Let’s chat about scientific notation and exponents! I have found that the simplest skills in math are often the most miscalculated and confusing for students. Exponents and scientific notation can fall into this trap.
It is important with both exponents and scientific notation that students understand that they show a different way to represent a value.
Before even showing an exponent, start by showing the expanded form like 7*7*7*7*7. You can start by asking students:
- Is this the most efficient way to write this?
- Would 7*5 give you the same result? Why or why not?
Tip: I have learned the hard way to NEVER use 2^2 in any of your early examples because it will just confuse students into thinking you multiply the base and exponent.
Easy, no-plan activity idea: A fun way for students to practice exponents is by using concentric circles. The inside circle is the base and the outside circle is the exponent. Assign students numbers 1-10 and have them rotate to a new partner each round. Students pair up, write down the exponent form, the expanded form, and then calculate the standard form. Keep rotating until your time is up.
Laws of Exponents
The laws of exponents are so fun! I love how students can build on their previous knowledge to come up with the laws themselves. For example:
On a Facebook thread, I recently saw a teacher say, “When in doubt, expand it out.” If a student forgets a law, all they need to do is expand it and calculate to discover the law again. That is something a student is more likely to do if you are modeling it consistently.
Because the laws are so accessible, this content really shines as a discovery-based lesson. Your students could also participate in a jigsaw. Each group becomes experts at their assigned law, then they present the law, the proof, and examples to their peers.
If you go the traditional teaching route, I recommend splitting this skill up over at least 2 days. Maneuvering the Middle 8th grade curriculum covers multiplying/dividing like bases, power to power, and product to power on day one. Negative and zero exponents are covered on day two.
I highly recommend an anchor chart with all of the laws for easy reference. Sometimes in my last class on a Friday, my brain needed to look at an anchor chart to give it the boost it needed (and I am the teacher).
Like I said before, scientific notation is just a different way to represent a value. Here is a great way to introduce why we might use scientific notation. Write down the mass of Earth and Mars on your whiteboard or project it. Make sure students will have to copy it down themselves since that is part of your point.
Start by asking students to read the numbers to you. You will get some funny responses. Then ask students to add them or subtract the masses. As students write and count all of the zeros and inevitably miscalculate or miscount the number of zeros, you can introduce why we used scientific notation. (Less room for error, more efficient) Scientific notation is similar to typing TTYL instead of typing “talk to you later.”
Tips for Scientific Notation
Avoid using right or left when describing the direction to move the decimal. Instead, emphasize that smaller numbers will have negative exponents and larger numbers will have positive exponents. This re-enforces the negative exponent law.
Speaking of exponent laws, scientific notation operations reinforce the laws of exponents. If you look at the vertical alignment, scientific notation only shows up in 8th grade (in TEKS and CCSS), so at least, it reinforces other important concepts that students will use in Algebra 1 and 2.
I have never (and will never) teach Science, but it did occur to me to look up the Texas Science standards, and take a look at this chemistry standard –
“C.2(G) express and manipulate chemical quantities using scientific conventions and mathematical procedures, including dimensional analysis, scientific notation, and significant figures”
An opportunity for cross curricular?! Wahoo! If this is something that has peaked your interest, here is a NASA themed exploration lesson with resources for practicing scientific notation. This demos activity is also a great science based activity.
What tips do you have for teaching exponents and scientific notation?