24-2012, 11:48 AM
 
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I found the old thread. Thanks! Here it is, in case someone else needs help with this.

http://www.proteacher.net/discussion....php?p=2672627
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Old 08-24-2012, 11:54 AM
 
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In the case of that particular table, I think it would help a lot to try to figure out what would happen for the in-between values (in this case, the even numbers). You've already noticed that if x increases by 2, y increases by 110, so it makes sense that if x increases by 1, y will increase by 55. (NB: That only works for linear relationships! Your son will get to a point, probably this year, where you can't do that anymore. But for now, use it.)

That number--the amount y increases if x increases by 1--is the coefficient on the x term in the equation. (It's also the slope of the line, when you graph it.) y = 55x +/- ????

To figure out what number to add to that, test it out with the first number. You can plug in the x and y values you've got on the chart. For instance, in your first row, x is 1 and y is 55. If you put that into the equation, you get 55 = 55*1 +/- ????. Well, since 55*1=55, in this case we don't need to add anything. And you're done: The equation is y = 55x.

It's never a bad idea to run a couple more lines of the data table through the equation, to make sure it really works at all points.

I hope that made some sense. I don't know any tricks for this; you just get good at seeing the pattern after awhile. I'm curious to see others' tricks, though!
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Old 08-25-2012, 05:12 AM
 
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Input/output charts should not be looked at by going down the output side. You are dealing with a relationship between the two. Think of it as a calculator. You type the input into the calculator. You do something to the input, hit enter and out comes the answer, or output.

If you put in 1 and multiply it by 55 out comes 55
If you put in 3 and multiply it by 55 out comes 165

Your rule is what works for each individual case. In this example the rule has to work for each number of hours.

If I know the rule I could figure out 100 hours without having to continue my chart like you would have to if you just compared the output (distance traveled)

Number of hours x 55 = distance traveled
55x=y
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