# Engaging students: Scientific notation

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kelley Nguyen. Her topic, from Pre-Algebra: scientific notation.

How could you as a teacher create an activity or project that involves your topic?

First, I would introduce the topic with a comparison towards abbreviating. For example, when text messaging, one could type “Idk” instead of “I don’t know.” For scientific notation, we’re getting a number and abbreviating it using powers of 10.

My activity would be a matching game, where there will be a set of pictures and a set of numbers (in basic units). I would ask the students to match each picture with one of the given lengths, e.g. a tree would be 5 meters in height. The students will then guess on more difficult pictures, such as the earth’s width or the length of the Atlantic Ocean from one continent to another. As they start working with these bigger numbers, I will introduce scientific notation, where one can shorten very small or very large numbers with the powers of 10. When it comes to these large numbers, students seem to be scared or uninterested in writing such lengthy numbers.

Another fun activity is to give half of my students a number and the rest of my students the numbers in scientific notation. Then, I can then ask them to find their match as they roam around the room.

How can this topic be used in your students’ future courses in mathematics or science?

Scientific notation can definitely help in mathematics when working with very small or very large numbers. When writing numbers such as 3,200,000,000, you can shorten the solution with powers of 10. In this case, we can rewrite the solution to be 3.2 × 109. This also goes for the length and width of very small or very large objects. For example, finding the length of a microchip in meters – that number would be entirely small, using a negative exponent of 10.

In science, scientific notation is especially important when dealing with mass, weight, etc. For example, when computing the mass of the sun in kilograms, one wouldn’t answer 1,989,100,000,000,000,000,000,000,000,000 kilograms. Instead, one will write 1.9891 × 1030. With this shorthand notation, students can move on to problems more quickly rather than spending the time to write and count out every zero. As scientists, they will learn that abbreviation is very useful when collecting data or computing expressions.

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

It has been debated on who discovered scientific notation, but there are many Greek mathematicians and scientists who contributed to the development of this notation. It was first brought about by Archimedes, who studied the Egyptian city of Alexandria. In one project, Archimedes used Greek letter numerals to calculate the number of grains of sand there were in the Archimedean universe. Of course, now, that’s quite impossible to do, but Archimedes did manage to compute that amount and resulted in a very large number. With that being said, that was the start to developing scientific notation and being able to notate very small or very large numbers as short expressions.

Other mathematicians and scientists that contributed to scientific notation include Galileo and Copernicus, who both played a big role in the world of science. Galileo used scientific notation when experimenting with the solar system. Copernicus had an idea of scientific notation when he was attempting to make a scaled model of the solar system.

References