Teaching operations with scientific notation has been a tough topic for me to teach in the past. I feel like every time I teach something it becomes easier and easier to teach. I learn from the students what works and what doesn’t. As I teach I also learn nuances about the topic that help me to support my students better. Teaching how to multiply, divide, add, and subtract two numbers that are in scientific notation lives as one of the greatest example of this process for me.
What I want my student to do with operation with scientific notation
Ultimately, we want our students to be able to apply all four operations to scientific notation and using that skill to answer word problems like the one above. This is a mix of a lot of skills. You have to focus on building on their strengths and the most vital information.
The first year that I taught this to be honest I hadn’t studied the process enough to really support students. I basically spoon fed them a whole bunch of steps and hoped they would remember it. Well, that doesn’t work, especially for students who struggle. They don’t memorize steps and remember them. They need things broken down for them and they need scaffolding to support their learning.
I can statements
When I sit down to plan a unit, I start by writing “I Can” statements to chunk out the learning. If you want to know more about this process read this post. Here are the I can statements that I had my students write in their notebooks for the operations with scientific notation unit.
- I can multiply and divide two numbers in scientific notation.
- I can add and subtract two numbers in scientific notation.
- I can adjust an answer to scientific notation.
- I can read a word problem and identify which operation will be used.
- I can solve a real-world people with operations and scientific notation.
This isn’t necessarily the perfect way to write them. But I can statements don’t have to be perfect- it’s more important to just get started. Then, you can change them as you go and make a note to change them for next year if something doesn’t work for you. Just having them as a road map will be powerful and lead you in your teaching as well as leading the students in their learning.
Want to grab this pre-printed “I Can” statements page, plus 20 more 8th grade topics and a blank template? Download this FREE resource right here!
I can multiply and divide two numbers in scientific notation
After we finish our discovery lab to introduce students to this topic, I start with a focus on multiplying and dividing in scientific notation. I choose to go with this one first because there are less steps. Also, I think students are less likely to confuse which process to use with which operation if you learn the one with more steps second. At this point we’ve already learned the properties of exponents, so the majority of students transfer those skills over to scientific notation very easily. We spend an entire day learning about and practicing multiplying and dividing numbers written in scientific notation.
I can add and subtract two numbers in scientific notation
Next, we shift to adding and subtracting with scientific notation. These two operations have the same steps as each other. The big difference is that with adding and subtracting you have to adjust the number with a lower exponent to be the same as the higher exponent before you complete the calculations. 
I try to shy away from talking about moving left and right with the decimals. My kids struggle to remember rules like that. I emphasize if you make the exponent bigger then, you make the coefficient smaller. They are very successful moving the decimal in the right direction this way. We spend a day learning about and practicing these two operations as well.
Once students have adjusted the exponent, all they have to do is add or subtract the coefficients and keep the base ten. Many of my students commented that they thought this is easier than multiplying and dividing. I love it when they start discussions like this because it means they’re invested in their learning.
I can adjust an answer to scientific notation
Often at the end of a multiplication or division problem in scientific notation you have to adjust the coefficient so that it’s between 1 and 10. We don’t practice this as a discrete skill unless there are students who need targeted instruction and feedback on this micro-skill within the bigger concept. Once again, I don’t use right and left because students get confused. They can, however, see if they’re making a number bigger or smaller. We emphasize that if you’re making the coefficient bigger then you need to make the exponent bigger. My students struggle so much less with this than when I used to teach with left and right.
One of my favorite parts of being a teacher is when I figure out a way that is better for students to learn something. There’s more than one way to do this, but I’ve learned that it’s better to teach students one way when they’re new to something. Then, let them get automatic at that one way before showing other options.
I can read a word problem and identify which operation will be used
This I Can statement may seem like overkill, but it’s a real struggle for many 8th graders. Honestly, many students can read a problem and know which operation to use, but there are many who are have no idea what to do. You may not have a lot of time to teach this and it could take days or weeks to really get students solid on this one, so just make sure that you’re emphasizing the characteristics of the different operations. Here’s how I talk about it with students:
- Adding is putting things together or stacking things
- Subtracting is taking things away
- Multiplying is repetitive adding or stacking the same thing multiple times
- Dividing is breaking something into groups
I avoid teaching them a whole bunch of keywords for each operations because those can be hard to remember and there are exceptions to those rules. The list above helps to build conceptual understanding over memorization.
I can solve a real-world problem with operations with scientific notation.
At the end of all the hard work we want our students to be able to apply their newly learned skills to solving real-world problems with operations and scientific notation. They’ll go through a problem and underline keywords, set-up the problem, and then solve it. This is where they have to put it all together. To practice we first dissected problems together, then they worked through some themselves.
Misconceptions about operations with scientific notation
The biggest downfall for students using solving problems with scientific notation is not knowing which operation to use. Another issue is when there’s something in the problem they haven’t seen before. For example, maybe one of the exponents is negative and students get thrown for a loop. Or maybe they’re asked to multiply by an integer instead of a number in scientific notation. While talking with students it’s important to build their confidence. Help them see that they do have the skills to attack something that requires a combination of their skills. It’s helpful if students see some of these “stretch” type of problems before testing to help build those synthesizing skills.
Take aways
Chunking the learning for students through I can statements can be a lifesaver for you and your students. I hope you’ll give them a try. They’re a simple addition to interactive notebooks that helps students keep on track with their learning and reflecting on all that they learn about operations with scientific notation. You can use the I can statements that I laid out for you above or you can make your own list. Also, be sure to download the free I Can statements that include this and other 8th grade topics already prepared for you.
For more activity ideas to get students practice with this topic, check out “9 Operations with Scientific Notation Activities“. To see the resources that shown above to support these I can statements, take a look at the operations with scientific notation task cards and knockout game. Thanks so much for reading. Until next time!
