In an NFL football game, the Bears scored a total of 41 points, including one safety (2 points) and two field goals (3 points each). After scoring a touchdown (6 points), a team is given the chance to score 1 or 2 extra points. The Bears, in trying to score 1 extra point after each touchdown, missed 2 extra points. How many touchdowns did the Bear get?
Football
- Thread starter mathxyz
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Where are you struggling on this one?mathxyz said:
41 points
1 Safety: 41 - 2 = 39 points in other ways
2 Field Goals: 39 - 6 = 33 points in other ways
x = # of touchdowns
x-2 = # of extra points
6*x + (x-2) = 33
7x - 2 = 33
You do the rest.
Really, what was it that caused you not to solve this one?
tkhunny
Why did I struggle with this football question?
Well, I have never been able to master the skill of creating equations from the given information in word problems. This is a BIGGGGG problem for so many students. I know that for some, like Gene, yourself and many others, word problems just come so easily. For others, it is a DAILY struggle that is almost not funny.
Why did I struggle with this football question?
Well, I have never been able to master the skill of creating equations from the given information in word problems. This is a BIGGGGG problem for so many students. I know that for some, like Gene, yourself and many others, word problems just come so easily. For others, it is a DAILY struggle that is almost not funny.
- Joined
- Apr 12, 2005
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- 11,339
[SOAPBOX]
Yes, I have seen this BIGGGGGGG problem in many, many students. As I work with them in an appropriate atmosphere, I find a very, very large percentage of students with such problems are ONLY afraid of them. There is NO intellectual, organizational, or logical barrier preventing the student from learning to do it. Many such students are so sure they can't do it, that I sometimes have to challenge them, attempting to remove deeply held beliefs.
One girl, now a very good friend of mine, was told by her father for 15 years(!) that she was stupid, that she couldn't possibly succeed at anything. She was SURE she had no chance at passing math. When she came to me for math help, I listened to her story and told her immediately that her father was simply wrong. Quite a social risk, I realize. It took 2½ years(!) to get that foolish abuse out of her head. She can do math, now. She even argues with her teachers on appropriate occasion. She subsequently moved on to a university where she succeeded. Her deep-seeded belief system was just wrong. It required both of us to be strong enough to rip it out of her, throw it on the ground, and stomp it until it was lifeless. Not every student is quite this dramatic.
I encourage many simply to: relax, take a deep breath, ignore any thoughts that you cannot succeed, clear your mind, let go of any anger toward anyone or anything, and learn to succeed. There are very, very few who cannot succeed. There are very, very many who can succeed if they are given proper guidance. Also, very unfortunately, girls/women seem to have this problem far more often than boys/men. It's just a piece of societal stupidity we have to live with until enough people learn better.
You keep stating that word problems are easy for some people. Were they easy from the beginning for these people? I doubt it. We learned. We tried. We failed quite a few times. We got an idea or two every now and again. Me, personally? I got 'C's and 'D's in Algebra I. I got 'D's and even failed a quarter in Algebra II. Things turned around pretty well after that.
So, where do you stand? The big question is, are you willing to submit a little of your strong will to someone who can help you learn math or are you going to continue to hide behind your assumed inability and learn virtually nothing? It is of very little value to learn to solve specific problems. The REAL value is in learning how to think, and how to organize your thoughts, so that you can solve a great variety of problems.
My views. I welcome others'.
[/SOAPBOX]
Yes, I have seen this BIGGGGGGG problem in many, many students. As I work with them in an appropriate atmosphere, I find a very, very large percentage of students with such problems are ONLY afraid of them. There is NO intellectual, organizational, or logical barrier preventing the student from learning to do it. Many such students are so sure they can't do it, that I sometimes have to challenge them, attempting to remove deeply held beliefs.
One girl, now a very good friend of mine, was told by her father for 15 years(!) that she was stupid, that she couldn't possibly succeed at anything. She was SURE she had no chance at passing math. When she came to me for math help, I listened to her story and told her immediately that her father was simply wrong. Quite a social risk, I realize. It took 2½ years(!) to get that foolish abuse out of her head. She can do math, now. She even argues with her teachers on appropriate occasion. She subsequently moved on to a university where she succeeded. Her deep-seeded belief system was just wrong. It required both of us to be strong enough to rip it out of her, throw it on the ground, and stomp it until it was lifeless. Not every student is quite this dramatic.
I encourage many simply to: relax, take a deep breath, ignore any thoughts that you cannot succeed, clear your mind, let go of any anger toward anyone or anything, and learn to succeed. There are very, very few who cannot succeed. There are very, very many who can succeed if they are given proper guidance. Also, very unfortunately, girls/women seem to have this problem far more often than boys/men. It's just a piece of societal stupidity we have to live with until enough people learn better.
You keep stating that word problems are easy for some people. Were they easy from the beginning for these people? I doubt it. We learned. We tried. We failed quite a few times. We got an idea or two every now and again. Me, personally? I got 'C's and 'D's in Algebra I. I got 'D's and even failed a quarter in Algebra II. Things turned around pretty well after that.
So, where do you stand? The big question is, are you willing to submit a little of your strong will to someone who can help you learn math or are you going to continue to hide behind your assumed inability and learn virtually nothing? It is of very little value to learn to solve specific problems. The REAL value is in learning how to think, and how to organize your thoughts, so that you can solve a great variety of problems.
My views. I welcome others'.
[/SOAPBOX]
Great Thinking
I like your reply and your words of comfort and encouragement.
Here you said:
"The REAL value is in learning how to think, and how to organize your thoughts, so that you can solve a great variety of problems. "
I agree with this statement one hundred percent. A lot of teachers, though, are to blame for the math problem in America. In schools across this country, teachers focus more on memorization than actual learning and creating a thinking student. They say, "Just memorize this formula and you can answer the question." This is a real stupid method of teaching. I believe that memorization is vital to us all. BUT we are missing the BIGGGG picture. Learning math is FAR MORE than memorizing formulas and equations. Your view?
I like your reply and your words of comfort and encouragement.
Here you said:
"The REAL value is in learning how to think, and how to organize your thoughts, so that you can solve a great variety of problems. "
I agree with this statement one hundred percent. A lot of teachers, though, are to blame for the math problem in America. In schools across this country, teachers focus more on memorization than actual learning and creating a thinking student. They say, "Just memorize this formula and you can answer the question." This is a real stupid method of teaching. I believe that memorization is vital to us all. BUT we are missing the BIGGGG picture. Learning math is FAR MORE than memorizing formulas and equations. Your view?
G
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Guest
mathxyz said:
Yes, this can be a problem. I recently had a pre-calculus teacher who told students if they didn't do the problem using exactly the method he showed us, it was incorrect. And his method wasn't even all that great. My advice: if you want to understand math, don't take a teacher's (or anyone's) word for anything. If a certain method works, then the reason it works is not because the teacher said so. There is a reason that someone figured out before anyone told him, and you can figure it out on your own too. Doing so and understanding the concepts will make solving math problems much simpler than looking up formulas in your memory bank to find an applicable one.
I've been fortunate enough not to run into too many teachers like this. My teachers usually encourage me to prove formulas discussed in class.
mathxyz said:
Absolutely.