MATH
WITH MR. HERTE
Pi Day
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Purpose: Pi Day is a day to celebrate mathematics in your school. It gives us the perfect springboard to allow our students to have fun while investigating mathematics concepts, being creative and even a little silly. If you have any ideas email them to me. I will eventually be attaching some of the materials to each activity so you can click onto it for more ideas. Pi Day Activities! Name That Circle! (9th -11th Grade) Students are shown a graph of a circle and the student that can correctly give it's equation wins! You can run it as a team competition or one on one. Be certain to go over the general equation of a circle first. For grade 9 or students who have not studied this keep all circles in the first quadrant. Examples Pi Digit Distribution (Elementary - HS) The younger students can look at the first 50 or 100 digits of pi and make a bar graph of the frequency of each digit. (How many times does 0 appear?) Students enjoy this rich data source for bar graphs. HS students find the mean of the first 100 digits (use scientific calculators/graphing calculators) Create circle graphs based on the digits -excellent use of protractors, fractions, decimals and angles if done by hand. Use spreadsheets to examine the distribution of the digits. Examples Rolling Along...(Elementary - Middle) Students collect various circular objects (cups, coins, cans, buckets, CD's) Using the large teacher graph paper students plot the diameter vs. the circumference. They simply line up the left side of the can (for example) on the origin and mark the right side of the can (diameter) along the x-axis (bottom of graph) They then take the can and mark a starting point on the can, and line up the starting point with the x-axis. They roll the can 1 revolution (1 roll) up and mark a point. Repeat for all the circular objects. What does the graph look like? (I got this activity from a friend Tricia from upstate NY) Calculate Pi (Elementary - Middle- High) Have the students measure the diameter and circumference of various circular objects using tape measures or use string and then use meter sticks. Have the students divide the circumference by the diameter. (I still fondly remember this from when I was in 7th grade) You could also graph the diameter vs. the circumference using the graphing calculator, (High School) and then use linear regression to find the equation. TI 83 Programs to Calculate Pi (Middle - High) Here are 3 programs that I wrote for the TI 83 Plus, but will work with most of the other graphing calculators. Pi Stream is a program that approximates pi streaming the digits on the screen so the student can see the digits lock into place. The Pi program illustrates the number of iterations it takes to get more and more precise approximations. Piaccura (Pi Accurate) takes the first few terms and then averages the high pi value and the low pi value to double the precision. Pi Programs Pi Chain (General) Create the longest Pi Chain ever! We have a NEW CHAMP! The students in Madison Junior High, Madison, NJ set a new "world" record of 2,201 digits!!! Their teacher Ms. Prill wrote in very proudly. Great job to those students at Madison Junior High! Well, this certainly gives us something to strive for. In 2000, the students in Williamstown Middle School (NJ) created one 1846 links long as it wrapped its way through the hallway! Make up a color scheme 10 colors one for each number. Example: 0 is green, 1 is yellow, 2 is blue, etc. Pi Chain Pi Quilts (General) I got this idea from Pat Walsh. Start with a 10 by 10 grid and have the students color in the squares starting in the center, spiraling outward. Each number has a different color above. Each student gets a different 100 digits of Pi, attach all the squares in the same fashion (center square is the first 100 digits, and then spiral the squares outward) Circle Graphs (Middle) Great idea for those of you with an assessment exam at the end of the year! Have the students conduct a survey of something of interest to them. Favorite music, sport, school lunch -whatever. Students then calculate the fraction of the total for each. They convert it to decimal and multiply by 360 degrees and then create a circle graph of that data. Students enjoy this due to their personal decision of topic, the coloring aspect and the social nature of conducting a survey. Teachers like it due to the many skills that are used in it. (protractors, decimal, fraction, percent conversions -conducting "fair"/ unbiased surveys) Examples Surface Area of a Sphere (Middle - HS) I'll get the exact reference in a couple of days but this idea came from a January of February article/submission in the NCTM Mathematics Teaching in the Middle School. They didn't suggest it for Pi Day but that's what I immediately thought of. Take a sheet of paper and cut it into small right triangles (easier to calculate the area of each) Glue the triangles onto the tennis ball and calculate the surface area of it. The article has great pictures and references. Check it out! Pi Decoration -Give the students a LARGE Pi symbol and have them decorate it/incorporate it into a drawing. I also got this idea from Pat Walsh. Pi Mobile -I just got this idea while typing the above activity. Give students a Pi template and have them cut out colorful pi symbols from cardstock. Attach each new pi to the bottom of the one above (1 on top 2 beneath) Hey, this will make a Pi Fractal!!!) Pi Mobile Materials Pi Day Songs These songs were written by some of Mr. Herte's students Pi Songs Happy Birthday! Sing Happy Birthday to Albert Einstein and Waclaw Sierpinski (Sierpinski's Triangle) Pi Advertisement Interdisciplinary Project This idea comes from Crystal Maclin, a teacher from Cleveland, Ohio. "The Smell So Good Perfume Company has developed a new unisex fragrance called Pi. The company executives need an ad campaign that will embody the true meaning of Pi, its historical background and capture the attention of their target audience (ages 16-25). It is you job to create this advertisement." Ms. Maclin allows the advertisements to be video commercials, radio (audio), or magazine/newspaper ads. She uses Pi Day for presentations. Students are graded on math information, technical stuff (i.e. time limit, editing, etc.), creativity and effort, and references. Contests and Games Circle NIM (Elem - HS) Give two students an official game board. (actually just a sheet of white computer paper) I print in large letters "Official Game Board" just for fun. Each student gets 3 different size circles you can give them 2 or 3 of each size. The object of the game is to place the last circle on the Official Game Board. Rules: You can't move anyone's circle that's already been placed. You can't have any portion of your circle hang over the Game Board. You can't overlap any other circle. This is a great strategy game and also reinforces the idea of area though no calculations are used in the game. It's About... (Middle - HS) This is all about estimation. For those of you who enjoy memorizing pi digits this will not sit well with you. Students use the value of Pi = 3 in this fast paced mental calculation game. Give the students a circle with either a radius or diameter. The first one to give you the correct area or circumference (using pi = 3) gets a point or wins a piece of candy. For older students find the volume of a sphere or the surface area of a sphere. You could also find the length of an arc. It's all about estimation and it reinforces the idea that a quick estimate is a useful tool. Examples Pi Digits Create a Hall of fame or grade-wide school records. Students memorize the digits of pi and the student that memorizes the most can win a prize, trophy, certificate -whatever. I have the students memorize the first 10 digits as part of a homework assignment but the rest is up to them if they wish to participate. The Finley Middle School records are as follows: 6th grade 70 digits; 7th grade 307 digits and 8th grade 157 digits! There's a nice web site called the Pi Trainer that you can use to run the finals of a competition or to learn the digits. You type in the digits that you know and it tells you how many digits you have correct and the next five digits. -All in good fun don't take this too seriously. Pi Digits Archimedes Contest (All Grades) I created this after having read the story "Death of Archimedes" in "Fantasia Mathematica" by Clifton Fadiman. Any story of Archimedes Death will do though. He died while drawing circles...-much more to the story and it inspired Sophia Germain to become a mathematician so it's perfect for our students. This contest gives students that are not the best mathematicians a chance. Each student is given 2 sheets of OFFICIAL PAPER. They are given 2 chances, one per sheet to draw the most perfect freehand circle. They may not turn their paper, or hold their hand as if it were a compass. (Great ideas though!) Just one simple loop. Circles must be the approximate size of a coffee cup. Students then hand in the one circle they want to have entered. I do this on a class-wide basis and believe it or not it's an easy contest to judge. I make them draw the size of a coffee cup because we always have one lying around and it may be helpful to judge. Around Town... (Elementary - Middle) I got this idea while driving... Students are given 2 minutes to write down as many things as they can think of that are circles. CD's, Buttons, coins, etc. Winner is the student with the most. This contest could also be run like "Boggle" where you throw out any item that any other student thought of and crown the winner as the student with the most original items. Circle Songs (All Grades) See how many songs you can name that have to do with circles, hoops, rings, etc. You'll find many entries from people across the United States. You can add to this list by emailing me. Circle Songs Button Contest (All Grades) Last year the logo above was inspired by one of my 7th grade students. You can have a contest for the button design and then using a Badge-A-Minute machine make up the buttons. I have the simplest version and it only takes me a couple of hours to crank out 300. Last year I mistyped 2 of the digits wrong and had to throw away 300! OUCH! I used it as an example of checking your works with the students. I guess that batch is now a Finley collectors item. Poster Contest (All Grades) Be sure to give the students a theme. Last year's theme at our school was "Circles, Circles Everywhere" Song Contest (All Grades) There are two wonderful Pi Day songs on the web see the links. This will be my first year having the song contest so I hope that my students will be able to contribute to the song pool. Poetry Contest (All Grades) Be sure to give the students a theme. Last year's theme at our school was "Circles, Circles Everywhere" I had many rhyming poems but also free verse and even an over achieving Haiku!
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