Input output table - completely stumped

1

123blueberrypie

New member
Joined
Sep 5, 2020
Messages
3
InputOutput
FourFive
ThreeTen
Eight
Nine
OneOne hundred

This is my son’s homework for Algebra 1, he is in 7th grade but gifted in math. This is the second week of virtual school and they are just starting to learn about functions. The other input output tables we found functions like y=2x + 3, things like that, not too hard. I’m having him just kind of trial and error with educated guesses to figure it out, maybe there is a better way. The rest of the page had numerals in the tables; this is the only one with words. The only pattern I can see is the output is the next number with the same first letter, if I think about spelling out the words as a clue, but that can’t be right because that’s not really an equation, right? He’s been absolutely swamped with work and missed all the chances to ask the teacher for help. Please help, we are so stuck! It’s going to be tough this year with 45 minutes of class time on Zoom per week (with 80 other kids!). I’m glad I found this resource, thanks so much.
 
123blueberrypie said:
InputOutput
FourFive
ThreeTen
Eight
Nine
OneOne hundred

This is my son’s homework for Algebra 1, he is in 7th grade but gifted in math. This is the second week of virtual school and they are just starting to learn about functions. The other input output tables we found functions like y=2x + 3, things like that, not too hard. I’m having him just kind of trial and error with educated guesses to figure it out, maybe there is a better way. The rest of the page had numerals in the tables; this is the only one with words. The only pattern I can see is the output is the next number with the same first letter, if I think about spelling out the words as a clue, but that can’t be right because that’s not really an equation, right? He’s been absolutely swamped with work and missed all the chances to ask the teacher for help. Please help, we are so stuck! It’s going to be tough this year with 45 minutes of class time on Zoom per week (with 80 other kids!). I’m glad I found this resource, thanks so much.
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Please confirm:

The last word (6th row - including heading) of the input column is "One".

I suspect it is "Ten".
 
I agree with what you said. The output is the next number that starts with the same letter.

This works since for any input you will never get back more than one output.
 
Jomo said:
No, I did not know that. I learn so much from this forum. BTW, did my raise request get reviewed yet?
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All of your salary was debited against your tuition and rent for the corner.
 
123blueberrypie said:
InputOutput
FourFive
ThreeTen
Eight
Nine
OneOne hundred

This is my son’s homework for Algebra 1, he is in 7th grade but gifted in math. This is the second week of virtual school and they are just starting to learn about functions. The other input output tables we found functions like y=2x + 3, things like that, not too hard. I’m having him just kind of trial and error with educated guesses to figure it out, maybe there is a better way. The rest of the page had numerals in the tables; this is the only one with words. The only pattern I can see is the output is the next number with the same first letter, if I think about spelling out the words as a clue, but that can’t be right because that’s not really an equation, right? He’s been absolutely swamped with work and missed all the chances to ask the teacher for help. Please help, we are so stuck! It’s going to be tough this year with 45 minutes of class time on Zoom per week (with 80 other kids!). I’m glad I found this resource, thanks so much.
Click to expand...
I want to make a comment about the problem itself.

In studying functions, you should be discussing only functions that are clearly defined; definition is an essential part of math. This problem should be thought of only as a fun puzzle, because it is a matter of guessing, and guessing is not really the same thing as math (though it can be almost as much fun). If I were the teacher (or author) I would have given some indication of that, to keep kids from worrying too much if they don't see an answer, or aren't sure their answers are right.

You have a very good guess, and I think you are right. Khan has implied a very nice guess if the last input had been Ten. Both are guesses, and you can't prove they are right or wrong for their respective problems. So the key is this: Don't take problems like this too seriously; just have fun with it. In fact, the same is true with real math: If something gets overwhelming, set it aside, because you (both!) have time to learn it.
 
joshuaa said:
did you try this magical formula?

[MATH]f(x) = \frac{40x^2 - 295x + 555}{3}[/MATH]
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Wow, this works!! How on earth did you figure this out?? Is there a way to do it on a calculator or something? I’m surprised that it’s such a complex equation for these algebra beginners. Thank you!
 
123blueberrypie said:
Wow, this works!! How on earth did you figure this out?? Is there a way to do it on a calculator or something? I’m surprised that it’s such a complex equation for these algebra beginners. Thank you!
Click to expand...
That is absolutely not what students were intended to find! It's a demonstration that there is never only one solution to this sort of puzzle: any set of values can be obtained by a polynomial formula, by fitting a curve to the points in the graph.

Your own answer is almost certainly what was intended, based on the context and the use of words.
 
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