Welcome STEM Classmates

Greetings and good evening to anyone from my STEM (Science, Technology, Engineering and Math) Vertical Math workshop who copied down my URL in class today and decided to check out the site. Thank you for stopping by.

Keep in mind that the earliest posts on the blog date back to the time when I was trying to get my students involved, and before that period of time when blogger.com was blocked from schools. The comics start a bit later.

Feel free to leave a comment to let me know you were here. Anonymous is fine!

Also: I just want to add, if you start reading from the most recent comic, you might be a little confused. That's the 700th strip and it contains references to jokes and events and topics and characters from the previous 699 strips.

Problem of the Day: Factorials

I was going through old papers and torn magazine pages stored in folders that I hadn't looked at in years, finding stuff to recycle. I happened to glanced at a calendar of daily problems, most of which were either too advanced for the classes I was teaching at the time, or just a little too involved. However, one simple problem jumped out at me, and I decided to file that one away for next year. It's definitely a question that needs the solver to explain how he arrived at the answer, and would give me insight into their thinking.

I made a second problem based on the original. Here they both are:

1. Find the largest prime factor of (87!)(88!).

2. Find the largest prime factor of 87! + 88!

Why I love the problems: first, students needed to know something about factors, prime numbers and factorials. Second, seeing a number like 88!, that student whose first instinct is to reach for the calculator will have to put it down and find a new approach.

Answers below. Stop reading here if you didn't figure them out yet.

The answer to problem 1 is fairly straightforward. The factors of 87!*88! are
1 * 2 * 3 * ... * 87 * 1 * 2 * 3 * ... * 87 * 88.
There is no need to make factor trees to find the prime factorization (an approach students might take). The largest prime factor would be the largest prime number not greater than 88. That would be 83.

(If a student guessed 87, show them that 8+7 = 15, which is divisible by 3, so 87 is divisible by 3. Or just have them divide 87 / 3 and see that they'll get 29.)

The answer to problem 2 requires a little work. We want a factor of the sum, but factors are for products, not sums. No problem. Let's make a multiplication problem out of it.

87! + 88!
= 87! + 87!(88)
= 87!(1 + 88)
= 87!(89)

The largest prime factor of 87! is still 83. But 89 is a prime number, so it's the largest prime factor, which is another reason why this is such a neat little problem: 89 isn't in the initial problem, but every whole number less than 89 is!

I think that this is a great journal-type question to assess their understanding of concepts and their ability to communicate a solution. And it will fall in nicely with whatever they're calling "differentiating of instruction" this semester. (Yes, they mentioned a new term at the last department meeting, but I neglected to write it down or even really care.)

P.S. The first problem is mine. The second is the original.

A Funny Thing Happened ...

(Click on the cartoon to see the full image.) (C)Copyright 2012, C. Burke. All rights reserved. A funny thing happened on the way to my class blog ... The students weren't using it, so I made some bonus comics. I doodled and diddled, and threw in some old jokes. Next thing I know I have recurring characters, both human and numerical, all developing personalities, in my own geeky version of "Sesame Street" where such could exist side-by-side. (Except that they're never actually existed side-by-side, I think.) This was definitely the most ambition thing I've done to date -- and those last two words scare the hell out of me. There were other things that I left out of this. Not just illustrations to go with the text, but other text that didn't fit. And I wanted as many characters as I could squeeze in, but some were just faces and the stick figures wouldn't blend in well. That's enough for today. I need a break. It's hot. -- Chris Burke

Declaring Independence

(Click on the cartoon to see the full image.)
(C)Copyright 2012, C. Burke. All rights reserved.

It's a fact: i can declare as much as i will, but i will never be completely independent of others.

Watch Where You're Walking

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(C)Copyright 2012, C. Burke. All rights reserved.

One does not simply tell ten-year-old jokes when one has filler to fill.

... Or does One?

Kiss Today Goodbye

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(C)Copyright 2012, C. Burke. All rights reserved.

If I knew a mathematical express for luck, I'd wish it for you.

After a number of years, real world changes are in the future, but I'm hoping this comic remains the same.
Or improves at a constant rate of growth. Or something like that.

Breakthrough

(Click on the cartoon to see the full image.)
(C)Copyright 2012, C. Burke. All rights reserved.

And you know that this is the way it would go down.

Abraham Lincoln: Mathematician -- Book Two

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(C)Copyright 2012, C. Burke. All rights reserved.

There is a subset of set P, the set of people, which is always a subset of set F, the set of fooled people.
There are times when the set P and set F are equivalent.

EDIT:It's Friday evening, so this is still today's strip. I updated the chart. It didn't seem right to me last night, and I tweaked it. I just didn't tweak it correctly. Oopsie. Lincoln must've been better at this than I am.

What's Wrong, Son?

(Click on the cartoon to see the full image.)
(C)Copyright 2012, C. Burke. All rights reserved.

The biggest lie here would be if I told you that I knew everything going on in this comic.

Okay, it's like this: a month or two ago, I follow a link to an article on lie algebra, so I have a punchline, but I need the setup. Then I see the bit about SO(n). Perfect. If I can make this a Father-Son joke, I have myself a Fathers Day strip.

Except that last week, I research it again, and I can't find the article. Seriously. Google sent me to a wiki page, which, apparently, has been updated in the meanwhile, and the reference isn't there. Moreover, to be honest here, I haven't a clue where or if I actually saw a reference to "dA". What is that? Integration? Matrix algebra? Fevered imagination yearning to finish the joke? No clue.

But I do know one thing.

I know the correct pronounciation of "lie", so you don't need to point that out.

This and That ...

We got the results of our students' Algebra Regents exams. Not as good as we'd like or hoped for, but isn't that always the case? A few surprises: people passing whom I wouldn't have expected going in (happy surprise), and a couple that I'd thought would sail comfortably through hit some rough waters (sad surprise). There's always August. And tutoring before then.

Consolation prize: A few of the more advanced students took the test again to improve their grades as they head toward college. Glad that they came back and did well. That made the teachers and the A.P. happy.

Tangent: Speaking of the A.P., some of you might be wondering "Why in Dante's Nine-Point Circle in the A. P. in the End-of-Year Review comic blue? "

If you're new (or if you forgot), that goes back to this comic strip about our Star Teachers.

Happy Fathers Day 2012

This is my first Fathers Day without my father. I'm just going to leave a link to one of my favorite comics:

Generations X+1, X and X-1

Happy Fathers Day to everyone.

End-of-Year Review

(Click on the cartoon to see the full image.)
(C)Copyright 2012, C. Burke. All rights reserved.

To all the wonderful and dedicated Assistant Principals out there: please note that it's the teacher who is the target of the joke here, and not the hard-working ensurer of quality instruction for the entire department. Good job, you!

EDIT: I was relating this joke to a coworker, who immediately made a comment about "dark sarcasm in the classroom".
Dang! Should've seen that one. If nothing else, that should have been the 'alt' text.