## Archive for March 30, 2015

### What If?

My favorite question is, “Why?” (And my favorite answer is, “Because.”) But not far behind is the question, “What if?”

What if a baseball player swings a bat with the proper speed, but starts swinging 0.01 seconds too late? What if I could earn 6.3% on a real estate investment instead of 1.4% in a Roth IRA, but had to pay capital gains taxes? What if I tried to walk through a revolving door with a pair of skis on my shoulder?

“What if…?” questions don’t always have to be mathy, ya know.

The beauty of Excel is that you can repeatedly ask “What if…?” questions and then explore to your heart’s content.

Overheard in math class:

“It’s not that I don’t

wantto do all those math problems,” Julia said to her teacher. “I’m just saying, if we put them into a spreadsheet and let Excel do its thing, we can have an extra 20 minutes for recess.”

Sure, one of the powers of Excel is reducing the tedium associated with calculations, but a much greater power is its ability to allow for deep exploration of math topics in a short period of time.

Art Bardige and Peter Mili agree. That’s why they’re giving away spreadsheets that allow students to explore mathematics.

Their **What If Labs** allow students to investigate questions like:

- What if you used Excel to design a house?
- Is the world population growing at a faster or slower rate than 50 years ago?
- Instead of wood, nails, and string, what if you used a graph and coordinates to create string art?

The spreadsheets are useful, fun, educational and — dare I say — beautiful. Not to mention, free.

Art believes that teaching math with Excel has two benefits. First, it fosters business skills by having students learn the basics of the most ubiquitous business application on the planet. Second, it empowers students by giving them complete control to explore on their own.

I concur with Art’s philosophy.

Excel is one of my best friends. I use it to test conjectures, especially for probability problems about which I don’t have any intuition — or, more often, when my intuition is wrong!

One of my favorite problems, which was discussed in the post Fair and Square in 2011, is the following:

Three points are randomly chosen along the perimeter of a square. What is the probability that the center of the square will be contained within the triangle formed by these three points?

Unsure how to attack this problem, the answer was estimated using an Excel simulation. From the insights gained by that simulation, a solution eventually revealed itself.

Would I have solved that problem without Excel? Maybe. Probably. But without Excel, it would have taken longer, and I might not have had the same deep understanding of the underlying structure.

Kudos to Art and Peter for providing a free resource that will let other students benefit from that same type of insight.