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Let's play with powers of 10

Created: 2022-07-08

Author(s): Jaya Ramchandani, UNAWE

To understand the very diverse scales in Nature —from the smallest meaningful length (Plank’s length) to the size of the observable Universe, let’s familiarize ourselves with orders of magnitude or powers of 10! In this activity, students play a game of cards to achieve this goal and marvel at the range of lengths of objects in our universe!

Materials

This activity comes with a card game which need to be printed.
The card game is made of four sets corresponding to different levels that don’t need to be used all together or in sequence and can be used individually, being of different difficulty levels.

^–35

^–10

^–9

¹⁰

¹¹

²⁶

Tips for printing: You can find the cards to be printed in A5 format back to front (attached file AstroEDU_2203_Powersof10_CardsA5.pdf).
For educators without access to a printer that prints A5 back to front, use the file AstroEDU_2203_Powersof10_CardsA4.pdf to print on regular A4 paper and fold the paper back to front.
We also recommend laminating the cards.

You can also allow students to use the internet for research if available.

Goals

Learn through a fun and group activity
Understand the mathematical concept of orders of magnitude with practical examples
Compare length scales of various orders, from the smallest to the largest scale in Universe

Learning Objectives

Awareness, Understanding, Knowledge

Expand their spatial awareness
Understand the concept of orders of magnitude
Learn fun facts about different objects from the nanoscale to the universal scale
Express a number by its order of magnitude
Relate object lengths to their order of magnitude

Inspiration, Enjoyment, Creativity

Learn through a fun and group activity

21st Century Skills

Apply critical thinking to order cards from smallest to the largest scale magnitudes
Apply collaboration skills to solve problems as a group

Perception, Attitude, Values

Wonder at how big and small objects in the Universe are

Background

Powers of 10 are a useful mathematical tool to comprehend the scale of our Universe.

The smallest measure of length with any meaning is the Plank’s length 0.00000000000000000000000000000000001 m.

Using powers of 10, we can also write this as 1 × 10 ^-35 m or simply 10 ^-35m. 10 is called the base number and 35 is called the ‘exponent’ On the larger end of the scale is the co-moving size of observable space itself, 100,000,000,000,000,000,000,000,000 m. We can write this as 1 × 10 ²⁶ m. We can represent any number using powers of 10 or orders of magnitude. Scientists prefer this scientific notation to write down values of numbers. For example 4500 m can be written as 4.5 × 10 ³ m and 0.045 can be written as 45 x 10 ^-3.

This game is based on Wikipedia’s article on ‘Orders of magnitude (length)’.

Full Description

Before the Lesson

Print the cards and plan your lesson.
Choose which sets of cards you would like to use, depending on the difficulty levels.

For EASY LEVEL, Blue card set, MOLECULAR TO HUMAN

For MODERATELEVEL, Green card set, HUMAN TO ASTRONOMICAL

For ADVANCED LEVEL, Red card set, SUB-ATOMIC TO MOLECULAR

For DIFFICULT LEVEL, Yellow card set, ASTRONOMICAL TO COSMOLOGICAL

During the lesson

Start the lesson with a basic introduction to powers of 10 by showing one of the resources listed under ‘Further Reading’. Then explain the ‘Background Information’ on a black / whiteboard OR play this game only after the concept has been introduced to them before.
Extra: Emphasize the difference between the ‘base’ and the ‘exponent’.
Now start playing: distribute the card sets to student groups
Ask them to place the cards with the picture face up in a random order.
Explain that the students should arrange the cards from smallest to largest lengths.
Then ask them to guess the order of magnitude and write it on a post it and stick it on the picture.
Finally ask them to turn the cards around to see if they were right.
Have a discussion in groups about what they got right and what they missed out on. Were they surprised? Be around to break their misconceptions.
The last step is for each student to submit a question / two for the KAHOOT quiz based on their interest.

Evaluation

Easy

Depending on the class in which this activity is used (mathematics, physics, etc.), students submit 1 or 2 questions for a Kahoot quiz: https://getkahoot.com/ The quiz is then conducted with the whole class.

Some example questions:

The wavelength of visible light is 400 to 700 nanometers. Express this in powers of 10 (in meters)?
Astronomers estimate there are about 100 thousand million stars in the Milky Way alone. Express this number using powers of 10.
What is the smallest power of 10 that would exceed 999,999,999,991?

Difficult

Create a set of cards of progressing orders of magnitude of energy or time. Specify a range to simplify the task. (Understanding by Design task)

Curriculum

This activity can be used in multiple contexts. It can be used to improve understanding of exponentials in a math class or it can be used to reinforce the idea of the scales of Nature in a physics class.

Additional Information

The concept or progressing orders of magnitude can be extended to various physical quantities like energy, frequency of light, frequency of sound, temperature, power, etc.