Embedded Files
Learning Intention:
Learning Intention:
investigate the relationship between the diameter and circumference (perimeter) of circles and the relationship between the radius and area of circles.
investigate the relationship between the diameter and circumference (perimeter) of circles and the relationship between the radius and area of circles.
Circumference of a circle
Circumference of a circle
-For any circle the circumference is always just over three times bigger than the diameter.
-For any circle the circumference is always just over three times bigger than the diameter.
-The exact number is called π (pi). (We use the symbol π because the number cannot be written exactly).
-The exact number is called π (pi). (We use the symbol π because the number cannot be written exactly).
-When we are doing calculations involving the value π we have to use an approximation for the value (3, 3.14, 22/7, π button on a calculator. )
-When we are doing calculations involving the value π we have to use an approximation for the value (3, 3.14, 22/7, π button on a calculator. )
-Pi is an irrational number. That means it has a decimal component that never repeats and never ends. It goes on forever and ever with no pattern.
-Pi is an irrational number. That means it has a decimal component that never repeats and never ends. It goes on forever and ever with no pattern.
Tasks:
Tasks:
Using materials provided, measure the circumference and diameter of a variety of circular objects. Complete the table:
Using materials provided, measure the circumference and diameter of a variety of circular objects. Complete the table:
2) Answer the following questions:
2) Answer the following questions:
1. What do you notice about the Mystery Ratio for each object?
1. What do you notice about the Mystery Ratio for each object?
2. What whole number is this ratio near?
2. What whole number is this ratio near?
3. The mystery ratio has a special name: pi. Based on the activity you did, create a mathematical definition for pi. Use the vocabulary you have learned in your definition. (Hint: Look at the column headings of your table)
3. The mystery ratio has a special name: pi. Based on the activity you did, create a mathematical definition for pi. Use the vocabulary you have learned in your definition. (Hint: Look at the column headings of your table)
4. Look at the mystery ratios on your worksheet. How close do your ratios come to 3.14?
4. Look at the mystery ratios on your worksheet. How close do your ratios come to 3.14?
5. Why might your ratios be a bit different? Think of more than one reason if you can.
5. Why might your ratios be a bit different? Think of more than one reason if you can.
6. Someone brings a huge pizza into the room and tells you that the diameter of the pizza is 1.2 meters. Use your knowledge of pi to estimate what the circumference of the pizza is. (You do not need a calculator. Just estimate.)
6. Someone brings a huge pizza into the room and tells you that the diameter of the pizza is 1.2 meters. Use your knowledge of pi to estimate what the circumference of the pizza is. (You do not need a calculator. Just estimate.)
7. Would you rather have a pizza that has a circumference of 50 centimeters or a diameter of 50 centimeters? Explain your answer.
7. Would you rather have a pizza that has a circumference of 50 centimeters or a diameter of 50 centimeters? Explain your answer.
π = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 (to 200 decimal places)!
Pi to 1,250,000 digits
Other Pi Activities
Other Pi Activities
Celebrating Pi Day with EquatIO Mathspace
These next Pi-themed activities were all created using EquatIO Mathspace, which makes it easy for you to save, share and assess digital math activities. Try them out below.
Activity 1: https://equat.io/yymg-z4ux
You can’t celebrate Pi Day without mentioning pie. Help your students build their understanding of radius, diameter and area with this fun activity. Yum!
Activity 2: https://equat.io/5vma-cvu7
Here’s a great visual to get your students practicing fractions. (It’s a good idea to use it AFTER the lunch break!)
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