New GEOMETRY Product on Horizon

Hi everyone,

Josh here with an announcement.

Singing Turtle Press is poised to come out with a new product. It will be an eBook that I have written, and it deals with geometry and geometric figures.

This eBook makes a lot of use of color in teaching geometric concepts and figures. I have found the use of color a very handy tool for differentiating concepts in math education in general, and in geometry in particular.

I have two requests for comments to this post:

1)  Would anyone like to guess how I have used color in Geometry in this upcoming eBook?

2)  Would anyone like to share ways that you have used color in Geometry in your own teaching?

It would be fun and interesting to hear some of your ideas on these topics. Just add a comment to this post, or send an email to:  josh@SingingTurtle.com

The “Ladder of Primes”

Remember the best teachers you had? Remember how they made their classes come alive? How one of the ways they made things exciting was by using analogies — little stories that connected new concepts to things you already knew and understood?

Educational researchers today are studying what makes analogies such an effective teaching tool. They have found that the use of analogies is one of the best techniques for making concepts “stick.” By relating that which students need to know to that which they already do know, teachers create bridges in understanding, and those bridges give students a way to grasp a new and difficult concepts.

The same holds true in math class. If we teachers use powerful analogies that make concepts more memorable, students are more likely to enjoy the lesson, and as a result, they’ll be more likely to remember what was taught.

I would like to present a quick-and-easy analogy that helps students learn about our number system, on the one hand, and which also helps students work with fractions, on the other hand.

The analogy is to something I call the “Ladder of Primes.”

Summertime Geometry Scavenger Hunt

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.

Monday the 13th

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.

Find the LCM (aka LCD) in Two Easy Steps

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.

Find the LCM in a way that makes sense! (Part 2)

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?

Find the LCM in a way that makes sense! (Part 1)

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.

Short Break

Hello everyone,

During this transition between the end of the school year and the start of summer, I will be taking a break from blogging. The break will be either one week or two weeks … I’m not quite sure yet. In any case I will be back in touch in the early-to-mid part of June.

Best,

—  Josh

 

 

James Bond Math Challenge

Math in the movies … if there ever was a cool way to explore math, this has to be it. And if you missed my earlier posts on this, check them out here and here.

I was looking through the links to movies with math themes, and a question came up.

On the site showing the movies, the text says that there are “mathematical themes and patterns motivated by math” in the introduction scene for the James Bond movie, Casino Royale, this clip:

I’ve watched the clip a few times, and I have my own ideas as to mathematical themes and patterns.

Quick Easy Way to Untangle Confusion re: “Greater” and “Less”

Whenever I can find a memory trick that helps students get something straight, I use it. Students needs to remember so many things in algebra, so whatever help we can give them is well appreciated.

So recently I stumbled upon a memory trick that helps students tell which of two numbers is greater and which is less.

Let's Reduce Mistakes in Algebra!

You might be thinking:  greater and less?! Why would any student have trouble with that? Well, before students hit negative numbers and absolute value, there is generally little trouble. The greater numbers are the larger numbers, the lesser numbers are the smaller numbers. And kids basically know what we mean by larger and smaller whole numbers, when they are dealing with positive numbers and zero.

But when students encounter negative numbers, some things change.
While 10 > 5,   – 10 IS not > – 5. Instead:  – 10 < – 5.

As if that were not enough, absolute vale comes along and makes things still more confusing, since it takes the value of any number and makes it positive. So now:

abs. value of – 10 > abs. value of – 5