Operations with Scientific Notation

My goal was to take a mathematical standard and write a lesson plan for it. Not just any run-of-the-QBG-mill lesson, but one that gives students an opportunity to experience and learn math in a different way with technology. You see, I’ve learned about this thing called TPACK that has blown my mind. Basically, TPACK is a way to describe what should be happening in every modern classroom. There are three main parts to TPACK: technological knowledge, pedagogical knowledge,  and content knowledge. They all overlap and come together to form this framework we teach in. I wanted this lesson to be a good combination of all three parts. In other words, a technologically strong mathematical lesson using the best pedagogical practices was my goal.

TPACK Reproduced by permission of the publisher, (c) 2012 by tpack.org

Pedagogically, the rationale of this lesson encourages students to “notice and wonder” (Fetter, 2016) about numbers in scientific notation how they can perform operations with them. Students will get statements involving very large or very small numbers, some in standard notation and some in scientific notation. Students will record what they notice and wonder about the statement. Perhaps they will notice one number is written in a different form than the other number and wonder what that means. They may wonder just how many times larger one object is than another.  The teacher acts as only guide with students with phrases like, “Tell me what you noticed about the statement,” making sure to leave the main analyzing process to student. (A potential roadblock is openly and freely sharing what they have wondered. Then, to get them to wonder about the topics/standard that is supposed to be covered in this lesson.  Students should come up with questions that demand using basic operations to solve: how many times one will fit in another, how different are the two objects, and so on.)

Sci Notation Photo
Screenshot of the applet made by Cary and Michael Huang at

Technologically, to answer their “wondering” questions, they will go this applet which allows students to actually see and interact with objects of various lengths (in scientific notation) in the universe, relative to each other. This will give students a better sense of what scientific notation means and the comparisons of, for example, Nix and Earth. I see students playing with this site, and reading a lot of interesting facts about the various objects and how they compare. I also expect them to use their calculators and discover what scientific notation looks like on their calculator. My hope is they can learn to use their calculator to explore products, quotients, and differences. Using a calculator for scientific notation might need to be modeled a little more, but this will get them started. The technologies used in meaningful ways by students is the web-based app and their calculators.

Mathematically (content), using calculators and letting web-based applications like Wolfram Alpha (not part of this lesson) will allow students to explore what math really is about. It’s not about calculations: it’s about something much bigger. Math is a broad, creative, visual subject (Boaler, 2015) that isn’t explored as deeply as it could be because students get stuck on the calculations. Allowing machines to do the calculations is a way to bring classes up to date as they are only be tools to understanding and doing real math (Wolfram, 2014). Watch the following two videos below to see some more amazing descriptions of this.

In the lesson, I’ve put what is to be displayed (whether on a screen or a poster) in text boxes. When they are to be displayed is read in the body of the lesson. The link to the web-based application is as is written in one of those boxes (and included here).

Lesson Plan Scientific Notation Operations Document

Lesson Plan Scientific Notation PDF For everything in the right place (some images/text boxes are in odd places in the embedded document above)


This lesson is the outcome of the work I discussed in this blog post.

Dr. Conrad Wolfram’s TED talk on letting machines do the calculating so we can do the math:

Dr. Jo Boaler’s video on math mindsets: 


Boaler, J. (2015). Boosting Math. Video found through you cubed at Stanford University. Retrieved from https://youtu.be/bxrPy1fjVU4

Fetter, A. (2016, April 15).  An Alternative to SWBAT. Talk  presented at the 2016 NCTM Annual Meeting: Math Forum Ignite event, San Francisco, CA. Retrieved from https://www.youtube.com/watch?v=8ssjZvR__QQ

Wolfram, C. (2014). The UK needs a revolution in the way maths is taught. Here’s why… .  The Guardian. Retrieved from https://www.theguardian.com/education/2014/feb/23/maths-teaching-revolution-needed-conrad-wolfram




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