The Art (Benjamin) of Problem Solving

When I saw him in the crowd at Twitter Math Camp '15, I knew I recognized him from somewhere. Then it hit me...it was Art Benjamin, famous mathemagician and speaker whose DVDs I had shown in my classes some time ago. I was completely starstruck, and my colleague had to calm me down a bit...but then...then he was actually going to do a show for us? WHAT?? It was absolutely amazing. Art Benjamin is not only brilliant, he has an energy about him that catching to others. His love of math is pure and he engages his audiences by multiplying large numbers in his head (he converts some of these numbers to words to help him!)

Today in my Problem Solving Class, I showed this amazing and highly recommended Ted Talk video. Here, Mr. Benjamin squares 2 digit, 3 digit, 4 digit, and yes, even 5 digit numbers in his head, much to the surprise of his audience. He even can tell audience members the day they were born if they tell him their birthdays.

My students were in awe. They were perplexed. How did he do it? Well, we googled and found this video next, where he explains the secrets of how to square a two-digit number in your head.

And they could do it! Well, some could do it in their heads...it was hard! 

Here is his method.

Take any two digit number and square it:

For example, 23x23

First, find a number more or less than the number that is easier to square...in this case, we will use 20. Twenty is 3 less than 23, but you also have to go up 3 more than 23, like this:

26

|

(3 up)

|

23

|

(3 down)

|

20

Now, multiply the bottom and the top numbers: 20 x 26...easy to multiply 2x26 and add the 0, and get 520. Then, take the number you added or subtracted (3, in this case), and square it (9) and add it to the 520, and you get 529. 

Well, of course we had to try this out. We went to the Algebra 2 class next door and showed our newly learned talent during their brain break. They were impressed, and we taught them how to do it. Then a tour came in. I think the student on the tour was a bit scared when I excitedly asked her to pick a number any number, and we would square it for her. I just could not contain myself. 

So why does this work? Well, it's all about FOILing, if you don't mind that word. Essentially, what we did to square 23 was to say:

23x23 = (23 + 3)(23 - 3) + 3x3

Art Benjamin may explain it better, so watch the videos!

The other day I saw on twitter that he wrote a new book The Magic of Math: Searching for X and Figuring out whY, so I had to buy it. It's fantastic, and I can't wait to share more gems with my students.

But this is still not the best news. The best news is that I found his website, and I saw that he does shows. Lots of them. And he is doing one near my school. And I contacted him. And I contacted my head of upper school. And GUESS WHAT!! Art Benjamin is coming to do a show at my school in March! I am so excited. When I told my students that, they couldn't believe it. They can't wait, and neither can I. The president of my math club came into our class after we showed his videos, and we told him that he was coming to the school. His eyebrows went to the back of his head. He had watched a series of his videos before. He was so impressed that Art Benjamin will be at our school. So am I. I am so happy my school is hosting him, and I can't wait for his love of math to rub off on our students.