Number Game

mathdad

mathdad

Full Member
Joined
Apr 24, 2015
Messages
925
See attachment for a discussion math question posted by Michael Sullivan at the end of one of the early review sections of the college algebra textbook. It is a question for for classroom discussion between teacher and students or among students in little study groups.
 

Attachments

  • 20240905_104536.jpg
    20240905_104536.jpg
    477.4 KB · Views: 6
mathdad said:
See attachment for a discussion math question posted by Michael Sullivan at the end of one of the early review sections of the college algebra textbook. It is a question for for classroom discussion between teacher and students or among students in little study groups.
Click to expand...
Why are you posting this?

-Dan
 
mathdad said:
I enjoy math discussion far more than, here is the answer next question, please.
Click to expand...
So, discuss it! Don't just demand that others discuss it, while you sit back and watch. That's not how you learn (and it's not what this question is there for).

You know we want to you share your thoughts first. That's how tutoring works.
 
Dr.Peterson said:
So, discuss it! Don't just demand that others discuss it, while you sit back and watch. That's not how you learn (and it's not what this question is there for).

You know we want to you share your thoughts first. That's how tutoring works.
Click to expand...
I cannot think of a number between 1 and 10 whose square also lies between 1 and 10. The number is not 3 because 3 is not greater than pi. I will quickly say that no such number lies between 1 and 10.
 
mathdad said:
I cannot think of a number between 1 and 10 whose square also lies between 1 and 10. The number is not 3 because 3 is not greater than pi. I will quickly say that no such number lies between 1 and 10.
Click to expand...
This is what you should have said in the initial post, asking a specific question about the problem.

Read the question again:

1725630810206.png

What is a "number"? Does it say "whole number"? No. Does the fact that it says to round to two decimal places make it clear that you should consider non-integers in the interval? Yes.

If the square of x is less than 10, what does that tell you about x itself?

Now think some more. It's actually a fun problem.
 
Dr.Peterson said:
This is what you should have said in the initial post, asking a specific question about the problem.

Read the question again:

View attachment 38569

What is a "number"? Does it say "whole number"? No. Does the fact that it says to round to two decimal places make it clear that you should consider non-integers in the interval? Yes.

If the square of x is less than 10, what does that tell you about x itself?

Now think some more. It's actually a fun problem.
Click to expand...

The number is between 1 and 10. This I read in the problem.

The square of the number I must find is rational and between 1 and 10.

Does this mean the number itself must be the square root of a number between 1 and 10? You say?

It is larger than pi. If I truncate pi, I end up with 3.14. Yes?

Originally, I said that it could not be 3.
What about a number slightly larger than 3?

I started playing around using my calculator. I think the number is 3.16.

Here’s why I selected 3.16 after several tries:

It’s between 1 and 10. This I know.

Its square (3.16)^2 is about 9.99, which is between 1 and 10.
It is sightly larger than my truncated result for pi (3.14).

I will bravely say that the "mystery" number is 3.16.

You say?
 
mathdad said:
I will bravely say that the "mystery" number is 3.16.
Click to expand...
Let's check it:
  • Is it between 1 and 10? Yes
  • Is its square rational? Yes, it's 9.9856.
  • Is its square between 1 and 10? Yes.
  • Is it greater than pi? Yes, 3.16 > 3.14159... (But you can't just compare it to 3.14; 3.141 is greater than that but less than pi.)
So it is a valid answer.

I would have done something like this:
  • The number has to be between pi = 3.14159... and sqrt(10) = 3.16227..., so if it is a multiple of 0.01, it can be either 3.15 or 3.16.
  • So either of those can be the answer; in fact, the number itself could be the square root of any rational number between pi^2 and 10 (that is, between 9.8696... and 10. It doesn't say the number itself has to be rational, or a multiple of 0.01.)
If I took your approach (which in a sense is quicker), I might just round pi up to 3.15, and find that it works. That's perfectly sufficient.
 
Dr.Peterson said:
Let's check it:
  • Is it between 1 and 10? Yes
  • Is its square rational? Yes, it's 9.9856.
  • Is its square between 1 and 10? Yes.
  • Is it greater than pi? Yes, 3.16 > 3.14159... (But you can't just compare it to 3.14; 3.141 is greater than that but less than pi.)
So it is a valid answer.

I would have done something like this:
  • The number has to be between pi = 3.14159... and sqrt(10) = 3.16227..., so if it is a multiple of 0.01, it can be either 3.15 or 3.16.
  • So either of those can be the answer; in fact, the number itself could be the square root of any rational number between pi^2 and 10 (that is, between 9.8696... and 10. It doesn't say the number itself has to be rational, or a multiple of 0.01.)
If I took your approach (which in a sense is quicker), I might just round pi up to 3.15, and find that it works. That's perfectly sufficient.
Click to expand...
Very good. I always look for interesting textbook problems in addition to my regular posts.
 
topsquark said:
Why are you posting this?

-Dan
Click to expand...

So, why are any of you continuing to reply and/or enable this troll!? I continue to report him and there to see
if it will get him banned..
I want results. My disappointment with the math helpers in tolerating the troll is huge.
 
lookagain said:
So, why are any of you continuing to reply and/or enable this troll!? I continue to report him and there to see
if it will get him banned..
I want results. My disappointment with the math helpers in tolerating the troll is huge.
Click to expand...
GFY!!!!!
 
You must log in or register to reply here.
Top