## Posts tagged ‘homework’

### Math Problems for 2016

“What homework do you have to do tonight?”

I ask my sons this question daily, when I’m trying to determine if they’ll need to spend the evening doing word study or completing a math worksheet, or if we’ll instead be able to waste our time watching The Muppets or, perhaps, pulling up the animated version of Bob and Doug Mackenzie’s *12 Days of Christmas* on Dailymotion.

When I asked this question last night, though, the answer was surprising:

We have to do our reading, but we already completed

yourmath problem.

*My* problem? I had no idea what this meant. So they explained:

It’s not a problem you gave us. It’s one we got from [our teacher], and it says, “This problem was written by Patrick Vennebush.”

I was puzzled, but then it dawned on me. I asked, “Does it have a monkey at the top with the word *BrainTEASERS*?”

“Yes!”

“Which problem?”

“It’s about the word CAT.”

I knew the problem immediately. It’s the Product Value 60 brainteaser from Illuminations:

Assign each letter a value equal to its position in the alphabet (A = 1, B = 2, C = 3, …). Then find the product value of a word by multiplying the values together. For example, CAT has a product value of 60, because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

How many other words can you find with a product value of 60?

As it turns out, there are 14 other words with a product value of 60. Don’t feel bad if you can’t find them all; while they’re all allowed in Scrabble™, the average person won’t recognize half of them.

You can see the full list and some definitions in this problem and solution PDF.

This problem resurfaced at the perfect time.

With 2016 just around the corner, no doubt many math teachers will present the following problem to students after winter break:

Find a mathematical expression for every whole number from 0 to 100, using only common mathematical symbols and the digits 2, 0, 1, and 6. (No other digits are allowed.)

And that’s not a bad problem. It gets even better if you require the digits to be used in order. For instance, you could make:

**2**= 2^{0}+ 1^{6}**9**= 2 + 0 + 1 + 6**36**= (2 + 0 + 1)! × 6

But that problem is a bit played out. I’ve seen it used in classrooms every year since… well, since I used it in my classroom in 1995.

So here are two versions of a problem — the first one being for younger folks — using the year and based on the Product Value 60 problem above:

How many words can you find with a product value of 16?

How many words can you find with a product value of 2016?

There are 5 words that have a product value of 16 and 12 words that have a product value of 2016 (**spoiler**: those links will take you to images of the answers). As above, you may not recognize all of the words on those lists, but some will definitely be familiar.

### A Father’s Day Gift Worth Waiting For

Alex made a Father’s Day Book for me. Because the book didn’t make it on our trip to France, however, I didn’t receive it until this past weekend. It was worth the wait.

The book was laudatory in praising my handling of routine fatherly duties:

I loved when you took me to Smashburger.

I appreciated when you helped me find a worm.

I love when you read to me at night.

I love when I see you at the sign-out sheet [at after-school care]. It means I can spend time with you.

But my favorite accolade — surprise! — was mathematical:

I liked the multiplication trick you taught me. Take two numbers, find the middle [average], square it. Find the difference [from one number to the average], square it, subtract it. (BOOM! Done!)

Priceless.

The trick that I taught him was how to use the difference of squares to quickly find a product. For instance, if you want to multiply 23 × 17, then…

- The average of 23 an 17 is 20, and 20
^{2}= 400. - The difference between 23 and 20 is 3, and 3
^{2}= 9. - Subtract 400 – 9 = 391.
- So, 23 × 17 = 391.
**BOOM! Done!**

This works because

,

and if you let *a* = 20 and *b* = 3, then you have

.

In particular, I suggested this method if (1) the numbers are relatively small and (2) either both are odd or both are even. I would not recommend this method for finding the product 6,433 × 58:

- The average is 3,245.5, and (3,245.5)
^{2}= 10,533,270.25. - The difference between 6,433 and 3,245.5 is 3,187.5, and (3,187.5)
^{2}= 10,160,156.25. - Subtract 10,533,270.25 – 10,160,156.25 = 373,114.
- So, 6,433 × 58 = 373,114.

Sure, it works, but that problem screams for a calculator. The trick only has utility when the numbers are small and nice enough that finding the square of the average and difference is reasonable.

Then again, it’s not atypical for sons to do unreasonable things…

Son: Would you do my homework?

Dad: Sorry, son, it wouldn’t be right.

Son: That’s okay. Can you give it a try, anyway?

I’m just glad that my sons understand math at an abstract level…

A young boy asks his mother for some help with math. “There are four ducks on a pond. Two more ducks join them on the pond. How many ducks are there?”

The mother is surprised. She asks, “You don’t know what 4 + 2 is?”

“Sure, I do,” says the boy. “It’s 6. But what does that have to do with ducks?”

### My Son’s New Joke

My son is doing his math homework — he’s in first grade, so it involves writing a certain number, spelling that number, and finding all occurrences of that number in a grid of random numbers called a “Number Hunt.” Based on today’s number, he came up with the following joke:

What number is mostly even but not even?

Eleven.

Not a great joke, to be sure… but as good as most jokes on his dad’s blog, and he’s only six years old.

The homework was frustrating (for me), because my sons are capable of much more.

When my sons ride their bikes through the parking lot, they solve problems involving parking space numbers, the digits on license plates, and other numerical things. They ask me to create “math challenges” for them to think about as they ride. Yesterday, they solved the following three challenges:

- Which license plate has the greatest product if you multiply its four digits together? (The license plate format in Virginia is LLL-DDDD, where L is a letter and D is a digit.)
- How many different license plates are possible with the format LLL-DDDD?
- Each of the three rows in our parking lot has a different number of cars. If our parking lot had a fourth row, how many cars would there be in the fourth row?

For Question 1, Eli realized that the license plate with {9, 7, 6, 5} would have a greater product than the license plate with {9, 7, 6, 3}, since 5 > 3. But then he realized that {9, 9, 8, 2} would be even greater, and he correctly determined that the product is 1,296.

For Question 2, Alex thought it would be 144. His argument was that there would be 6 ways to arrange the letters and 24 ways to arrange the digits, and 6 × 24 = 144. We talked about this, and I pointed out that his answer would be correct if we knew *which* three letters and *which* three digits we were using (and they were all different). He and Eli reconvened and eventually claimed there would be 26^{3} x 10^{4} possible license plates… and being the good father that I am, I let them use the calculator on my phone to find the product.

For Question 3, the number of cars in the three rows was 2, 5, and 8. They extended the pattern and concluded that there would be 11 cars in the non-existent fourth row.

So you can understand why I’d be frustrated that Alex’s homework involved writing the number 11 repeatedly. I thought about telling him not to do it, but then I imagined the following conversation:

Alex: Would you punish me for something I didn’t do?

Teacher: Of course not, Alex.

Alex: Good, because I didn’t do my homework.

Or perhaps he’d just fabricate an excuse:

I thought my homework was abelian, so I figured I could turn it in and then do it.

And finally — should abelian be capitalized?

### Giving Thanks

The end of the year is a good time to reflect and be thankful for all that we have. I have two fantastic, five-year-old sons who love math and their daddy — what more could a man want?

Eli is thankful, too. This is the note he wrote to his teacher for the Math Enrichment homework she asked him to complete during the holiday break:

When I asked why he was thankful for homework, he said, “Because this was fun!”

Checking sales on Amazon Author Central tonight, I was thankful to the 299 folks who bought a copy of *Math Jokes 4 Mathy Folks* from December 17‑23, making it the best-selling week for my silly joke book yet. In fact, between Thanksgiving and Christmas, an astounding 928 people bought my book; people who, apparently, are unaware that they could have gotten not one but two venti, decaf, sugar-free, non-fat, vanilla soy, extra hot, no foam, mocha cappuccinos with three shots, light whip, extra syrup, cinnamon and sprinkles at Starbucks for the exact same price. Oh, well… their loss.

These numbers represent a sales increase of nearly 40% compared to the 2011 holiday season. My financial planner previously predicted that I’d be able to retire at age 65; but, if this trend continues, I might be able to retire at age 64 9/10.

Allow me to take this opportunity to thank all of you, whether you read my blog posts religiously in 2012, stopped by only once in a blue moon, bought *Math Jokes 4 Mathy Folks* from a local, independent bookstore, or stole a copy from your local library. I appreciate your support, in whatever form it takes.

Wishing you peace, joy, and happiness in 2013, y’all. May you occasionally laugh so hard that milk comes out of your nose.

### Back to Pencils, Books, Dirty Looks

The fall semester is underway. Here are some jokes for you, no matter your level.

For professors…

Mathematical conferences are very important. They demonstrate how many faculty a department can operate without.

For graduate students…

Why is grad school like a hot bath?

Because after you’ve been there for seven years, it ain’t so hot anymore.

For undergraduates…

An undergraduate student said to his statistics professor, “You know, I hate being a full-time student and mooching off of my parents. I’d really rather have a job.”

The professor says, “You’re in luck! I just heard that the President of the University is looking for a bodyguard and chauffeur for his beautiful daughter. You’ll be expected to drive her around in his Mercedes, accompany her on overseas trips, and satisfy her sexual urges. He’ll provide all meals and supply all of your clothes. You’ll be given a two-bedroom apartment above the garage, and the starting salary is $75,000 per year.”

The wide-eyed student says, “You’re kiddin’ me?”

The professor replies, “Well, yeah… but you started it.”

And for high school kids…

“Why don’t you work on your math homework with Sarah anymore?” a mother asks her daughter.

“Would you do your homework with a lazy slug who just copies all of your work?” says the daughter.

“Well, no, I suppose I wouldn’t,” says the mother.

“Yeah, well, neither will Sarah.”

### Free Copy of My Book

A few days ago, a seventh‑grade math teacher and assistant baseball coach sent me the following request:

I would love to have a copy of

Math Jokes for Mathy Folks, but I am financially unable to purchace it right now because my wife is unable to work and hasn’t been approved for disability.

Now, I like to think I’m a generous guy, but I am unable to send a free copy of my book to everyone who asks for it. A little‑known fact about the publishing industry: The majority of authors actually have to pay for copies of their own book. It’s an interesting percent problem. I pay 50% of retail price plus shipping to purchase copies of my book, but I then receive a 15% royalty on the discounted price of every copy I purchase. (You can do the math to figure out how many books I could give away for free before going bankrupt.)

So I sent the following reply:

Send me your favorite joke(s), mathy or not, and I’ll send you a copy of the book.

My correspondent responded quickly with three jokes, two of which I had never heard before. A copy of my book is in the mail to him, and his jokes are pasted below for your reading pleasure.

What’s a seventh grader’s favorite excuse for not doing homework?

I have a solar‑powered calculator, but yesterday it was cloudy.The student’s second semester seemed so much like her first that she hoped she could graduate sooner by combining like terms.

How is an indecisive third‑base coach like multiplying or dividing by a negative integer?

In both cases, the sign changes.

Incidentally, you can download one chapter of *Math Jokes 4 Mathy Folks* for free by clicking the following button:

### Father’s Day Reflections (and Other Transformations)

I just got a new stepladder. Don’t get me wrong, it’s a fine stepladder. I just wish I had gotten to know my real ladder.

I had the privilege of knowing my real father.

At age 15, my father faked a birth certificate and joined the Navy. When he was 18, he received a dishonorable discharge — after allowing him to fight in Japan during the last two years of World War II, the Navy finally learned that my dad was under age when he enlisted. So, what did he do? He joined the Army. Before he was 21, he had been to each of the 50 states and had traveled around the world 4 times.

My father had only a sixth-grade education, but he believed in the power of school and learning. It was not easy to get my dad to part with his money. When I was in third grade, my teacher asked me, “If you have two dollars, and you ask your father for another three dollars, how much will you have?”

“I’d have two dollars,” I told her.

“Young man,” she said, “you don’t know your arithmetic.”

“No, Mrs. Wargo,” I said, “you don’t know my father!”

But he often gave me $20 for a good report card, and I was the first kid in my school to have a Commodore 64 with a disk drive. When I graduated high school, my family was subsisting on my father’s disability pension, and I considered working for a year to save money before enrolling in college. “You’re too damned smart,” he said. “Send in the forms. We’ll make it work.”

My father passed away in December 1994. The last words he said to me were, “You’re my pride and joy.” Father’s Day is always a little rough for me, but it’s a good time to reflect. I continually ask myself, “Am I a man that my father would be proud of?”

Are you kidding? I have to believe my father is smiling down from Heaven, saying, “That’s my boy! Yeah, that geeky one there! He’s the author of a math joke book and math joke blog, ya know.”

For all you math dads (and sons, too), here’s some humor for today:

Son: Dad, can you do my homework for me?

Dad: I’m sorry, son, it wouldn’t be right.

Son: That’s okay. Can you try anyway?

I spent today with my twin four-year-old sons, hiking, doing KenKen (more on that later), playing the anagram game, and helping them figure out how the number of “cheers” we do with our glasses at the dinner table is related to the triangular numbers. What a great day. Happy Father’s Day!