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Pi Day is an opportunity to break up the routine and celebrate an amazing number with connections to so many relationships
In the past several years I have fully transitioned from memorizing digits, crafty skylines built from pi, and finding your birthday in pi to a focus on the amazing relationships and patterns that involve pi (which is really what mathematics is about anyway.) The activities below are a loose progression, although many can be used or adapted for numerous levels.
Desmos Collection
Interactive app to show circle cuts.
Leonardo DaVinci designs
Pi Day Facts
Different ways of thinking about Pi Video
Pi and Bouncing Masses Video
Relationship of perimeter of circles to pi: I knew by definition this was the ratio of circumference to diameter. It wasn't until I actually until I measured various diameters with string and physically used the diameter around that circle to really understand this.
Even the beginning activities offer an insight few people really understand about pi.
Desmos Activity: Donkey Kong Circles gives meaning and practice for circumference and area.
Desmos Activity: Exploring Circumference and the proportional relationship.
Bubble pi: Students blow bubbles with straws on their desks and measure the diameter and circumference. They record the data and build a line of best fit to discover pi!
Slides with closure video and data collection spreadsheet
Sara VanDerWerf has many introductory resources for circles and pi
Area
Pi is related to the area of a circle: I will be honest, I memorized this in high school. In college, I briefly connected the area of increasing polygon sides. There are SO many ways to see this relationship!
Desmos activity Exploration on Area formula of circle (using a triangle)
Desmos Activity illustrating the visual of a radius squared. This is how 7th grade visualizes this relationship.
Parallelogram Desmos Activity using parallelogram to approximate area.
Polygon Area Desmos Activity showing increasing sides leads to circle area and perimeter (helpful for the full lesson if students have done Ch8 IM2)
3 Act Task by Tap into Teen Minds the first includes Pi relationship in circumference, and the second in area.
Buffon's Needle
Buffon's Needle (interesting place with pi in probability) I did this with hot dogs in person... I think I will use Otter Pops next time since it felt a little wasteful and bothered some of my vegetarians. The only thing I don't like about the virtual simulation is it automatically gives the pi calculation.
Here are the intro slides I used (they are NOT professional quality)
Sectors, Arcs and Radians
Activity Exploration on circle arcs and sectors (Pizza Pie)
Activity Exploration on meaning of radian and relationship to trigonometry (really for IM 3 and beyond.)
Desmos Activity: Unit Circle War
Other interesting relationships beyond traditional curriculum
e^(iπ)=-1 in a new way of thinking (Group Theory)
This Desmos Activity uses the rotation for multiplying complex numbers for Euler's number
e^(iπ)=-1 using Maclaurian Series (Uses polynomial approximation from Calculus- (this was the first time I remember feeling the joyous connection of so many math ideas!)
Taylor Approximation of Pi Desmos Graph
Math Medic Resources
Math Medic Resources
Will Insomnia Cookies Deliver to Your House? Geometry - Unit 8 Day 1 - Equation of a Circle
What’s the Size of the Pizza? Geometry - Unit 8 Day 9 - Area and Circumference of a Circle
How Much Pizza Did You Eat? Geometry - Unit 8 Day 10 - Area of a Sector
How Far Apart Are the Exits? Geometry - Unit 8 Day 11 - Arc Length
A Spin on the Ferris Wheel Geometry - Unit 8 Day 2 - Circle Vocabulary
The Circle Family Algebra 2 - Unit 3 Day 8 - Transformations of Circles
The Unit Circle Algebra 2 - Unit 9 Day 7 - Unit Circle
Can You Give Me That in Twizzlers? Precalculus - Unit 4 Day 3 - Radians and Degrees
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