Least Common Multiple (LCM)

teaching View Comments
Feb 282007

Yesterday, we covered the concept of a multiple. Today, we’re going to look at finding the least common multiple (LCM) of two numbers.

Since we created a list of multiples for 4 yesterday, let’s start with that list.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Now let’s find the LCD for 4 and 5. We’ll need to make a list of some of 5′s multiples.

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Like we did when we were trying to find the GCF for two numbers, we going to stack our two lists together.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5: 5, 10, 15, 20, 25, 30, 35, 40, 45,  50

Now, let’s highlight the numbers on both lists.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Both 20 and 40 are highlighted in the lists, but because 20 is smaller, it is the Least Common Multiple for 4 and 5.

Being able to determine LCM will help you as you work with fractions. It will allow you to create equivalent fractions quickly and well.

Posted by Rebecca at 2:26 pm Tagged with:

Math education

education View Comments
Feb 282007

It’s slowly becoming apparent that math education is failing our students across the country. This could be for any number of reasons- shorter school days, an overextended curriculum, fewer math teachers available to teach the material, the increasingly shorter attention span of students. The list goes on.

Out here where 60% of our high school students failed an exit exam with no fractions on it, we’re up against an interesting problem- a series of adopted curricula (YouTube video) that does little to address communicating actual math to our elementary students, leaving them ill-equipped to deal to a high school math program that leaves even experienced math teachers wondering.

Until a national math curriculum can be agreed upon and implemented, we have to figure out how to address this growing problem. Being weak in math is absolutely crippling. So much of what we do is based in math. Daily activities like shopping or cooking require some understanding of decimals and fractions. Many careers, especially those in any science, engineering, or business discipline, are heavily steeped in algebra and trigonometry.

Letting it go isn’t acceptable, but letting it stay in its current state is doing today’s students a disservice. These are kids who would much rather understand what they’re doing, despite their protests, than continue moving on to higher math levels because it will supposedly raise their self-esteem. I can tell you from experience, socially promoting these kids frustrates them. They know they were promoted to stay with their peers, and an unusually high number of them resent it because they know they don’t understand the new math they have to learn because they don’t understand what’s it’s built on.

What can we do? We can work to help these students become stronger in the basics. Even if all you do is get workbooks in various grade levels and help your student work through them, you’re giving them a much better chance at succeeding in math education. I’ve also recently started a math blog that tries to cover various topics to help students struggling with their homework (or parents struggling to help their students with their homework).

Do something. Take action. Your student will really appreciate it, even if they never say it out loud.

Posted by Rebecca at 9:38 am Tagged with:

What is a multiple?

teaching View Comments
Feb 272007

Let’s start out today by defining “multiple”.

Multiple: the result of multiplying the target number by another number

It sounds simple enough, right? As simple as the definition is, it’s amazing how many people confuse “multiple” and “factor“. A little care in your work will help you avoid making this common mistake.

To find multiples of a number, start multiplying it by other numbers. For example, let’s look at some of the multiples for 4:

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

If you’re looking at this list and thinking this list looks a lot like the multplication facts for 4, then you’re right.

Multiples are really that simple.

Posted by Rebecca at 2:10 pm Tagged with:

Art in math

creativity View Comments
Feb 272007

I’ve never been shy about the fact I can’t draw.

I can do nearly any other art you put in front of me, but the only way I’ve ever been able to draw (and Dead Bunny brilliantly illustrates this) is with either a School Tools book (which they sadly no longer make) or a Geometer. You give me a way to make geometric shapes, I can finally draw something other than stick figures.

Designing awe-inspiring pieces through geometry isn’t just a draw-inept artist’s means of creating. It’s actually one of the most ancient forms of designing. Take a look around at ruins, at less-ancient European cathedrals. You’ll find the most intricate, eye-catching designs in mosaics and stained glass windows, all done in the piecing together of geometric shapes.

Feeling a little draw-challenged? Start working in geometric shapes!

Posted by Rebecca at 11:19 am Tagged with:

Real life tomb raiders

anthropology View Comments
Feb 272007

I love following fictional archaeologists. I’ve always enjoyed playing Tomb Raider. I hated missing episodes of Relic Hunter. The last Indiana Jones movie is one of my favorite ways to pass a rainy afternoon.

Last year, I spent a good portion of the dig season following the adventures of real-life archaeologists as KV 63 was excavated.

I’d never be able to convince myself to do anything more volunteer on a dig (and I really need to find myself doing that at some point), but I do love the idea of archaeology. You get to poke around where people lived. If you’re really lucky, you find something, however small, that tells you something about how those people lived. Even better, you find something that leaves you wondering about the originating culture. It’s a mystery, a puzzle to be solved. And I love a good puzzle!

While some people do get to chase their dreams of being a professional archaeologist, many are left unable to land so much as a research position. Some of them change professions. Others become unlicensed archaeologists, turning into the mercenary tomb raiders fiction loves to show off for us.

It’s just fascinating. Some people are content to be amateur archaeologists. Some people leave you wondering what they were taught in their archaeology courses. My museum science-trained self can’t help but wonder what goes through the minds of these “tomb raiders” as they’re unearthing and selling these artifacts off the grid.

Posted by Rebecca at 11:02 am Tagged with:

Prime factorization

teaching View Comments
Feb 262007

The first post in this mini-series addressed factoring using multiplication facts and the rules of divisibility. Today, we’re going to factor a number into its primes.

A prime number is any number that can be divided only by itself and 1. Some people find this a more useful way to find common denominators,and it can actually make simplifying radical expressions much simpler.To start factoring a number to its primes, we need to either apply the multiplication facts or the rules of divisibility to it.

Let’s use 72 for this example. 72 is 8 * 9.

72
/\
8 9

Neither 8 nor 9 is prime, so we’re going to factor both of them. We know that 8 is 4 * 2; and 9 is 3 * 3, so let’s add those to our factor tree.

72
/ \
8   9
/\  /\
2 4  3 3

Now we’re getting somewhere! Both 2 and 3 are prime, leaving us only the 4 to factor. The factor tree looks like this now.

72
/ \
8   9
/ \  /\
2 4  3 3
/\
2 2

I’ve bolded the prime numbers at the end of each branch so we can see them clearly. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3.

If you use this method to find GCFs, then you’ll need to find all the primes both numbers have in common and multiply them back together. For example, if you were comparing 72 to 12, you’d find that both numbers have two 2s and a 3 in their list of prime factors. 2 * 2 * 3 equals 12, so 12 would be the GCF for 12 and 72.

Posted by Rebecca at 9:57 pm Tagged with:

Experiment and grow

finding my path View Comments
Feb 262007

“If you’ll not settle for anything less than your best, you will be amazed at what you can accomplish in your lives.”- Vince Lombardi

So often, my students tell me they can’t do the skill we’ve just discussed. A lack of self-confidence is often part of what has brought them to me anyway, so I smile softly and ask them why? They always tell me they don’t know why, but they know they can’t do a problem. I make them try one anyway, usually with a, “Give it a try. You just might surprise yourself.”

This conversation usually repeats itself while the student is working on mastering the skill, but when the same skill shows up later, the student often tackles it without thinking, simply because they know they can do it.

Sometimes, we face a skill that we’re positive we’ll never master, or a situation we’re sure we’ll never make it through successfully. Because a fear of failure has become ingrained in our society, so many of us walk away from the skill or situation, giving up on ourselves for fear of failing.

What we’ve really done is sold ourselves short.

When you try something outside your comfort zone, when you refuse to let yourself give in to the fear of potential failure, you give yourself the chance to grow, to find out you can succeed in unfamiliar territory. That is one of the greatest confidence builders out there.

Don’t sell yourself short. Don’t be afraid to fail. Don’t be afraid to try. Amaze yourself with what you can do when you put your mind to it.

Posted by Rebecca at 11:01 am

The writing pyramid

writing View Comments
Feb 262007

It occurs to me that this would actually make a great writing exercise.

It would force you to really focus on what you’re trying to say, encourage you to not waste words.

I think it would lead to tighter writing on both a small and large scale. The math geek in me is already seeing this as scalable to larger projects (their fault for working out of 100).

I’m going to have working on incorporating this into my writing practice.

Posted by Rebecca at 8:50 am

Greatest Common Factor (GCF)

teaching View Comments
Feb 252007

Yesterday, we reviewed how to factor a number. Today, we’re going to use that skill to work on determining the greatest common factor (GCF) for two numbers. This skill is most often useful when trying to come up with a common denominator for two fractions that you want to add or subtract.

Let’s find the GCF for 12 and 15.

Yesterday, we factored out 12. Let’s review that list.

12: 1, 2, 3, 4, 6, 12

Now, let’s factor 15. We have the identity factors of 1 and 15. A quick run through the rules of divisibility tells us that 15 is divisible by 3 and 5. Let’s look at our factor list for 15.

15: 1, 3, 5, 15

To determine the greatest common factor for 12 and 15, we stack the two lists.

12: 1, 2, 3, 4, 6, 12

15: 1, 3, 5, 15

Now we determine what numbers are on both lists.

12: 1, 2, 3, 4, 6, 12

15: 1, 3, 5, 15

Both 1 and 3 are bolded on both lists, but becasue 3 is the larger number, it is the greatest common factor of 12 and 15.

Posted by Rebecca at 8:58 pm Tagged with:

Book review- She’s Such a Geek

books View Comments
Feb 252007

I was pretty excited when I first heard about She’s Such a Geek. Essays written by women who have more than flirted with math, science, engineering, writing, and gaming? I was so there!

In fact, I highly recommend it to my students. It’s that good.

I’ve also started reading the main blog, occasionally following links to an entry written by one of the author’s at her own blog. I have yet to be disappointed.

I’ve been wrestling with my own sense of geek ever since I moved to Washington. Once upon a time, I watched nearly every science fiction television show. I liked playing in the chem lab, even if I hated balancing equations. Despite a bad showing in both algebra and geometry, I did exceptionally well at precalculus and calculus. I’ve always played on any computer I came near…up until I got my own computer. Now I play on my laptop, and play on other computers if I don’t have my laptop handy. I’ve always played any nearby video game I could, even while not owning my own. (The boys fixed this at Christmas when they gave me my much-loved DS Lite.) I take great pride in the fact i was an informal science teacher, and would still drop everything to help kids explore science topics. I love being a math tutor, and laugh at the fact that girls who suffer from the mindset that girls can’t do math are often placed with me to help shake them of that horridly old-fashioned notion. It’s a rare day that goes by where I’m not watching anime, and the fact that I have three unread manga on my shelf scares people.

A lull in my access to gaming and the availability of decent sci-fi shows led me to this feeling that I was completely out of touch with all of it, and in fact had no right to claim any of that life I grew up with. My friends here often respond to something I do or say by simply saying, “Geek.” I fight it. I fight it tooth-and-claw. I really feel like I just can’t claim that at all, like I’m a fake.

She’s Such a Geek has actually changed my mind. Even if I did have that gap in my life experiences, it doesn’t change the fact that I have geek tendencies, that I am a geek. I’ve been slowly trying to make peace with the fact that I actually am a geek. The fact I’m not the same flavor or level of geek as my roommates or friends is immaterial because I am my own weird blend of geek that is still a valid form of geek.

I was a geek. I am a geek. I will forever be a geek. SSAG really helped me understand that.

Where it lost me is in the attempt of many of the essayists to come to terms with both their geekiness and their femininity. In so many cases, there was talk of sex (the act, not gender) was key to making or breaking their careers. At one point, one of the essayists left me asking the same questions I was asking of William Gibson’s Cayce Pollard. Why did I need to know about certian things that are inherent to being a woman simply because of human anatomy and biology? I get the gender issues. I was one of two girls in a gaming group (the best group of people I’ve ever hung with), I was the oddball girl in charge of the Pokemon League and my LARP chapter, but I was also one of the guys…even if the guys knew full well I was a girl. Maybe I just ran into the right groups of male gamers.

Women can do math, science, and technology. Fine. Good. I completely agree with that (because if I didn’t, I’d be a huge hypocrite). Women face old-fashioned, unfounded stereotypes. Yep. True story, and many of us have fought those in our own way. Women either have to completely suppress their sexuality or overwork it to get anywhere in a room full of guys. Um…check your calendars, ladies. While I have had a little too much fun using the fact I’m a girl to get things to happen within a gaming group, I have never needed much more than that to gain whatever power I’ve needed, and I’ve watched groups completely shredded by girls who have either suppressed or overused their sexuality.

It’s going to be hard to gain any sort of equal footing for both genders when the act of sex (both completely present and completely absent) continues to be such a major part of the equation.

Anyway, I’ve gone off on a tangent inspired by one of the last essays in the book. Just go read the book. Make the girls in your life read it. It’s worth it.

(Because I think it’s a bit funny, I’m sitting here watching one of my favorite movies, Contact, simply because I stumbled upon it while trying to find something else entirely. This is my idea of a chick flick!)

Posted by Rebecca at 10:59 am Tagged with:
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