From Nanoscopic to Astronomical ~ Introducing “Powers of Ten” Day (Oct.10)

My students and I first celebrated POWERS of TEN DAY in 2014. My 3rd-5th-graders see the film on their first day of class and we discuss it (see “POWERS of TEN and COSMIC EYE ~ Mind-Expanding for Students), but October 10th is the perfect day to revisit the film and introduce a few advanced math and science concepts related to relative size and scale, exponential growth, and disciplines that deal with very large and very small numbers.

Here are several lessons and activities you might incorporate to celebrate POWERS of TEN DAY:

(1) Explain the meaning of “powers of ten” using the basic concepts presented in this video. You can share the video or use it as a guide in presenting the lesson yourself.

(2) Introduce students to math problem solving and terminology related to exponents. You can share this video teaching or use it as a guide for teaching the concepts. The song in the video below complements the lesson and includes an explanation of three types of numerical expressions (exponent form, expanded form, and standard form). Pause the video during the POP QUIZ at the end to test your students’ understanding.

Older and more advanced students might be ready for an introduction to negative exponents. MATH IS FUN has a very good explanation HERE, one that your some of your students could easily read and understand on their own. Students intuitively understand that negative exponents of positive integers result in numbers smaller than one. Using calculators, they can divide to find decimal equivalents of powers of ten with negative exponents (e.g. 10 to the power of negative one = 0.1, to the power of negative two = 0.01, etc.)

(3) Have students practice what they know or have learned about exponents by playing games. POWER STRUGGLE is one I created for older students that will help them become more familiar and comfortable with exponents. The EXPONENTS GAME (free download) is a more basic alternative. You can also find a QUESTION TRAIL activity HERE and some colorful activities and station activities HERE.

(4) Help students make connections to square numbers and square roots and introduce cube roots. See Square Numbers and Square Roots for a lesson that includes a fantastic NRich Maths problem called “One Wasn’t Square.”

(5) Show the 9-minute film “Powers of Ten” or the 3-minute film “Cosmic Eye (both found HERE) If your students have already seen it, you could show just the first few minutes and then pause it. Ask, “Why do you think I’m showing this to you again?” See if any students make the connection to the date. There are other suggestions in my previous post, too.

(6) Play the Powers of Ten Game! ~ NISE (National Informal Stem Education Network) has created some amazing resources to reinforce the concepts of nanoscale based on the powers of ten, including a game. All of their educational resources are FREE and can be found HERE. The video below explains how the game is played. Note: the video is addressed to museum directors and exhibit designers.

(7) Introduce nanotechnology. In the future, I hope to share a mini-unit on nanotechnology, but POWERS of TEN DAY is the perfect time to expose students to this topic. Here is an introductory video that is quite well done! NANO.gov offers additional educational resources HERE for teachers of students K-12, and a page for students HERE.

(8) Introduce SCALE. Your students might also enjoy this INTERACTIVE SCALE of the UNIVERSE! Click on ENGLISH, then START and you can use the sliding scroll bar to zoom in and out of the universe! If you have any problems, try accessing the interactive HERE.

You can include an introduction to the astronomical unit (AU) and how things are measured in space. HERE is a good starting point. There are many great resources to use in lessons about measuring distances in space. Students could make a scale model of the solar system using playdough and even simulate their relative distances from one another on your school playground as explained in this project.

Your students could create a display that shows the relative sizes of some very small things. Not visible in this photo of my students’ display is the depiction of a human hair, which is about 90,000 nanometers in diameter, and the explanation that a piece of notebook paper is 100,000 nanometers thick! This was a big hit in our school and involved a great deal of calculation and collaboration to create it to scale!

(9) Discuss the importance of ZERO and GOOGOL. You can find explanations and activities related to GOOGOL HERE, and a student-friendly presentation about the concept and uses of ZERO IN THIS VIDEO. You might also want to explain why any number to the power of zero equals one. I recommend THIS VIDEO as one to watch yourself (not to share with students); you will learn some kid-friendly ways to explain this concept.

(10) Introduce exponential growth to students. Many students have encountered math problems that are choices such as: Would you rather be given a million dollars or a penny that doubles every day for 30 days? (the answer HERE). This problem is related to exponential growth, a concept explained well in the video below. A live demonstration, fun to share with students, can be viewed HERE. You can also discuss with students the many ways exponents are used across disciplines. HERE is a fantastic source of information about the use and importance of exponential growth in many disciplines including microbiology, environmental studies, financial planning, politics, computer programming, and even seismology.

There you have it – TEN IDEAS for celebrating POWERS OF TEN DAY. Do you have lessons, videos, or ideas you can add to these? If so, please leave your comments below so that we can all benefit!

If you are interested in learning about other special days to celebrate with high-ability students, check out the Holiday/ Seasonal page. Subscribe to this blog if you’d like updates when new resources and ideas are added!