A few weeks ago Brilliant Quotes tweeted a quote from Duke Ellington: “A problem is a chance for you to do your best.”

I immediately thought of problems students are given in mathematics classes because this quote applies to those problems.

It also applies to any other kind of problem a person may face. Sometimes those problems are much more challenging than problems involving numbers. All problems are opportunities for us to do our best.

Let’s find the factoring information for a relatively easy number – 393.

- 393 is a composite number.
- Prime factorization: 393 = 3 x 131
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 393 has exactly 4 factors.
- Factors of 393: 1, 3, 131, 393
- Factor pairs: 393 = 1 x 393 or 3 x 131
- 393 has no square factors that allow its square root to be simplified. √393 ≈ 19.824

Is 393 in any Pythagorean triples?

**393**-524-655 which is [3 – 4 – 5] times 131**393**-25740-25743 which is [131-8580-8581] times 3- Primitive 393-8576-8585
- and Primitive
**393**-77224-77225

At the end of his post a-promise-broken, Established1962 tells a personal and very funny story involving his copy of Duke Ellington’s autobiography, “Music Is My Mistress.” The quote above is included in that book.

Very motivational! Is this how you persuade your students to solve more problems?

Good idea! I’ve mostly thought of what this quote could do to motivate ME! Now I will have to share it with my students as well.