## Posts tagged ‘video’

### Math Pranks

Jeff Gordon recently pulled a prank on a blogger who claimed that one of Gordon’s previous pranks was fake. The video received 10 million views in its first two days, so it’s doubtful you haven’t seen it… but just in case (warning: PG-13)…

Now that’s a pretty good prank. Especially since it involves revenge.

But my favorite prank ever is a math prank. I don’t want to ruin it by telling you anything about it, so just watch…

That’s pretty good, no? Now be honest…

April Fools Day is just around the corner. Pretty cool that this year’s date is a palindrome in the U.S. (4/1/14) and a repeating number (1.4.14) in other countries. Here are a few more pranks to get you in the spirit.

In 1975, Martin Gardner published a *Mathematical Games* column with “Six Sensational Discoveries that Somehow or Another have Escaped Public Attention.” Among them was the claim that the following expression yields an integer value.

Not so much a prank as an optical illusion, the following image shows two tables that appear to be drastically different in size, yet both tabletops consist of the same parallelogram (one rotated 90° from the other). Cool, huh?

And finally, here’s a number trick.

- Start with a three-digit number
*abc*(|*a*–*c*| > 1). - Reverse the digits to form the three-digit number
*cba*. - Subtract the smaller from the larger.
- Now reverse the digits of the result.
- Add the numbers from Steps 3 and 4.
- Cube the result.
- Add 3,000,000.
- Add 40,000.
- Add 900.
- Use the following list to convert the digits of your answer into letters.

0 – R

1 – S

2 – L

3 – N

4 – F

5 – T

6 – P

7 – I

8 – O

9 – A

Enjoy!

### Jim Rubillo Receives Lifetime Achievement Award

Jim Rubillo has been a member of the National Council of Teachers of Mathematic (NCTM) for more than 1.4 billion seconds. For his four decades of service to improve mathematics education, he received a Lifetime Achievement Award at the 2013 NCTM Annual Meeting.

Jim was the Executive Director of NCTM from 2001 to 2009, and he was my supervisor for the last five of those years. But he was more than just my boss — he was also a mentor, friend, and problem-solving companion. So when Ann Lawrence, chair of the Mathematics Education Trust, called to ask me to prepare a tribute video for Jim’s award ceremony, I was honored by the request.

I didn’t want to prepare a talking head video — I have a face for radio — yet I don’t have access to elaborate film equipment. Consequently, I opted to create a PowerPoint presentation with narration, which I then uploaded to authorSTREAM. Here it is, for your viewing pleasure.

Prior to its showing at the awards ceremony, Ann Lawrence mentioned that the tribute video had been created by me. Upon hearing this, Jim murmured, “Oh, no…” (Truth be told, I think I was rather kind.)

One of the many reasons that I loved working with Jim is that he always had a good math problem at the ready. He shared more problems with me than I can count, but here are two of my favorites:

- What percent of the numbers in Pascal’s Triangle are even?
- Many years ago, it was believed that the Earth was the center of the cosmos. This was a reasonable hypothesis — it appears that the Sun rotates around the Earth. But if Earth were the center of the solar system (instead of the Sun), and if Mars rotated about the Earth, what would it have appeared that the path of Mars was?

Both of these problems have non-obvious answers, which is a trademark of the problems that Jim likes to share. Jim often looks at things with a unique perspective, and he willingly talks math with anyone who’s willing to listen. Consequently, Jim was an exceptional choice for this award, and I’m proud to call this lifetime achiever my friend.

### Turn the Page

After eight fantastic years as the Online Projects Manager at NCTM, it’s time for my next chapter. On Monday, I become the Director of Mathematics for Discovery Education, leading a team that will build digital math techbooks for K‑12. I’m looking forward to building something great. As I mentioned during my interview, “I’m not coming to Discovery to create a textbook; I’m coming to create a *movement*.”

Leaving is such sweet sorrow. I’ll miss my friends and colleagues at NCTM, and I’m sad that I’ll no longer be creating resources for Illuminations. On the upside, my departure brought three stories worth sharing.

**A Day Off**

My last day at NCTM was February 28. That evening, I mentioned to my sons that I would not be going to work the next day. “Do you know why not?” I asked them. Alex suggested, “Because it’s Dr. Seuss’s birthday?” I love that! Celebrating the birth of Theodore Seuss Geisel certainly seems like a great reason for a federal holiday, but the truth is that I was just taking some time off between jobs.

**Lesson Learned**

The east coast was hit with a snowstorm during my time off, and both the NCTM and Discovery offices were closed. Had I been employed by either organization, I would have spent a day at home with pay. Instead, I spent an upaid eight hours designing the Vennebush Family Flag and playing Uno, Swish, and Qwirkle with the boys, while my gainfully employed wife dialed in to back-to-back-to-back conference calls. Moral: Check the forecast before quitting a job prematurely.

**A Parting Gift**

One of my colleagues at NCTM gave me a broken calculator. (And, no, this isn’t just a cheesy, elaborate set-up for a silly math problem.) The calculator used to be a normal, fully functioning, scientific calculator, but now it can’t add, subtract, multiply or divide without making an error. The good news is that the error is very predictable. The following video shows the results when using the calculator for four basic arithmetic problems.

The following (incorrect) results are shown in the video:

- 310 + 677 = 982
- 13 × 15 = 190
- 512 ÷ 64 = 3
- 75 – 10 = 60

And after the last problem, continual presses of the equal key should repeatedly subtract 10, but instead it shows consecutive results of 45, 30, 15, and 0.

Can you discern the pattern?

### (Lack of) Math Videos

I just saw a math video that showed a technique for multiplying two-digit numbers. I’ll share this trick with you in a minute. But I am dismayed that this video — along with so many other math videos I’ve seen on the web — are willing to *show* these tricks but not *explain* them. So I’m going to provide the trick, which I thought was pretty cool, along with an explanation as to why it works.

Before I do, though, I have to vent. Math videos on the web are a real problem. The ones I’ve seen generally do very little to promote conceptual understanding. Instead, the videos present skills without explanation, and the implicit message is that you don’t need to understand why it works — just do exactly as the videos say, and you’ll get the right answer. The issue is that students then see mathematics as a series of disconnected rules they need to memorize, instead of seeing it as the beautifully interconnected discipline that it is.

Arrgh.

Okay, I’ll now step down from my soapbox and share the trick with you…

Take two numbers, both between 10 and 99, that meet the following criteria:

- Their tens digits are the same.
- The sum of their units digits is 10.

Here are some problems that meet these criteria:

- 22 × 28
- 74 × 76
- 33 × 37
- 55 × 55

I will now state the obvious — there are only 81 multiplication problems to which this trick applies. Still, I think it’s fun to explore the math underlying the trick.

To find the product, then, follow this process:

- Take the tens digit, and multiply it by one more than itself.
- Multiply the units digits.
- Finally, concatenate (put together) these two results to make a three- or four-digit number. (As noted in the comments below, if the result of Step 2 is a one-digit number, you’ll also need to put a 0 in front of it.)

Let’s take the first problem above, 22 × 28, to see how this works in practice.

- The tens digit is 2, so multiply 2 by one more than itself: 2 × 3 = 6.
- The units digits are 2 and 8, so multiply them: 2 × 8 = 16.
- Consequently, 22 × 28 = 616.

More generally, the trick could be explained with symbols. If the tens digit of each number is *n*, and the units digits are *p* and *q*, then we’re trying to find the product of (10*n* + *p*)(10*n* + *q*). Using the FOIL method from algebra gives

(10*n* + *p*)(10*n* + *q*) = 100*n*^{2} + 10*n*(*p*) + 10*n*(*q*) + *pq *= **100 n^{2} + 10n(p + q) + pq**

But since the criteria implies that *p* + *q* = 10, this becomes

100*n*^{2} + 10*n*(*p* + *q*) + *pq* = 100*n*^{2} + **100 n** +

*pq*

This can be further refined to

100(*n*^{2} + *n*) + *pq*

and the important point, then, is realizing that *n*^{2} + *n* = *n*(*n* + 1)*.* Which is just another way of saying that we’re going to take the tens digit, *n*, and multiply it by one more than itself.

And that’s it. The first part of the expression above, 100(*n*^{2} + *n*), gives the hundreds (and perhaps the thousands) digit, and the second part, *pq*, gives the tens and units digits.