## Posts tagged ‘even’

### Don’t Get Mad, Get Equal

The title of this post is a modification of a common idiom. It doesn’t make much sense, but if people are allowed to use *even* when they mean *equal*, then vice versa.

A math terminology debate over these two words occurred in our house yesterday.

While walking my dog, I found a shiny, new penny. When I got home, I told my sons that whoever guessed the item I found could have that item. To my dismay, my mother-in-law, father-in-law and wife started making suggestions. “Maybe it’s a penny,” my wife suggested. “Or a quarter,” said my mother-in-law. “Or a dime,” said my father-in-law. I looked at my dog. *C’mon, boy, you’re the only one who hasn’t said anything. Why don’t you suggest that it could also be a nickel and make this game completely devoid of fun*, I thought.

But kudos to Eli for what he did next. “Is it a *coin*?” he asked, and I could almost see his five-year-old brain thinking that this would make him a winner no matter which of the suggested coins it was.

“It sure is!” I said, beaming, and handed him the coin.

We play games like this all the time, and each of my sons wins in roughly equal proportions. But upon seeing Eli receive a penny, my mother-in-law must have sensed favoritism. She pulled out her coin purse and handed some coins to both boys. When the dust settled, Eli had two nickels and three pennies, but Alex had just one nickel and three pennies. Alex asked why he had received fewer. It was just an oversight, and Grandma gave him another nickel.

“Now we have an even number of coins,” Eli said.

“Actually, you have an *equal* number of coins,” I corrected. “Five isn’t an even number.”

“Oh, come on,” said my mother-in-law. “They’re five years old.”

“I’d rather them not use math words incorrectly,” I said. “You’d correct them if they called a firetruck an *ambulance*, wouldn’t you?”

“That’s different,” she said.

*Only because you know the difference between a firetruck and an ambulance, but not between even and equal*, I thought. But I didn’t say anything.

As it turns out, the Google dictionary lists *equal* as a synonym for *even*. In that case, however, *equal* means *being in equilibrium* or *balanced*, not *having the same number or value*, so there is a subtle distinction. Then again, the Google dictionary also gives *regardless* as the definition for *irregardless*, which isn’t even a word, and if it were, it should mean the opposite of *regardless*, right? The work of lexicographers often reflects *how* we speak and not how we *ought* to speak, so it won’t be long before *equal* and *even* have the same definitions.

**What do you think? Are even and equal synonyms? Are there other math words that are used interchangeably but shouldn’t be?**

My mother-in-law and I often have these little exchanges, but for the most part, we get along well. She is an exceptionally wonderful grandmother, she is generous and kind, and her penchant for dark beers makes her an instant friend. I love her dearly.

Yet these debates make me realize why other folks disparage their in-laws. If my mother-in-law and I had these debates and she weren’t otherwise wonderful, I might speak ill of her, too. And then I might make math mother-in-law jokes like the following:

I’ve got nothing against polygamy. I just don’t know how one man could tolerate that many mother-in-laws.

Or this one from comedian Les Dawson:

My mother-in-law caused an argument in a pub, and a half dozen men dragged her to the floor, screaming. The barman turned to me and asked, “Aren’t you going to help?”

“Nah!” I said. “Six should be plenty!”

Not long ago, I was told that I only had three months left to live. So my wife and I moved in with my mother-in-law, knowing it would feel a whole lot longer. One night, the three of us sat down for dinner, and my wife opened a bottle of wine. My wife read from the label, “Full-bodied and imposing, with a sharp bite and a bitter aftertaste.” She took a sip. “I think that’s a perfect description!” she said.

“Me, too,” I added. “But how does the winemaker know your mother?”

### Parity and Modular Arithmetic at Bath Time

I am not an expert in early childhood education, so when I was asked to give a presentation at the National Head Start Conference, I had to find a way to establish credibility. I told the audience, “Though I’m not trained as a pre-school teacher, I currently have a pre-school classroom with two students.” I then showed a picture of my twin sons.

Did it establish credibility? I’m not sure. But it was enough to encourage a mother of twins to share some advice with me.

“The best thing we ever did,” she said, “was use even and odd days. One kid got to choose on even days, the other kid got to choose on odd days.” This struck me as sheer brilliance. At the time, my wife and I had a series charts to keep track of whose turn it was: one for who got the Mickey Mouse plate at dinner; one for who got to sit on the passenger side in the car; one for who got to go first when we played *Chutes and Ladders*; and another fifteen or so for other minutia. It was driving me batty, so this suggestion was a game-changer.

When I returned home from the conference, we immediately implemented this system. We explained to the boys that Alex would get to choose things on odd days, and Eli would get to choose things on even days. (The selection wasn’t arbitrary. Eli would get even days since both *Eli* and *even* started with an *e*.)

Eli said, “But Alex will get to choose two days in a row, on the 31st and the 1st.”

Good point. We decided that the 31st would be mommy and daddy’s day to choose (and in leap years, we’d also claim February 29).

This system worked well, even at bath time, when both boys wanted to sit near the front of the tub to have access to the spigots. Since they took baths every third day, the odd/even system was just fine. Until recently.

About a week ago, we decided to do baths every second day. For this scheme, the odd/even system had three fatal flaws:

- Because of months with an even number of days, there would be strings of up to 31 consecutive baths where the same child would have the choice. (For instance, if baths occurred on even dates in September, they’d also occur on even dates in October; but then in November and December, all baths would occur on odd dates.)
- In any given year, Alex would get the choice between two and five times more than Eli would. (It depends on whether it’s a leap year or not, and on whether the sequence started on an odd or even day in January. But in every case, the system unfairly benefitted the child who receives the choice on odd days.)
- Allowing the 31st to be mommy and daddy’s day to choose doesn’t fully solve the problem. Plus, it smacks of favoritism when a parent chooses one child over the other (for anything).

Uh-oh. I feared that a new chart would be created, and we’d be returned to the bleakness we knew before the even/odd system had been implemented.

I had to act quickly.

Luckily, I was able to devise a new system, and in the process I taught Alex and Eli about modular arithmetic. As a family, we created the chart shown below. The columns indicate those numbers that are congruent to 1, 2, 3, and 0 modulo 4. As shown, Alex would get the choice on days congruent to 1 or 2 mod 4, and Eli would get the choice on days congruent to 3 or 0 mod 4.

But as you can see, this system still unfairly benefits Alex. The solution? Alex does not get the choice if a bath occurs on the 30th of a 31-day month. On those days, I suggested that a coin toss would be used to determine who gets the choice. “If it’s heads, Alex gets the choice; if it’s tails, Eli gets the choice,” I said.

Both boys seemed uncomfortable with this. For some reason, they inherently distrust coin tosses.

So we agreed that we would roll a die instead. “If the roll is even, Alex gets the choice; if it’s odd, Eli gets the choice,” I suggested.

“No,” said Eli. “I get even.”

Such is life in a house with mathematical twins. Everything is a debate. I’m just thankful that it’s a debate about numbers and not about eating broccoli.

### Reap What You Sow

Yesterday, our home owner association paved and painted the parking lot behind our townhouse. My twin three-year-old sons, Alex and Eli, were fascinated by the large, white numbers that now adorn each parking spot. They counted all of the numbers out loud, which ranged from 16 to 37. “Where is 1?” Alex asked.

The lot behind our house is Parking Lot B; spaces 1‑15 are in Parking Lot A. I probably should have explained this to him, but instead I just said, “There’s no number 1 in our parking lot. This lot begins with number 16. Isn’t that an odd number with which to begin a parking lot?”

He responded, “No, daddy. Sixteen is an **even** number, actually.”

I suppose that’s what I deserve for teaching my kids about parity before their fourth birthday.

This incident reminded me of the following joke, which appears in a slightly different form in *Math Jokes 4 Mathy Folks*:

A teacher asks her class, “How can you divide 25 sugar cubes among 3 cups of coffee so there is an odd number of cubes in each cup?”

Bekkah responds, “Put one in the first cup, and put 12 in each of the other cups.”

“But 12 isn’t an odd number,” the teacher replies.

“Sure it is,” Bekkah replies. “Twelve is a very odd number of sugar cubes to put in a cup of coffee!”

This joke is typically told so that the teacher asks students to divide 14 sugar cubes into 3 cups of coffee, and the student says to divide them as 1, 1, and 12. I never liked that version, though, because the problem as posed by the teacher is unsolvable — that is, there is no way to divide 14 sugar cubes such that there is an odd number in each cup. Yes, I know it’s only a joke… but I like to think that a teacher would only ask a question that had a solution.