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Math Lessons and Worksheets
Pi is Irrational
Pi is an irrational number. This means that pi cannot be written as a fraction of two whole numbers and that the decimal digits of pi continue infinitely without any repeating pattern. Pi is roughly 3.14159265358979323846.... Using computers, pi has been calculated to many million of digits past the decimal point. For many purposes, using the approximation 3.1416 is sufficient. Good approximations for pi are 22/7 and 355/113.
Pi is used in many calculations, including finding the circumference and area of a circle, and the volume and surface area of a sphere, cone, and cylinder. Pi is also used in geometry, probability and statistics, and many other fields.
(radius = r)
|2π r||π r2|
(radius = r)
|4π r2||(4/3) π r3|
(radius = r, height = h)
|2π r h (without the ends)||π r2 h|
The Name Pi
Mathematicians began using word pi (the Greek letter π) for this ratio in the early 1700s; the name pi was given to this number because p is short for perimeter.
Pi Day is a mathematical holiday celebrated by math classes on March 14th (3/14), with the peak celebration occuring at at 1:59 p.m (3/14 1:59). Pie, pizza, and other round foods are often served at Pi Day celebrations.
Write Eight Round Things
Think of and write eight round things. Then, for each word, write a sentence containing the word. Sample answers: pie, disk, pie plate, necklace, plate, circle, wheel, pupil of the eye.
Write Eight Round Things in Categories
Think of and write eight round things in categories, including: food, sports item, school item, household item, animal, article of clothing, part of a vehicle, astronomical object. Then, for each word, write a sentence containing the word. Sample answers: pizza, basketball hoop, globe, plate, sand dollar, bracelet, steering wheel, moon.
Draw Four Round Things
Draw four round things. Below each item, write its name.
Draw Four Spherical Things
Draw four spherical things. Below each item, write its name.
A Printable Worksheet
In this worksheet, the student measures the circumference and diameter of three circles, and then calculates the ratios of the circumferences to the diameters (approximating pi). The student will need a ruler and a short length of string or yarn (a bit less than a foot long); the yarn is used to measure the circumferences. Or go to the pdf version.
What is Pi?
A Printable Worksheet
A printout about what pi is. Measure the circumference and diameter of four printed circles, then determine what relationship between the circumference and the diameter gives a constant value (pi). This printable worksheet demonstrates to the student that pi is the ratio of a circle's circumference to diameter, for any circle The student will need a ruler and a short length of string or yarn (a bit less than a foot long); the yarn is used to measure the circumferences. Or go to the pdf version.
|All-Purpose Check-Off Card
Print a card that is good for many occasions, including Happy Birthday, Valentine's Day, Mother's Day, Father's Day, Congratulations, Graduation, Get Well Soon, Pi Day, Easter, Christmas, Hanukkah, Ramadan, Anniversary, New Year or Many Thanks. Just print the card, then check off the appropriate occasion.
Label Lower-case Greek Letters
Label the lower-case Greek letters.
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