Let's Celebrate Pi Day on March 14th!

March 14 is Pi Day because March is the third month, and with 14 as the day, we get the first three digits of pi - 3.14! On Pi Day, nerds, geeks, and mildly interested geometry students alike come together and wear pi-themed clothing, read pi-themed books and watch pi-themed movies, all the while eating pi-themed pie. 

Pi is an irrational number that approximately equals 3.14. It is the number you get if you divide the circumference of any circle by its diameter, and it's the same for all circles, no matter their size. You can estimate pi for yourself by taking some circular things like the tops of jars or round plates and measuring their diameter and their circumference. Then divide the circumference by the diameter, You should get an answer something like 3.14. It should be the same every time (unless you measured wrong).  In other words, π is the number of times a circle’s diameter will fit around its circumference

Actually, 3.14 is only approximately equal to pi. That's because pi is an irrational number. That means that when you write pi as a decimal it goes on forever and ever, never ending. (It is infinite.) Also, no number pattern ever repeats itself.

Usually in math, we write pi with the Greek letter π, which is the letter "p" in Greek. You pronounce it "pie", like the pie you eat for dessert. It is called pi because π is the first letter of the Greek word "perimetros" or perimeter.  What is interesting is that in the Greek alphabet, π (piwas) is the sixteenth letter; likewise, in the English alphabet, the letter "p" is also the sixteenth letter.

But hold your horses!  Whether you like it or not, pi is everywhere. Here are a few more places it has popped up:

1. The main character in the award-winning novel (and 2012 film) Life of Pi nicknames himself after π. 
2. A circular room in the Palais de la Découverte science museum in Paris is called the pi room. The room has 707 digits of pi inscribed on its wall. (The value of pi has now been calculated to more than two trillion digits.)
3. In an episode of Star Trek: The Original Series, Spock commands an evil computer to compute π to the last digit which it cannot do because, as Spock explains, “The value of pi is a transcendental figure without resolution.”
4. Pi is the secret code in Alfred Hitchcock’s Torn Curtain and in The Net starring Sandra Bullock.

Here is more arbitrary information related to pi that I found interesting.

1. If you were to print one billion decimal values of pi in an ordinary font, it would stretch from New York City to Kansas (where I live). 

2. 

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   3.14 backwards looks like PIE. 
3. "I prefer pi" is a palindrome. (It reads the same backwards as forwards)
4. Albert Einstein was born on Pi Day (March 14) in 1879.

All this information about pi and circles can be found in a Pi Day Crossword. It includes two different math crossword puzzles about Pi Day and features 20 words that have to do with pi or circles. One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same vocabulary is used for each crossword, each grid is laid out differently. Answers keys for both puzzles are included.

By the way, notice my "handle" of Scipi.  The Sci is for science (what my husband teaches) and the pi is for π because I teach math.

Finding the Greatest Common Factor and Least Common Multiple

The most common method to find the greatest common factor (GCF) is to list all of the factors of each number, then list the common factors and choose the largest one.  Example: Find the GCF of 36 and 54.

1) The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

2) The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.

Therefore, the common factor(s) of 36 and 54 are: 1, 2, 3, 6, 9, 18.  Although the numbers in bold are all common factors of 36 and 54, 18 is the greatest common factor.

To find the lowest common multiple (LCM), students are asked to list all of the factors of the given numbers. Let's say the numbers are 9 and 12.  

1) The multiples of 9 are: 9, 18, 27, 36, 45, 54.

2) The multiples of 12 are: 12, 24,  36, 48, 60.

As seen above, the least common multiple for these two numbers is 36.  

We often instruct our students to first list the prime factors, then multiply the common prime factors to find the GCF. Often times, if just this rule is given, students become lost in the process. Utilizing a visual can achieve an understanding of any concept better than just a rule. A two circle Venn Diagram is such a visual and will allow students to follow the process as well as to understand the connection between each step. For example: Let’s suppose we have the numbers 18 and 12.

1) Using factor trees, the students list all the factors of each number.

2) Now they place all the common factors in the intersection of the two circles. In this case, it would be the numbers 2 and 3.

3) Now the students place the remaining factors in the correct big circle(s).

4) That leaves the 18 with a 3 all by itself in the big circle. The 12 has just a 2 in the big circle.

5) The intersection is the GCF; therefore, multiply 2 × 3 to find the GCF of  6.

6) To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle.

3 × GCF × 2 = 3 × 6 × 2 = 36. The LCM is 36.

This is an effective method to use when teaching how to reduce fractions,

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I have turned this method into a resource for Teachers Pay Teachers. It is 16 pages and begins with defining the words factor, greatest common factor and least common multiple. What a factor tree is and how to construct and use a Venn Diagram as a graphic organizer is shown. Step-by-step examples are given as well as student practice pages. How to use a three circle Venn Diagram when given three different numbers is explained. Two pages of blank pages Venn Diagrams are included for classroom practice. To learn more, just click on the price under the resource cover on your right. A free version is also available.

Dividing Fractions Using KFC (Keeping, Flipping and Changing)

Ugh - It's time to teach the division of fractions. My experience has been that many students forget which fraction to flip and often, they forget to change the dreaded division sign to a multiplication sign. The other evening,  I was helping my 5th grade granddaughter with her homework. Really, she had completed it by herself, but she wanted me to check it. At the top of her paper were the letters "KFC". I asked her what they meant, and she replied, "Kentucky Fried Chicken." Now I have taught math for years and years, and I had never heard of that one!

She explained that the "K" stood for keep; "F" for flip, and "C" for change. Let's suppose the problem on the left was one of the problems on her homework paper.

First, she would Keep the first fraction. Next, she would Flip the second one, and then Change the division sign to a multiplication sign...like illustrated on the right. She would then cross cancel if possible (In this case it is).  Finally, she would multiply the numerator times the numerator and the denominator by the denominator to get the answer.

She was able to work all the division problems without any trouble by just remembering the letters KFC.

Yesterday, I was working in our college math lab when a student needed help. On the right is the problem he was having difficulty with. (For those of you who don't teach algebra or just plain hate it, I am sure this problem looks daunting and intimidating. Believe me, my student felt the same way!) 

First I had the student rewrite the problem with each fraction side by side with a division sign in between them like this.

Doesn't it look easier already? I then taught him KFC. You read that right! I did! (I figured if it worked for a 5th grader, it should work for him.) Surprisingly it made sense to him because he now had mnemonic device (an acronym) that he could easily recall. He rewrote the problem by Keeping the first fraction, Flipping the second, and Changing the division sign to a multiplication sign.

Now it was just a simple multiplication problem.  Had he been able to, he would have cross canceled, but in this case, he simply multiplied the numerator times the numerator and denominator by the denominator to get the answer.

So the next time you teach the division of fractions, or you come across a problem like the one above, don't panic!  Remember KFC, and try not to get hungry!

Dump and Divide - Converting Fractions to Decimals

When working with fractions, my remedial math college students are never quite sure which number to divide by. This same thing often occurred when I taught middle school and high school. So the question I had to answer was, "How can I help my students remember what number goes where?"

First, the student must understand and know the vocabulary for the three parts of a division problem. As seen in the problem above, each part is correctly named and identified.

Side Note: The symbol separating the dividend from the divisor in a long division problem is a straight vertical bar with an attached vinculum (you might have to look this word up) extending to the left, but it seems to have no established name of its own. Therefore, it can simply be called the "long division symbol" or the division bracket. I wish it were named something fancier, but sometimes plain and straight forward is the best!
Now let's look at a fraction that the student is asked to rewrite as a decimal. The fraction on your right is two-fifths and is read from top to bottom as two divided by five. That's easy enough, but when my students enter this into their calculators, many will put in the 5 first, and then press the

division sign, followed by the 2. Of course, they get the wrong answer. Now let's look at the dump and divide method.

First, dump the 2 into the calculator. Then press the division sign; then divide by 5. The answer is 0.4.

I am aware that many of students are not allowed to use calculators; so, let's look at how this method would work using the division bracket. We will use the same fraction of 2/5 and the same phrase, dump and divide.

First, take the numerator and dump it inside the division bracket. (Note: Use N side instead of inside so that numerator and N side both start with "N".) Now place the 5 outside of the long division bracket and divide. The answer is still .4.

Dump and Divide will also work when a division problem is written horizontally as a number sentence such as: 15 ÷ 3. First, reading left to right, dump 15 into the division bracket. Now place the 3 on the outside. Ask, "How many groups of three are in 15?" The answer is 5.

Try using Dump and Divide with your students, and then let me know how it works. You can e-mail by clicking on the page entitled Contact Me or just leave a comment.

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Something Else to Think About:  

Since many students do not know their multiplication tables, reducing fractions is almost an impossible task. The divisibility rules, if learned and understood, can be an excellent math tool. The resource, Using Digital Root to Reduce Fractions, contains four easy to understand divisibility rules as well as the digital root rules for 3, 6, and 9. A clarification of what digital root is and how to find it is explained. Also contained in the resource is a dividing check off list for the student. Download the preview to view the first divisibility rule plus three samples from the student check off list.