Lesson .

Whirling Wonder: A 'Pi in the Sky' Math Challenge

Subject

Math

Grade Levels

9-12

Time Required

Under 30 mins

Illustration (split-screen) of helicopter on Earth flying compared with Ingenuity flying on Mars.

Overview

The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the eighth set, students use the mathematical constant pi to determine how quickly the Ingenuity helicopter's blades must rotate in order for it to fly.

Materials

Pi in the Sky 8: Whirling Wonder worksheet – download PDF
Pi in the Sky 8: Whirling Wonder answer key – download PDF (also available as a text-only doc)

Background

On the right hand side of the image, the Perseverance Mars rover looks forward toward the camera. In the lower left, the Ingenuity helicopter sits on the surface of Mars.

NASA’s Perseverance Mars rover took a selfie with the Ingenuity helicopter, seen here about 13 feet (3.9 meters) from the rover on April 6, 2021.

Credit: NASA/JPL-Caltech/MSSS

Joining the Perseverance rover on Mars is the first helicopter designed to fly on another planet. Named Ingenuity, the helicopter is a technology demonstration, meaning it's a test to see if a similar device could be used for a future Mars mission. To achieve the first powered flight on another planet, Ingenuity must spin its blades at a rapid rate to generate lift in Mars’ thin atmosphere. In Whirling Wonder, students use pi to compare the spin rate of Ingenuity’s blades to those of a typical helicopter on Earth.

Procedures

Joining the Perseverance rover on Mars is a small helicopter named Ingenuity. With twin counter-rotating blades spanning 1.2 meters, Ingenuity is a test of new technology and is designed to achieve the first powered flight on another world.

Despite Mars having less gravity than Earth, the atmosphere on the Red Planet is much thinner than it is here on our home planet. This makes it challenging to lift off the ground on Mars. To generate enough lift for Ingenuity, engineers determined that the helicopter's blades need to rotate at approximately 250 radians per second on Mars.

How fast – in rotations per minute – do Ingenuity’s blades spin?

How does that compare to a typical helicopter on Earth with blades that spin at 500 rotations per minute?

› Learn more about the Ingenuity helicopter

› Download PDF.

Credit: NASA/JPL-Caltech

Assessment

Illustrated answer key for the Sample Science problem

› Download text-only answer key (doc)

Extensions

Pi Day Resources

educators.

Pi in the Sky Lessons

Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

students.

NASA Pi Day Challenge

The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

students.

How Many Decimals of Pi Do We Really Need?

While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

students.

18 Ways NASA Uses Pi

Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

educators.

10 Ways to Celebrate Pi Day With NASA on March 14

Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.

students.

Infographic: Planet Pi

This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

students.

Mobile & Web Backgrounds

Can't get enough pi? Download this year's NASA Pi Day Challenge graphics as mobile phone and web meeting backgrounds:

educators.

Pi Day: What's Going 'Round

Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.

Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.

Related Lessons for Educators

educators.

Make a Paper Mars Helicopter

In this lesson, students build a paper helicopter, then improve the design and compare and measure performance.

Related Activities for Students

students.

Code a Mars Helicopter Video Game

Create a video game that lets players explore the Red Planet with a helicopter like the one going to Mars with NASA's Perseverance rover!

students.

Make a Paper Mars Helicopter

Build a paper helicopter, then see if you can improve the design like NASA engineers did when making the first helicopter for Mars.

Multimedia

students.

Infographic: Planet Pi

This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

Whirling Wonder: A 'Pi in the Sky' Math Challenge

Overview

Materials

Background

Procedures

Assessment