## Search found 15 matches

- Wed Jun 12, 2019 2:27 pm UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**4599**

### Re: "tricky" factoring problem

So there's a whole family of solutions with unit:odd ratios. (1:1, 1:3, 1:5, ...) These are related to Pythagorean triples with last terms differing by 1. OEIS A055112. There's also a whole family with difference of 2 between the ratio (3:5, 5:7, 7:9, ...) These are related to OEIS sequence A069072....

- Wed Jun 12, 2019 12:51 pm UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**4599**

### Re: "tricky" factoring problem

I have found the parametrization to these pairs of quadratics. The expessions a = -(3k-1)(5k+3) b = 2(k+2)(k-5) c = -2(k+2)(5k+3) d = (k-5)*(3k-1) satisfy ab=cd and a+b=c-d. As mentioned before, they can be multiplied by the same scaling factor, which I haven't explicitly included. For example: For...

- Wed Jun 12, 2019 12:38 pm UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**4599**

### Re: "tricky" factoring problem

Wow. I wasn't expecting such a rapid response! Yes that definitely was a typo about 6*s^2. Of course we teach the quadratic formula :) But factoring is a fun puzzle to play. I went and asked another teacher and he quickly suggested we take a look at examples and see if we could find another and we d...

- Tue Jun 11, 2019 4:54 pm UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**4599**

### "tricky" factoring problem

I teach algebra 2 and we spend a lot of time practicing and (hopefully) mastering factoring quadratics. My favorite time comes when we've got the "what multiplies to c and adds to b" down but then x^2+5x-6 shows up and everyone jumps on 2 and 3 but forget about the negatives. This is my ex...

- Mon Feb 05, 2018 7:05 pm UTC
- Forum: School
- Topic: Dealing with "smart" but lazy teenagers
- Replies:
**7** - Views:
**8348**

### Re: Dealing with "smart" but lazy teenagers

I'm a math teacher, but it's not so much for my students, as for the 12th graders that are on my team in general. In particular a student who won't submit things for his English teacher because he says he's already done them, or something. We can't grade a zero. I think I was just venting when I wro...

- Mon Feb 05, 2018 3:46 pm UTC
- Forum: School
- Topic: Dealing with "smart" but lazy teenagers
- Replies:
**7** - Views:
**8348**

### Dealing with "smart" but lazy teenagers

Hi all, I'm a high school teacher and deal with "smart" but lazy teenagers most days... I'm sure we were all there once, I know I was. I know I've read some not-so-witticisms about "what do you call a smart, lazy person" and something about unemployed being the punchline, but I'm...

- Wed Nov 08, 2017 1:49 pm UTC
- Forum: Mathematics
- Topic: Structure of a Maths Lesson
- Replies:
**3** - Views:
**3053**

### Re: Structure of a Maths Lesson...

I'm a high school teacher, and my lessons tend to go similarly to yours. I probably don't make my students work enough individually, but that's mostly b/c as soon as they are given any freedom they go very much off task... I just got back from a math teacher conference this weekend and it's energize...

- Tue Mar 01, 2016 9:05 pm UTC
- Forum: Mathematics
- Topic: Help with the Chain Rule
- Replies:
**21** - Views:
**4005**

### Re: Help with the Chain Rule

The chain rule applies for nested functions. I like to think of them as having an inner and out part. I teach my students, in addition to the notation you've written that the chain rule is the following sentence: "the derivative of the outside, with the inside unchanged, times the derivative of...

- Wed Oct 28, 2015 4:43 pm UTC
- Forum: Mathematics
- Topic: Euler totient and powers of 2 minus 1
- Replies:
**10** - Views:
**2434**

### Re: Euler totient and powers of 2 minus 1

That's a neat function.

2^n-1 is related to mersenne primes, which certainly have an interesting GCD's

2^n-1 is related to mersenne primes, which certainly have an interesting GCD's

- Thu Mar 19, 2015 11:43 am UTC
- Forum: Mathematics
- Topic: Pythagorean Triples
- Replies:
**2** - Views:
**1586**

### Re: Pythagorean Triples

Upon a rereading, and your encouragement, I totally get it now. I must have been tired when I first went looking. Your explanation of the curves connecting similar m and n values is what was eluding me. Thanks. Pretty neat.

- Tue Mar 17, 2015 11:51 am UTC
- Forum: Mathematics
- Topic: Pythagorean Triples
- Replies:
**2** - Views:
**1586**

### Pythagorean Triples

I'm a high school math teacher who came to the profession from an economics background who is slowly working through a math major and beyond (complex analysis is next...) I'm probably not allowed to post links yet, but the 4th image on the wikipedia page for Pythagorean Triples blows my mind. http:/...

- Tue Mar 25, 2014 9:11 pm UTC
- Forum: Mathematics
- Topic: linear algebra
- Replies:
**5** - Views:
**2797**

### Re: linear algebra

I took a linear algebra class while I was brute forcing my teaching certificate (yay Econ major!). I loved it. The math was simple, but the relationships were glorious. We didn't do many application problems (yaw, pitch, roll was about it,) but thinking about the applications since then have been gr...

- Fri Jun 28, 2013 8:12 pm UTC
- Forum: Mathematics
- Topic: Clever High School Math Problems
- Replies:
**31** - Views:
**14104**

### Re: Clever High School Math Problems

That's a great one. I'm going to file that away in pack problems.

- Mon Jun 17, 2013 12:28 pm UTC
- Forum: Mathematics
- Topic: Clever High School Math Problems
- Replies:
**31** - Views:
**14104**

### Re: Clever High School Math Problems

Having sex is the answer, right? It might be a little inappropriate for the US market... That first type, the sum of 2 numbers (ages) is this, their product that (though we'd been doing differences, b/c it makes for easier systems) and it still gave some of them troubles. Real world applications, th...

- Fri Jun 14, 2013 5:38 pm UTC
- Forum: Mathematics
- Topic: Clever High School Math Problems
- Replies:
**31** - Views:
**14104**

### Clever High School Math Problems

I teach primarily high school freshman Algebra I and Geometry, maybe Calc next year (fingers crossed) Do any of you remember a favorite problem posed in high school? The sort of problem that stopped you and made you think. My favorite is: A mother and child weigh x, the father and child weigh y, and...