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. 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 I had not studied the process enough to really support students. I basically spoonfed 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 chunk out the lessons through writing “I Can” statements. 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 when I am teaching operations with scientific notation.
- 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 is not a perfect way to write them. Don’t worry that your I can statements aren’t the right ones. You can change them as you go and make a note to change them for next year if something doesn’t work for you. Having them as a road map will lead you in your teaching as well as leading the students in their learning.
I can multiply and divide two numbers in scientific notation
After we finish our discovery lab I start with 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 have already learned the properties of exponents and the majority of students transfer those skills very easily. We spend an entire day learning about and practicing this objective.
I can add and subtract two numbers in scientific notation
Next, we shift to adding and subtracting. 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 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 this one as well.
Once they 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 think this is easier than multiplying and dividing. I love it when they start discussion like this because it means they are 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 will have to adjust the coefficient so that it is 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 with in the bigger concept. Once again, I don’t use right and left because students get confused. They can however, see if they are making a number bigger or smaller. We emphasize that if you are making the coefficient bigger then, make the exponent bigger. I use to teach with left and right and my students struggled.
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 is more than one way to do this, but I have learned that it is better to teach them one way when they are new to something and let them get automatic at the one way.
I can read a word problem and identify which operation will be used
This may seem like overkill, but it is 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 are emphasizing the characteristics of the different operations.
- 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 people 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 real-world problems with operations and scientific notation. They will 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. You practice this by dissecting problems together.
Misconceptions about operations with scientific notation
The biggest downfall for students is not knowing which operation to use. Another issue is when there is something in the problem they haven’t seen before. For example, maybe one of the exponents is negative and they get thrown for a loop. Or maybe, they are asked to multiply by an integer instead of a number in scientific notation. Throughout your talk with you students you will need to build their confidence that they do have the skills to attack something that is a combination of their skills. Give them some of these types of problems before they take a test and help build these synthesizing skills.
Chunking the learning for students through I can statements can be a lifesaver for you and your students. You can use the I can statements that I laid out for you above or you can make your own list. For resources that support these I can statements check out our operations with scientific notation task cards and knockout game.
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