Purpose

The purpose of π Day is to bring to life the circle concepts that the students learned in the classroom. In

addition, this event will allow the students to review those circle concepts prior to the End-Of-Course Test

administration.

Division A

includes, but not limited to:

On March 1st, all students who are enrolled in

Math 2 will have the opportunity to enter one of the

following divisions. Each division will be judged

separately by a panel of judges using the following

criterion:

Illustration of π and/or Circle Concepts (20 pts)

Mechanics (10 pts)

Presentation/Display (10 pts)

Overall Effect (10 pts)

The deadline for all submissions is

Thursday, March 11, 2010 by 3:30 PM.

clothing/apparel

caricature

comic strip

collage

diorama

drawing

jewelry

mobile

monologue

mural

origami

painting

photograph

poster

sculpture

3D model

Division B

includes, but not limited to:

advertising campaign

board game

brochure

children’s book

creative story

letter

limerick

newspaper

jingle

“Pi”ku

poem

rap

song

timeline

Activity Procedure

Prior to π Day, all students who are enrolled in a Math 2 course will sign up for 4 events of their choice.

On π Day, during their scheduled class period, the students will report to a designated area and receive their π

Passport. This π Passport will outline their sequential agenda. To move to the next station, the student must get

an authorization stamp from the previous station.

When the student successfully completes each of the four tasks during their

scheduled class period, he/she will turn in their π Passport and receive a piece of pie.

Each student will be given 3 diagrams. For

each diagram, the student will determine the area of

the circle(s) and the area of the rectangle(s). After

all calculations are complete, the student will

determine the amount of waste (efficiency).

The students will be grouped

into teams of 3. Each teammate will

race to the designated table and receive

a question about arc length and/or

sector area. When the teammate

answers correctly, the next teammate

will be signaled to continue the relay. The first team

to finish the relay will be declared the winner.

Each student will be given

three round objects. For each

object, the student will measure

and record the object’s

circumference and diameter. The

gathered data will be plotted on a

scatterplot.

Each student will be given a real world

scenario which requires the use of π to solve it

correctly.

Each student will name

as many words as possible

without resources that contain

“pi”. The student who recites

the most words will be

declared the winner.

Students who participate in this

activity will conduct Buffon’s classic

needle experiment using parallel lines

and wooden dowels.

Each student will write all

of the circle terms that he or she

can remember in π minutes

(approximately 3.14). The station

supervisor will review the

answers and eliminate any terms

that were listed by more than one

student. The student with the most “unique” circle

terms will be declared the winner.

Using a tape measure, each student will

measure the circumference of his or her head.

Then, the student will use the measurement to

calculate the diameter of his/her head.

Each student

will be given the

specifications for

various sport balls

and the dimensions

of the classroom.

After choosing the

type of sport ball, the student will calculate how

many balls will fit in the classroom.

Each student will be

presented with a series of

individual angle measure

problems. When the student

has the final answer, in

scavenger hunt fashion, the

student will be instructed to

proceed to the next station based on their final

answer.

Beginning March 1st, participating teachers

in the LHS Math Department will collect loose

change. The teacher with the most change by

March 12 at 1:59 PM will have a whipped cream

pie put in his/her face. The proceeds from the

activity will go to Meals on Wheels Program.

.

.

.

.

πDay Choice Wheel

Directions:1. Choose 2 dot-

patterned activities.2. Choose 2 solid

activities.3. Everyone enjoys the

center activity.

Name ________________

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia

Directions:

1.Report to each station as directed by this πPassport.

2.Complete each assigned task.

3.Follow all school rules.

Station 5After all four assigned

tasks have been completed, report to the following station:

Station 4

Be sure to get the authorization stamp

after completion!

Station 3

Be sure to get the authorization stamp

after completion!

Station 2

Be sure to get the authorization stamp

after completion!

Station 1

Be sure to get the authorization stamp

after completion!

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia

Retrieved from www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs

How to Calculate Pi

by Throwing Frozen Hot Dogs

Throwing a pie in someone's face is good. Throwing food at pi is better. Believe it or not, of all the countless ways to approximate the most prolific irrational number in the universe, there are none quite as interesting or as surprisingly satisfying as throwing perfectly good food around your kitchen. In fewer steps than it takes to circumscribe your house in a circle of baguettes, you, too, can easily add a slice of pi into your dinner menu tonight. The best part is...it really works!

Things You'll Need

Pen and Paper

Masking Tape

Calculator

Long, Thin, Straight, Stiff Food. Preferably a pack of frozen hot dogs

Steps

1. Select your food item to throw. There are a couple of qualifications. First, it must be long, thin, and straight, like a frozen hot dog, for example. There are lots of other items that fit this criterion including Otter Pops, celery sticks, and churros. (If you simply can't come to grips with throwing perfectly good food, see the Tips section for some additional ideas.) Second, it must be a reasonably stiff item. Third, it should be somewhere between 15 to 20 cm (6-8 inches) long. The experiment can be performed otherwise, but read on, and you will see why this size is optimal.

2. Select the spot from where you will throw your mathematical cuisine. You will probably need about 180-300 cm (6-10 feet) in front of you as you will be throwing straight ahead.

3. Clear the area. The place at which you are throwing should be devoid of objects that your food item could possibly run in to. So, if you are throwing in your kitchen, consider moving the table into another room or at least throwing in such a way that your food won't hit the table during its flight.

4. Measure the length of your projectile (e.g. your frozen hot dogs). A tape measure should do the trick. Be as accurate as you can, even down to the millimeter, for best results.

5. Lay down masking tape in parallel strips across the floor as far apart as your projectile is long. The strips should be perpendicular to the direction you will be throwing (see picture below). Do about 6-10 strips if your item is 15-45 cm (6-18 inches) long; fewer, if longer; more, if shorter.

Retrieved from www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs

The throwing set-up

6. Get a piece of paper and across the top make a column for “Tosses” and another column for "Crosses." The "Tosses" column is to keep track of how many times you throw your food item. The "Crosses" column is to keep track of how many times your item, once it lands and stops moving, is lying across one of the lines.

7. Now, get into position, and THROW YOUR FOOD! Throw just one item at a time. Once it is at rest, observe whether or not it is crossing one of the lines. If it is, put a tick under "Crosses" and a tick under "Tosses." If it isn't, just put a tick under "Tosses." Repeat this as many times as you like. You should start seeing some interesting results by around 100 to 200 throws (it doesn't take as long as it sounds, especially if you use a pack of 10 frozen hot dogs so you're not out retrieving the one hot dog after every throw).

8. Once you are done throwing your food, multiply the number of tosses by two and divide by the number of crosses. For example, if you threw 500 times, and it crossed 320 times, you would calculate 500 x 2 / 320. And, to your amazement, you will now have an approximation for pi! Now, don't you feel less stressed?

Tips

For those who are troubled by throwing perfectly good food, consider throwing sticks, dowels, or pencils. In fact, any item will do so long as it is long, thin, straight, and stiff.

If room is a concern, consider just drawing lines on a piece of paper and dropping toothpicks onto the paper from about 90 cm (3 feet) up. This definitely is not as refreshing as throwing food across the room, but it works.

The more the merrier! If two or three throw food together, you will get a better approximation faster because you will be able to get more throws in a shorter amount of time.

Warnings

Remember that this is an experiment, so the idea is not to TRY and get the food to land on one of the lines. Just throw it randomly towards the lines. It should still land amongst them, but don't jinx the experiment by encouraging your dinner to land onto the tape.

Resist the temptation to use bananas. Not only are they not really straight, but they really won't last more than 50 throws before creating a big mess. Really.

Though there is no food that is more fun to throw than hot dogs, the math buff will note that greater accuracy will be found the thinner the lines of tape and the thinner the food. Try uncooked spaghetti sticks, for example, for greater accuracy.

Celebrate Pi Day on or near March 14th

or the 314th

day of the year!

Surprising Results with Cylinders Excerpt from MCTM – Pi Day 2002

Bring a collection of cylindrical objects to class (e.g., various size spools,

cups or cans). Ask students to examine (by looking only) the base and

height of each object. Make a guess regarding which is larger – the

circumference of the base OR the height of the cylinder? To demonstrate

the answer, use masking tape to trace around the base of the first cylinder.

Cut the masking tape to fit just around the base. Now remove the masking

tape and put it up the side of the cylinder. Which is larger? Students are often surprised to find

that for most cylinders the circumference of the base is longer than the height. This helps

illustrate the significance of pi and its relationship to the diameter of a circle. As a follow-up

you might have students use a piece of construction paper to build a cylinder which is taller

than the base of its circumference or one that has the same height as the cylinder. How

common are cylinders with this characteristic?

Dropping Toothpicks (Commonly known as Buffon's Needle Experiment)

In 1777, Georges Leclerc Comte de Buffon, discover of the binomial theorem, proposed

dropping a needle on lined paper and asking for the probability of the needle crossing one of the

lines. The answer surprisingly is related to pi.

With your students in teams, make 300 drops of a toothpick (one

unit length) onto paper with several parallel lines one unit apart,

same length as the toothpick. Count the number of times the

toothpick crosses a line. This is a hit. The ratio of hits to 300

approaches 2/π. (hits):(total drops) approaches 2:pi.

Pi is approximated as 2 times the number of drops divided by the number of hits. Let your

students vary the needle length (L) and the distance (D) between the lines to see if your students

can propose a general formula involving L and D. For an excellent online simulation with

explanation, visit www.efg2.com/Lab/Mathematics/Buffon.html. A proof can be found in A

History of Pi by Peter Beckman.

Retrieved from Mathematics Educators of Greater St. Louis

www.mobot.org/education/megsl/pi.html

2

_

dropstotal

hits

One Million Balls Mrs. Sandy Fischl & Mr. Benson

Port Hope High School, Ontario

Hypothesis:

Could 1 million of balls fit into your empty classroom? Explain your reasoning.

Exploration:

1. Pick a ball from the “Sports-Balls Data Sheet”.

2. What are the dimensions of your empty classroom?

3. Calculate how many balls will fit into your empty classroom using the Data Sheet.

Conclusion:

How many of your sports balls would fill your classroom?

PI DAY SCAVENGER HUNT

Procedure

After you have collected your items, label each part of your entry,

place everything in a folder or large envelope with your name on it, and

turn the folder in to your teacher. Time may determine the winner.

You must turn in the items from at least 10 of the 14 categories

to be eligible for the first-place prize. All entries must be school appropriate.

You must be able to clarify or verify items in your entry, if requested.

Items

3 geometric solids which have circular cross-sections (turn in pictures,

labeled with the names of the solids)

.

1 US city with a ZIP code containing the first 5 digits of pi -- beginning

with the 3 (name the city and state)

4 capital letters of the alphabet – in block style – with rotational symmetry

(list the 4 letters)

1 US state which tried to legislate a value for pi (name the state and the

year in which the action was taken)

5 formulas which include π (give the formulas in symbols and tell what each

formula represents)

9 labels or advertisements for products which use circles in their name or

logo (turn in the actual labels or pictures from advertisements in

newspapers, magazines, or from the internet)

2 US cities with names that have references to something circular – cities

should not both be in the same state (name each city and state)

6 US state flags which include circles in their design (turn in pictures of

the flags)

5 sports or games which use a circle or a sphere in their play (turn in

pictures of the circles or spheres from the games, labeled with names of

the games)

3 famous people with birthdays on March 14 (give name and year of birth)

5 movie titles with references to something circular (list the movie titles)

8 kinds of candy that comes in circular pieces (turn in packages or pictures

of candy from advertisements or internet)

9 song titles with references to something circular (list the song titles)

7 recipes for different kinds of pie (turn in complete recipes