Note: You will need the complex math board or to add symbols with tape to your regular math board.

Mathematics fans around the nation are celebrating today because it is **PI** Day! When you hear of the word “Pi”, you probably think about a delicious treat of hot flaky crust filled with apples or blueberries or maybe even banana cream, but today we are going to be talking about a different kind of Pi.

SPELL FLAKY DELICIOUS BANANA

What is being celebrated today? PI DAY

How do you spell the kind of pie that we eat? PIE

What is another word for nation?

Pi is related to the study of _______________ . GEOMETRY

Pi is the name given to the RATIO of the CIRCUMFERENCE of a circle to the DIAMETER. What this means is that for any circle – regardless of how big or small it is, you can divide the circumference – which is the distance around the circle – by the diameter – which is the distance across the circle – and always get a value close to Pi depending on your measurement. (Show the student the visual representation of circumference and diameter.)

The relationship is expressed in the following formula:

SPELL RATIO CIRCLE DISTANCE

What’s the name for the distance around a circle? CIRCUMFERENCE

What’s the name for the distance across a circle? DIAMETER

VAKT: You can try to “prove” this relationship between Pi and circumference and diameter by measuring a the circumference and diameter of a household object and doing the math. How close to Pi did you get?

The VALUE of Pi is **3.14159265358979323846**… Pi is often written using the GREEK symbol Pi which looks like this π.

*Put a piece of masking tape with the Pi symbol on the board and practice having the student touch that symbol. Also add a decimal point to the board.*

VAKT: Draw the symbol for Pi.

What is the formula for finding Pi? C/*d*=π

From which alphabet does the name and symbol “Pi” come from? GREEK

Tell me the first few digits of Pi? 3.14

Given what you know about the word circumference, what do you think the word “circumnavigate” means?

What is intriguing about Pi is that Pi is an IRRATIONAL number. This means that the digits in Pi never end or repeat in a meaningful way. Many mathematicians have spent their lives trying to CALCULATE the digits of Pi, but before computers were invented, less than 1,000 digits of Pi had been calculated. After computers were invented the race was on to calculate as many digits of Pi as possible. Most recently a researcher at Santa Clara University managed to calculate pi to eight QUADRILLION places right of the decimal.

SPELL INTRIGUING UNIVERSITY MATHEMATICIAN

A researcher at Santa Clara University managed to calculate Pi to eight _____________ places. QUADRILLION

What kind of number is Pi? IRRATIONAL

What is one thing that is unique about irrational numbers? NEVER END OR REPEAT IN A MEANINGFUL WAY

What do most people use now to calculate the digits of Pi? COMPUTER

How would you define calculate?

Show me a calculation that you are able to do in your head.

Even though these computer driven calculations are ASTOUNDING, there are still those who prefer to MEMORIZE and orally RECITE the digits of pi as far as possible. The Guinness Book of World Records still has Chao Lu from China as the record holder after reciting 67, 890 digits, but a Japanese man named Akira Hagaguchi recited 100,000 digits of pi at a public event in Tokyo in 2006. He has created an intricate system to memorize Pi including ASSOCIATING each digit with a particular sound and weaving these sounds into stories.

SPELL INTRICATE CALCULATION MEMORIZE

In what book are the records for calculating Pi noted in? GUINNESS BOOK OF WORLD RECORDS

What’s another word for recite?

What’s another word for astounding?

Which country is the current Pi recitation record holder from? JAPAN

How many digits of Pi did Chao Lu recite? 67,890

Approximately how many more digits did Akira Hagaguchi recite? 100,000 – 67,890 = 32,110

Name one strategy that Akira Hagaguchi uses to memorize Pi. ASSOCIATING EACH NUMBER WITH A SOUND

Describe the system that you use to memorize things that are important to you.

Now it’s time to learn how to use pi in order to calculate things we need to know. There are several different ways in which Pi is used in mathematics. One of the most common is in finding the circumference of a circle. Circumference is the distance around a circle. The formula we use for finding the circumference of a circle is C =πd.

Using this formula, let’s try to find the circumference together of the following things.

The diameter of a nickel is 2cm. What is the circumference? C= π(2) = 6.28

The diameter of a circle is 3 cm. What is the circumference? C= π(3) = 9.42

Sometimes we will only know the radius of the circle and will be asked to find the circumference. The RADIUS of a circle is the distance from the center of the circle to any point on the circle. It is always 1/2 the length of the diameter.

VAKT: Draw a circle together. Draw the radius of the circle and then draw the diameter.

Given what we now know about the relationship between radius and diameter, what do you think we would do to find the circumference of a circular rug that has a radius of 4 feet? (multiply 4 x 2 and then multiply by Pi)

What if we are given the circumference of the circle and are asked to find the diameter?

The circumference of a CD is 28.26 cm, what is the diameter? 8.99

What is the radius? 4.49

The circumference of a circle is 15.7cm. What is the diameter? 4.99

We can also use Pi to determine the AREA of a circle which is the amount of space that is occupied by a circle. Let’s take a look at the circle below. In this example we know that the radius of the circle is11 feet. We want to determine how much space is being taken up by the circle as a whole. We can do this by using the formula for finding the area of a circle which is

A=πr^2

What is the formula for finding the area of a circle? A=πr^2

SQUARED means that we need to multiply the value of “r” by itself.

When we square a number, we must ____________ it by itself. MULTIPLY

Let’s find the area of a circle using this formula together. We will use **Pi = 3.14** to simplify our calculations.

Area of circle with 11ft Radius = ____________. 380.13ft

Area of circle with 9mi Radius = ____________. **254.46mi**

Area of circle with 7.4km Radius = ____________. 172.03km

What are we going to need to do if we only know the diameter of the circle, but still want to find the area of the circle?

In this example the diameter is 8 yards. What is the area of this circle? 50.26yds

Now we have a diameter of 16.8 meters. Let’s try to figure out the area of this circle. 221.67m

Now that you have done all of this fun math, lets grab some real pie and celebrate this special day of mathematical beauty!

A special song for Pi Day… https://www.youtube.com/watch?v=2CGWA_DzvDg

Creative writing:

The celebration of Pi Day was suggested by a physicist named Larry Shaw in 1988. If you could create a day of celebration, what would you want to

celebrate and why?

Sources:

http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/mar/13/pi-day-2015-memory-memorisation-world-record-japanese-akira-haraguchi

http://www.joyofpi.com/pifacts.html

http://www.telegraph.co.uk/news/worldnews/asia/japan/8834265/Japanese-mathematician-breaks-record-for-determining-the-value-of-pi.html

http://www.exploratorium.edu/pi/pi_activities/index.html

http://learning.blogs.nytimes.com/2015/03/12/throwback-thursday-the-pi-day-of-the-century/?_r=0

http://www.exploratorium.edu/pi/history_of_pi/index.html

http://www.mathgoodies.com/lessons/vol2/circumference.html