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ฯ€ Week 28: Pi Day Mathematics

Lesson Overview
Grade Level Grades 5-6
Duration 45 minutes
STREAM Focus M (Math), T (Technology), R (Religion)

Week 28: Pi Day Mathematics

๐ŸŽฏ Learning Objectives

STEM Objectives

Students will be able to: 1. Understand ฯ€ as a ratio and its significance 2. Calculate pi through measurement and simulation 3. Code a Monte Carlo simulation to estimate ฯ€ 4. Apply pi in engineering calculations

Faith Integration Objectives

Students will be able to: 1. Appreciate mathematical constants as part of God's ordered creation 2. Connect infinity of ฯ€'s digits to God's infinite nature 3. Recognize mathematics as discovering (not inventing) truth

Week 28: Pi Day Mathematics

๐Ÿ™ Faith-Reason Integration

Catholic Teaching Connection

Mathematical Truth โ€” Catholics believe mathematical truths are discovered, not invented. Pi exists whether or not humans know about it. This reflects God's ordered creation โ€” truth exists objectively, and we discover it.

Scripture Connection

"He has measured the waters in the hollow of his hand, and with the span of his hand marked off the heavens." โ€” Isaiah 40:12

Saint Connection

Fr. Marin Mersenne โ€” 17th-century priest who made significant contributions to mathematics and music theory. He corresponded with Descartes, Pascal, and other great mathematicians, seeing no conflict between faith and mathematical inquiry.

๐Ÿ“š Materials Needed

  • Circular objects and string

  • Rulers

  • Computers with Scratch (or calculators)

  • Pi digit sheets

  • Graphing materials

๐Ÿ“ Lesson Procedure (45 minutes)

Opening Prayer & Introduction (5 min)

Prayer: "God of infinite wisdom, Your creation contains beautiful mathematical truths. Help us explore the mystery of pi today and see Your order in mathematics. Amen."

Pi Day context (March 14 = 3/14):

  • "Pi appears EVERYWHERE in creation"

  • "Not just circles โ€” physics, probability, nature"

  • "It's irrational โ€” infinite non-repeating digits"

  • "Yet it's constant โ€” always exactly the same"

Wonder: "How can something be infinite yet constant? How can we know it precisely yet never write it completely?"

Measuring Pi (10 min)

Original discovery method:

  • Pi = Circumference รท Diameter

  • EVERY circle, EVERY size, SAME ratio!

Activity: 1. Measure circumference of circular object (string method) 2. Measure diameter 3. Calculate ratio 4. Compare to actual pi (3.14159...)

Class data collection:

Object Circumference Diameter C/D Ratio
Can 25.1 cm 8.0 cm 3.14
Lid 18.9 cm 6.0 cm 3.15

Discussion:

  • Why don't we get exactly 3.14159?

  • How could we be more precise?

  • What does "irrational" mean?

Monte Carlo Estimation (15 min)

Visual approach to pi:

Imagine a square with a circle inside it (circle touches all sides).

  • Drop random points in the square

  • Count how many land inside the circle

  • The ratio relates to pi!

The math:

  • Square area = (2r)ยฒ = 4rยฒ

  • Circle area = ฯ€rยฒ

  • Ratio: Circle/Square = ฯ€rยฒ/4rยฒ = ฯ€/4

  • So: ฯ€ = 4 ร— (points in circle / total points)

Scratch implementation: 

Set [in_circle] to 0
Set [total] to 0
Repeat 1000
    Set [x] to (pick random -100 to 100)
    Set [y] to (pick random -100 to 100)
    Set [distance] to (sqrt of ((x * x) + (y * y)))
    If distance < 100 then
        Change [in_circle] by 1
    Change [total] by 1
Set [pi_estimate] to (4 * (in_circle / total))
Say (join "Pi โ‰ˆ " (pi_estimate))

Students code and run simulation:

  • Try with 100 points

  • Try with 1000 points

  • Try with 10000 points

  • What happens as you increase points?

Key insight: "More samples = closer to true pi! This is called Monte Carlo simulation."

Pi in the Real World (8 min)

Where pi appears:

Circles and spheres (obvious):

  • Wheels, balls, planets

  • Area = ฯ€rยฒ, Circumference = 2ฯ€r

Waves and oscillation:

  • Sound waves, light waves

  • Pendulum motion

  • Electronics signals

Probability and statistics:

  • Normal distribution (bell curve)

  • Random walks

Physics:

  • Einstein's field equations

  • Heisenberg uncertainty principle

  • Period of pendulum

Nature:

  • River meandering ratio โ‰ˆ ฯ€

  • Spiral patterns

  • Eye structure

Engineering application:

  • Calculate gear circumference for robot

  • Determine wheel rotation for Sphero distance

Faith Connection (5 min)

Mathematical constants and God:

Pi is discovered, not invented:

  • "Pi existed before humans calculated it"

  • "We DISCOVER mathematical truth, we don't CREATE it"

  • "This is how Catholics understand all truth โ€” it exists objectively"

Infinity of pi's digits:

  • "Pi has infinite decimal places, never repeating"

  • "We can calculate more digits, but never ALL digits"

  • "God is infinite โ€” we can always know Him more, but never comprehend Him fully"

  • "Pi reminds us of infinity!"

Fr. Mersenne reflection: "Catholic priests and scientists have contributed to mathematics for centuries. They saw discovering mathematical truth as discovering God's creation."

Closing (2 min)

Pi celebration:

  • Share estimation results

  • How close did simulations get?

  • Appreciate the beauty of mathematics

Closing Prayer: "Thank You, God, for mathematical beauty. Thank You that pi is constant throughout the universe โ€” from atoms to galaxies. Help us see Your fingerprints in mathematics and pursue truth in all areas. Amen."

โœ… Assessment

  • Calculated pi through measurement

  • Coded Monte Carlo simulation

  • Compared estimates to actual pi

  • Connected mathematical constants to faith

๐Ÿ“Ž Home Connection

"We celebrated Pi Day (3/14)! Ask your child: 'What IS pi?' 'How did you estimate it?' 'Where does pi appear in the real world?' We discussed how mathematical truths are DISCOVERED, not invented โ€” they exist whether or not humans know them. This reflects Catholic understanding that truth is objective, created by God."

Lesson Version: 1.0 | **