Pi Day! Squaring the Circle

Π Pi Day!Squaring the Circle Goals for today’s lesson: Estimate Π Practice finding the perimeter of squares. Practice finding the perimeter (circumference) of a circle. Practice finding the area of a circle.

Finding a Circle’s Circumference Just a life is a lot easier with pie, math is a lot easier with Π! Today we’re going to try to find the circumference of a circle without using Π. • Will help you to understand what Π is. • Will help you to understand Π’s importance.

Using a Compass On a piece of scrap paper from your materials box, practice making circles using the compass.

Choose a Radius You’re going to draw a circle with a whole number radius of your choice. Use a ruler to set your compass to the desired radius.

Draw a Circle Now that you have set your radius, you will draw a circle on your worksheet. • Record the radius and diameter of your circle in your table. • Place the pointed tip of your compass where the lines intersect. • While holding your compass point firmly in place, gently rotate it from the top to draw a circle on your paper.

Square the Circle • Place a dot at each of the four places where the solid lines and the circle intersect.

Square the Circle • Using a ruler the keep your line straight, connect each one of those dots with a line. • Find the perimeter of the square you just drew. Record it in your table under “perimeter of small square.”

Square the Circle • Where the dotted line intersects the circle, make four more dots. • Hold a ruler edge against the side of your circle at this dot. Use your ruler to draw a straight line.

Square the Circle • When you are finished, your drawing should look like this. • Find the perimeter of the large square and record it in your data table under “perimeter of large square.”

Square the Circle • Notice that the perimeter of the circle is, on average, about halfway between the two squares. • A good estimate for the perimeter (circumference) of the circle would be about halfway between the perimeter lengths of the squares.

Square the Circle Find the median (halfway point) of the two squares’ perimeters. • Find the difference between the two squares’ perimeters. Record this in your data table. • large square perimeter – small square perimeter = difference • Divide the difference by 2. Record the quotient in your data table. • Add the quotient to the perimeter of the small square. Record this number in your data table as your circumference estimate • You have found the median of the two squares’ perimeters – the halfway point between the perimeters.

Estimate Π • In your data table, find your estimate of your circle’s circumference. • Divide the circumference by the diameter. • Record this number in your data table as your Πestimate. • Come write your Πestimate on the board.

So what is Π? • Greek letter. • English spelling “pi” • English pronunciation “pie” • Greek letters used as symbols in math and science.

So what is Π? • Any circle’s circumference divided by its diameter will always = Π. • Any circle’s diameter multiplied by Π will always equal its circumference. • Π represents a constant relationship (ratio) between diameter and circumference.

So what is Π? Think of it this way: Circumference and diameter are in a relationship. They use Π as the symbol for their constant love. Π d C

Calculator “Trick” • Your calculators have a Π button. • Whenever you are using Π in an equation, use this button. Ex: 3 × Π would be 3 Π =

Before We Can Eat … You must find the circumference of a pie!

Find the Circumference of a Pie • Get a pie. • Find your pie’s diameter using a ruler. • Hint: It may be easiest to sit the pie plate on top of the ruler. • Record the diameter in your data table. • Find the pie’s circumference. • Record the circumference in your data table.

Ready to Eat? Turn in your completed data table for a serving of pie.

Pi Day! Squaring the Circle