The Handshake Problem

or “How Many Clinks?”

If you’ve never tried to solve the Handshake Problem before, I’d highly advise trying it now.

Marcia is at an OWP Summer Institute with X students. On the first day of class, her teacher asks everyone to shake hands and introduce themselves to each other. How many handshakes were there? Brainstorm some ways you could find an answer.

Recently I was a demi-facilitator for the Oakland Writing Project Summer Institute 2015. I used a this problem as an example of a rich task with multiple entry points.  What phenomenal mathematical discourse erupted from a room of K-12 ELA teachers! So many “aha moments” and so many great discussions came out of our brief time together.

They must’ve had an awesome teacher.

Thanks to Barb, my math friends and I solve a version of this problem every time we go out to dinner, or at least every time we have drinks.  Instead of everyone shaking hands, Barb has us all clink each other’s glasses.  Instead of counting handshakes, we count clinks.

Same concept; much more fun application.

2 people? 1 clink. 3 people? 3 clinks.  4 people? 6 clinks.

Math Handshake Problem 2

The trick is to clink everyone individually.  You can’t simply do a group toast; you have to take the time to clink everyone else’s glasses. It only gets better with more people (said the math teacher).

The next time you get together with friends, don’t be afraid to propose this toast: “n x (n-1) / 2, where n = the number of friends!” Then count the clinks and compare your number to the algebra.



#xmath #handshakeproblem #clinks





I was out walking, wearing my new FitBit and tracking my progress around town. It’s one of the few things I can get the *%$# thing to do.  But that’s another story.

On my walk I noticed how my quaint little town has just upgraded the streets. They’ve added bike routes and nifty street signs letting us know how far away certain landmarks are.

Too bad they’re not quite right. Lost

 At a nearby intersection, I noticed the sign that read, “Downtown Royal Oak 0.8 miles.”  On the way home, I happened to glance the sign on the opposite side of the road.  Except it read, “Downtown Royal Oak 0.6 miles.”  Same intersection; different mileage.

FullSizeRender (3)       IMG_7859

Now I can believe that distances are approximations, but to have a difference of 0.2 mile at the same intersection?! And the farther corner had the lesser mileage!

We’re talking tenths, people…not hundredths. Of a MILE!

My FitBit isn’t even off by that much!

Does anyone else notice these types of things when they’re out and about?

So, in the words of Petula Clark:

Go Downtown (it’s that way)
Things will be great when you’re Downtown (except for the decimals)
Don’t wait a minute more, Downtown (there might be more signs)
Everything is waiting for you, Downtown (eventually, maybe)

Hey, Petula–just make sure you’re wearing a FitBit so you have some clue exactly how far Downtown really is.


#xmath #downtown #RoyalOak

Take This Card and Shove It

“Why Waiters Hate Gift Cards” was my alternate title.

We went to a certain wings hot spot last weekend with family.  When the bill came, we pulled out a $50 gift card.

The waitress came back with the adjusted bill and then we had to break out the calculators.


First we thought that an extra tip had been added on top of the automatic gratuity.  Upon further addition, we realized the everything still summed to the original bill amount.

But a nagging thought persisted: Why was the tip adjusted?

FullSizeRender (4)

Original Bill

FullSizeRender (1)

Adjusted Bill








Apparently when you pay with a gift card, the gratuity is no longer a percentage of the total bill; it then gets based on the net bill, AFTER the card’s value has been deducted.  Which means a much lower tip.  Which means the restaurant gets to keep that much more $$.

We didn’t get screwed; the waitress did.  Out of about $7 in this case–unless you do the MATH.  Also…there is the line that says, “+ Additional Tip.”

I bet those bastards in accounting came up with this trick to balance the books at tax time.

So, next time you are dining out, bear in mind that waiters most likely hate your gift card.  Remember that gratuities should be based on the subtotal price, BEFORE taxes and gift cards are applied.

Keep the waitstaff happy.  They have access to your food.  Cheers!




What Good is Algebra?

Recently I had a friend ask me, “What good is algebra? I’ve never used it.”

Math Algebra SomeEcard

Actually, you use algebra all the time in real life.  You’ve been working with algebra since you were little and noticed patterns. Algebra teaches you how to problem solve, as well as how to think logically and organize information–and that is something you will need to do in your everyday life, whether you think of it as algebra or not.

She didn’t believe me.

Just take the numbers out of any situation and ask yourself: What exactly am I really doing here?  How would I solve a real-life problem like this?

Math Area Model

She still doesn’t believe me, but at least she’s thinking and talking about algebra now.

The poet Sylvia Plath has a quote that wouldn’t take much to make it applicable to math:



#xmath #algebra



My Mom is a Math Badass

My daughters are 8 and 10.  I am a role model for them, so I need to be the best role model I can be.

And I’m good at math.

Women shouldn’t necessarily have to make that distinction, but until the world becomes a more equitable place, let me just say this:  I AM A MATH BADASS.

Am I the best? The quickest? The smartest?

Hell, no–but I am pretty great.

Work it, make it, do it,
Makes us harder, better, faster, stronger!

Recently I was offered a pretty great math leadership opportunity–and despite being flattered, it scared the &%$* out of me.

Not so badass now, am I?

After some deep contemplation and reflection, I ultimately accepted the role. I had to.  I have to be strong when I feel weak.  I have to be brave when I feel scared.  I have to be that badass role model for my girls.


That’s what I tell them when I go to PCMI.  Mommy has this badass math opportunity! (No, I don’t use that exact adjective–grow up). That’s sort of what I’ll tell them when I embark on my next math adventure. I want them to know it’s ok to be a woman and have amazing things happen–even things that may take them away from home. Nobody gives daddy such a hard time when he goes away on business. Mommy’s work is just as important.

I want my daughters to grow up without limits.  I want them to work harder and live stronger than I ever did.

And when they give their acceptance speeches for their awards and accomplishments, I want them to be able to say: “It’s because my mom is a math badass!”


#xmath #pcmisummer #pink #kanye #stronger #badass