What's Out There for The Plucking?

I borrowed this title from a wonderful presenter at the MCTM Fall Conference (thank you, Nancy English!). Watch out for a TON of helpful math links that I've discovered here at the conference! For example, have you heard of...

Geogebra?
Goanimate?
Animasher?
CoboCards?
Prezi?

And the list goes on! Stay tuned.

Algebra and Archaeology

 Cool. Carbon-14 dating explained.

Polynomial Division Pencasts Available!

Below is the first of two pencasts on polynomial division that are now available (at right). There will be at least one more posted soon on synthetic division (a MUST for College Algebra students!). Feel free to comment with questions or just comments!

Divide Polynomials I
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2 Sample Pencasts: Factoring Polynomials (and Comments update!)

Below are two of the many pencasts that are available to view on this blog. I create these pencasts often, so check back often! Pencasts are available to right of this page... just scroll down below "Followers". Have a request? Please leave a comment and/or email me. The Comments function should be working now! There was trouble for a while, but thanks to Blogger help, problem solved. If you wanted to post a comment on a previous post, please do so now. Thanks!

To view the pencasts below, just click on the yellow play button. There's audio, so turn up your volume. To view full screen, just click on "full screen" in top right corner of video.

Factoring 4 terms FBG
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Another Factoring Trinomial a is not 1
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Using Recycled Caps to Teach Prime Factorization

Note to educators: To demonstrate this lesson to the class at the whiteboard, I adhered pieces of a magnetic strip (only around $4 for a roll at Michaels!) to the tops of caps. I found the magnet to adhere better to the metal lids and Gatorade caps. The students shared their own cut-out pieces of paper that contained several prime factors. This is why I'm collecting caps so that ALL of my students will be able to use the caps along with me.


Review of terminology
Prime number: a number that has exactly two factors, just 1 and the number (e.g. 2, 3, 5, 7, 11, 13, ...)

Factors: numbers that multiply to get a number (e.g. the factors of 6 are 1, 2, 3, and 6)

Multiple: the result of multiplying by a whole number (e.g. the multiples of 4 are 4, 8, 12, 16, 20, ...)

GCF (greatest common factor): the highest number that divides evenly into the given numbers (e.g. the GCF of 4 and 12 is 4)

LCM (least common multiple): the lowest number that the given numbers divide into evenly (e.g. the LCM of 4 and 12 is 12)

Note: The GCF has to be NO GREATER than the lowest number in the set. And the LCM must be AT LEAST the highest number in the set. For example, in the pair of numbers 4 and 12 mentioned above, the GCF is 4 and cannot be greater than that lowest number. The LCM had to be at least the highest number 12. We'd never ask for the lowest common factor, for that would just be 1. And we'd never ask for the greatest common multiple... what are the common multiples of 4 and 12? (underlined)

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
12: 12, 24, 36, 48, ...

See? 4 and 12 have TOO MANY common multiples so we'd just ask for their LEAST common multiple. Now, here's how to reuse some caps to learn math...


The "Cap Method" for listing prime factors, finding the GCF and the LCM

First, define each cap. Here I let the silver cap = the prime factor 2, the blue cap = the prime factor 3, and the green cap = the prime factor 5.

To find the prime factorization of the numbers 18 and 24, use the factor tree or tower/ladder method (see the Pencast featured to right of screen). Write each number as a product of their primes with the caps:

Now, you can use the caps in the prime factors above to find the GCF of the numbers:

Next, you can use the prime factor caps to find the LCM of the numbers. One way to do it is to ask yourself a couple questions:

OR, we can refer back to the prime factorization and find the LCM another way:

In class today we used these methods to find the prime factorizations, GCF and LCM of the numbers 120 and 180. Using the caps seemed to simplify the process!

Where is this going? GCF can be used to reduce fractions. We also need to know how to find the GCF for factoring polynomials in algebra. LCM is used to find the LCD of fractions. We also need to know how to find the LCM and LCD for operations with rational expressions in algebra. These are such important topics.

We need your "Ensure", Gatorade and milk caps!

My math students and I need caps for math activities. The Ensure caps have a metal piece that help to teach all sorts of math things, from prime factorization to finding LCD of rational expressions in algebra. You don't need to take out the metal piece... I'm getting pretty good at that. ;-)  The Gatorade and milk caps come in different colors and hold magnets well for board lessons.

When you have some caps saved up, please drop them off at my office, I can pick them up (colleagues and students) or I will provide an address if you need one.

Our math students and I thank you! I will soon post a little lesson on how to use the caps to find the GCF and LCM of a pair of numbers. Later on I will post a lesson on finding LCD of rational expressions. Fun, huh? Thank you so much for your help!

Without a calculator: Is 3 a factor of 714?

Can you do this without a calculator? I sometimes have to remind my college students about this "trick". First, here's a terminology refresher. I will use the numbers 2 and 10 to explain:

2 is a factor of 10.
10 is a multiple of 2.
10 is divisible by 2.

Divisibility Rules
2 is a factor if the number is even (number ends in 0, 2, 4, 6 or 8)
3 is a factor if the sum of the number's digits are divisible by 3 (sum means you are adding; I'll explain).
5 is a factor if the number ends in 0 or 5.
6 is a factor if the number is even AND is divisible by 3.
9 is a factor if the sum of the number's digits are divisible by 9 (I'll explain).
10 is a factor if the number ends in 0.


So, back to the original question: Is 3 a factor of 714? According to the rule above, if we add up its digits:

7 + 1 + 4 = 12

Since 12 is divisible by 3, then so is 714.

Another question: Is 6 a factor of 714? How about 741? 
Answer: 2 and 3 are factors are 714 since the number passes "the 3 test" and since the number is even. But is 741 divisible by 6? Does this number pass "the 3 test"? Is it even? (answer below)*

Now, take a look at the multiples of 9: 9, 18, 27, 36, 45, 54, 63, ... If you add up the digits in each of those multiples:
1 + 8
2 + 7
3 + 6
4 + 5

Don't you get 9? So, is 9 a factor of 714? No it isn't since 7 + 1 + 4 = 12 and 9 doesn't divide into 12 evenly.

Is 9 a factor of the HUGE number 702,121,050? Well, find the sum of the digits:

7 + 0 + 2 + 1 + 2 + 1 + 0 + 5 + 0 = 

Now, we can use the Identity Property of addition and not include those zeros in the addition, right?

7 + 2 + 1 + 2 + 1 + 5 = 18

Since 18 is divisible by 9, so is the original number 702,121,050. Hmmm... I wonder if this stuff is the secret behind the Magic Gopher...

Here's some practice from the web along with answers.

(This reminds me that we may need a post about those awesome Properties of Real Numbers... and what are Real Numbers? Oh, so much to discuss!)



* 741 is not divisible by 6 (so 6 is not a factor of 741) since 741 is an odd number.

Revised 9/13/11

LOTS of multiplication facts practice sheets

My students at any level (Prealgebra on up) never know when to expect some timed multiplication practice worksheets. About.com has a lot of them free to print!

Home School Math Worksheet Generator -- FREE!

When I'm in a pinch and want to make my students some quick worksheets with answers, I go to Home School Math. My end-of-year Intermediate Algebra and beginning-of-semester College Algebra students may want to practice some radical simplifying here. Make your own worksheet! It's a little intimidating to create at first, but take your time and you'll figure it out.

More FREE printable worksheets: KUTA Software

Here's a website that has tons of free printable worksheets. This is one of the best websites that I've found for my students. Solutions are provided, too! Check out KUTA Software when you can. For your convenience, worksheets are divided by type below at the following links:

Prealgebra

Algebra 1

Algebra 2

Geometry

Math-Drills. Com -- Free Printable Math Worksheets!

Math-Drills.com has lots of free printable math worksheets. With school starting soon, I will be sure to start printing again so that my son can review before the fall semester begins!

InterActMath: Math help at your fingertips!

InterActMath.com is supplied by Pearson Education. Just about every Pearson math textbook is available with the click of a mouse. Click on the InterActMath.com link above, then choose a book from the pull-down menu. The books are listed alphabetically by author. You will see hundreds of problems from the textbook. You can choose the topic, choose a problem, then check your answer. There's help for each problem, too ("View an Example" and "Help Me Solve This").

Khan Academy -- FREE MATH VIDEOS!

 A former student emailed me about a website that helped him through College Algebra. In his words, he "couldn't have made it through without these videos." I checked it out. They have basic math, basic algebra, more advanced math and all sorts of subjects. And they're FREE! Here are some links:

Arithmetic videos

Algebra videos

More Algebra videos (mainly College Algebra)

Please reply/comment if you find a certain lesson that worked well for you!

Red Lobster Algebra!

Algebra on the Kid's Menu at Red Lobster!

In the words of one of my former students, this is "FANTASTIC!" The picture to the right is from the Kid's Menu at Red Lobster.

This is algebra. There's even the word "sum"! This is evaluating expressions in algebra! Urchin is like x, Anemone is like y and Coral is like z. See? If kids can do this, so can you! I'm working on a glossary of math terms for this blog. For example, the boldface words will be linked to their definitions. As I tell my students, if you don't understand the terminology, it's like sitting in a French class when you don't speak French. Math is a language.

Thank you, Red Lobster, for making my day!

The Impetus of this Blog

The following was taken from http://en.wikipedia.org/wiki/Barbie:

In July 1992, Mattel released Teen Talk Barbie, which spoke a number of phrases including "Will we ever have enough clothes?", "I love shopping!", and "Wanna have a pizza party?" Each doll was programmed to say four out of 270 possible phrases, so that no two dolls were likely to be the same. One of these 270 phrases was "Math class is tough!". Although only about 1.5% of all the dolls sold said the phrase, it led to criticism from the American Association of University Women. In October 1992 Mattel announced that Teen Talk Barbie would no longer say the phrase, and offered a swap to anyone who owned a doll that did.

So there you have it. I loved Barbie dolls when I was a kid, but good thing she didn't say anything like that in the '70s! This blog is for you, whether you are a student, parent, aunt, uncle, brother, sister or grandparent (did I get them all?). Stay tuned for helpful math hints and links. If you have any comments or questions, please post! If you have a question, I'm sure someone else does, too!