## Posts tagged ‘classroom’

### AWOKK, Day 8: KenKen in the Classroom

*Eight days a week…*

Yes, I know that this series is called **A Week of KenKen**, and I’m fully aware that there are only seven days in a week. But if the Beatles can love you for an extra day, then I can certainly write an extra post about KenKen. In case you’ve missed the fun we’ve had previously…

- Day 1: Introduction
- Day 2: The KENtathlon
- Day 3: KenKen Times
- Day 4: My KenKen Puzzles
- Day 5: Harold Reiter’s Puzzles
- Day 6: KenKen Glossary
- Day 7: KenKen Puzzle for 2016

Tetsuya Miyamoto created KenKen in 2004. Twelve years later, millions of KenKen puzzles are solved every day by people all over the world.

His original intent was not to create a global math sensation. Instead, he wanted to help his students improve their calculation skills, logical thinking, and persistence. Who knew that he would accomplish both?

KenKen puzzles are perfect for the classroom because they provide the same level of practice and repetition — sometimes affectionately known as *drill-and-kill* — as a worksheet full of problems, yet providing a significantly higher level of engagement.

Most students would have no more interest in answering the following questions than they would in removing their toenails with a pair of pliers:

*Use only the numbers 1-5, in how many ways can you…*

*write 300 as a product of 4 factors?**write 40 as a product of 4 factors?**write 13 as a sum of 5 numbers?**write 12 as a sum of 4 numbers?**write 5 as a quotient of 2 numbers?*

Yet wouldn’t students be willing to at least try this 5 × 5 KenKen puzzle? The cognitive demand is the same, but as any marketing guru or parent trying to get their kids to eat vegetables will tell you, it’s all about the presentation.

Because of the puzzle’s appeal and impact for students, the KenKen in the Classroom program was created. Every Friday, teachers who’ve signed up will receive free puzzles, which can be printed for distribution to students.

KenKen puzzles deal with a lot of mathematics beyond the four binary operations, including factors, parity, symmetry, modular arithmetic, congruence, isomorphism, algebraic thinking, and problem solving. Harold Reiter, John Thornton, and I wrote about these topics and how to use KenKen in a secondary classroom in the article *Using KenKen to Build Reasoning Skills*.

Even better than solving KenKen puzzles, though, is having students design their own. And to that very point… the 5 × 5 puzzle that appears above was created by my son Alex when he was 6 years old.

*I hope you’ve enjoyed reading this week of KenKen posts as much as I’ve enjoyed writing them. I’d love to hear your opinion of the series. Definitely check out the other items in this series with the links at the top of this post, and share your thoughts on all of them in the comments.
*

### Prime Time

One of the great joys of my current job is that I get to visit math classes. This is awesome, and I am incredibly grateful to the teachers who invite me to their classrooms. I’ve thought about returning to the classroom myself, but visiting is much better — I get to see magic and interact with kids, but I don’t have to worry about correcting misbehaviors, creating or grading tests, or filling out report cards.

I recently witnessed several great classes at Tincher Prep, a K-8 school in California. The students were the most collectively polite group of kids I’ve ever met, and the faculty was filled to capacity with intelligent, dedicated professionals. Students in first grade measured things with paper cut-outs of their foot, to get an appreciation for why we have standard measures. Kindergarten kids happily sang number songs and then counted by 5’s to figure out that it was the 75th day of the school year. Students in a middle school class were jumping out of their seats with excitement when playing a review game. In every class I visited, students were excited to be learning. What an awesome environment!

In one classroom, students were given the following assignment:

Complete this list of the first 10 prime numbers:

1, 2, ___, ___, ___, ___, ___, ___, ___, ___

John Derbyshire claims that Henri Lebesque was the last mathematician who considered 1 to be a prime number. The primary reason it should not be considered a prime number is that the Fundamental Theorem of Arithmetic — which states that every integer greater than 1 can be represented as the product of a unique set of prime numbers — will not hold. It also causes a problem with Euler’s Totient Function: for prime numbers, φ(*n*) = *n* – 1, but this rule is violated if 1 is considered a prime number.

The teacher who posed this problem to students, however, shouldn’t feel bad for including 1 as a prime number. Lots of professionals have trouble figuring out which numbers are prime…

- Mathematician: 3 is prime, 5 is prime, 7 is prime, and by induction, every odd integer greater than 2 is prime.
- Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is an experimental error,

11 is prime, … - Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, …
- Programmer: 3 is prime, 5 is prime, 7 is prime, 7 is prime, 7 is prime, …
- Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 — we’ll do the best we can, …
- Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release, …
- Biologist: 3 is prime, 5 is prime, 7 is prime, results have not yet arrived for 9, …
- Lawyer: 3 is prime, 5 is prime, 7 is prime, there is not enough evidence to prove that 9 is not prime, …
- Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime if 2/3 is deducted for taxes, …
- Statistician: Let’s try several randomly chosen numbers: 17 is prime, 23 is prime, 11 is prime, …
- Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
- Computational Linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a
*very*odd prime, … - Psychologist: 3 is prime, 5 is prime, 7 is prime, 9 is prime but tries to

suppress it, … - Casino Card Counters: 3 is prime, 5 is prime, and 7 is prime, but I’ll take 21 over any of them.

### Almost End of Summer

This is the point of the summer that, when I was a classroom teacher, I would start to panic, realizing that the start of the school year was just around the corner. “Oh, my goodness, they’ll be back in three weeks!” Now that I have an office job and kids of my own, it’s the point of the summer when I start to think, “Thank goodness, they’ll be back in school soon!”

For the teachers out there, here are a few jokes to ease you into the classroom…

Teacher: How far are you from the correct answer?

Student: Three seats, sir.Teacher: Did your parents help you with these problems?

Student: Nope! I got them all wrong by myself.Teacher: If I had five coconuts and gave you three, how many would I have left?

Student: I don’t know.

Teacher: Why not?

Student: Because all of our practice problems were about apples and oranges!Teacher: If you got $10 each from 10 people, what would you have?

Student: A new bike!

And a joke that isn’t about the classroom, but was told to me by a high school student in a classroom:

What do you get when you cross a bridge with a bike?

The other side.

(Though maybe “bridge bike sine theta” is a better answer?)