Here’s a nice summer-days math project …
I just happened to be looking at the NM Highway signs page online a couple of days ago when I saw this nice little list of signs, just below:
NM Highway Signs
I couldn’t help but notice that there are quite a few recognizable geometric figures on this page, and I thought, “This would be a cool thing to show to kids who either have studied, or are studying geometry.”
My suggestion: Show this to your children and ask them how many geometric figures they can recognize.
Today is Monday, the 13th.
So what, right?
Well, maybe not so fast …
If you have a mathematical/logical bent of mind, you might find that interesting.
Friday the 13th is generally considered a bad luck day. So if that is the case, you might wonder if Monday the 13th would be the logical opposite to Friday the 13th, a good luck day. Afterall, Friday is the end of the workweek, and Monday is the beginning of the workweek.
So in that sense, can it be said that Monday and Friday are opposites? And what might that imply.
So here is the challenge. Compose a logical argument as to whether or not Monday the 13th should be considered a lucky day.
That is the challenge for Monday, the 13th of June 2011.
HINT: You may want to include information about the “truth value” (truthiness, as Steven Colbert likes to say) of statements and their converses.
REWARD: The first person who presents a compelling logical argument, one way or the other, wins a $10 gift certificate toward the purchase of any Singing Turtle Press products. All comments must be posted by 1 a.m. on Tuesday, the 14th of June, this year.
This is really the “Week of the LCM” for me.
Just as I was finishing my last post, on a new way to find the LCM for a pair of numbers, I discovered another way to do the same thing.
Coffee, Pi and More
I was looking at the problems at the end of my last post, these problems:
b) 15 and 20; LCM = 60
c) 18 and 20; LCM = 180
d) 24 and 28; LCM = 168, ….
… when I noticed something.
In yesterday’s post on the LCM, I wrote about 375 pages on the topic, and then I said that I left out an idea. Hahaha, you probably thought. Very funny, Josh.
But never fear. I am not going to write another 375 pages on the topic.
What I do need to bring to your attention, though, is that there are two LCM situations that I did not take into account yesterday. So to present a complete picture, I need to explain (for those who have not already figured this out by themselves) how to use my new technique in those two situations.
Coffee, Pi and More
You will notice that in my write-up yesterday — and in the practice problems I provided — the gap always divided evenly into the smaller number. How convenient, right? In the first example, we had a gap of 3 dividing into 12; in the next, a gap of 4 going into 20. Of course this does not always happen. Consider a situation in which we want to find the LCM for 10 and 16. The gap of 6 (16 – 10 = 6) does NOT divide evenly into the smaller number, 10. So what would we do here? (more…)
I don’t know about you folks, but I’ve always been a bit disappointed by the various techniques for finding the Least Common Multiple (LCM) for a pair of numbers.
While there are several techniques that “work” — by which I mean techniques we can teach to students and have them learn quickly — I’ve known of no technique that makes good intuitive sense. In other words, I’ve known no technique whose underlying principle felt obvious.
Feeling frustrated, I started looking for a technique that would have that undeniable “ring of truth.”
Coffee, Pi and More
And so, after playing around in my “sandbox of numbers” for quite a while, I’m happy to report that I’ve finally found what I had been looking for.
In today’s post I will show you a way to find the least common multiple that makes sense, at least to me. I hope it will make sense to you as well.