After introducing students to scientific notation and converting from standard to scientific notation, it was time to move on to using the four operations with scientific notation. Once I chunked out the learning targets with “I Can” statements, I was ready to get things started. With this new topic, I again wanted to start with a discovery lab. I find my students so much more engaged over the whole unit when we start off with an introduction that asks students to discover first, before formal instruction. It gets them curious, which makes them much more invested in their own learning. I’m excited to share with you just how we started off this unit teaching operations with scientific notation through discovery.
This topic seemed different to me, so the discovery lab ended up being different from others we’ve done before. Teaching operations with scientific notation is really about teaching a process, not a conceptual understanding. So what was I going to ask them to “uncover” if it wasn’t a rule or pattern like so many of the other things we’ve studied this year? I had to really think about what it was that I wanted students to notice. What should they focus their attention on? What conclusions would students come up with that would make me feel like this activity was a success?
Step 1- Building background
Since students already had a background with scientific notation, this activity had to build on that understanding and push them forward. But like we always do in these introductory activities, I had them start by reviewing what they know and activating that prior knowledge. I asked students to label the parts of a number written in scientific notation.
Then, I asked students to give examples of when scientific notation would be used. I loved seeing the real world connections they came up with. And it provides context for the really, really big and small numbers we’re talking about.
Conducting trials Making observations with operations with scientific notation
Typically, the next step in our discovery labs is conducting trials and looking for patterns. But this time, we did something a little different. I presented students with worked problems and challenged them to determine what exactly was happening.
With the first problem showing multiplication of two terms written in scientific notation I walked them through step by step, asking questions. We looked at the first line, and the the second line. I asked, “What’s the difference between this line and the first line? What changed? Did something move? Was an operation used?” After answering those questions for the second line, we moved on to the third line and asked them again. I wanted students to get comfortable with the kinds of questions they would need to ask themselves later. I recorded the answers to those questions on my notes while students followed along.
After modeling the types of questions to ask, students got into partners and talked through the second and third worked problems. They recorded their observations and described what they thought happened. After a few minutes working with each problem, we came back together and had a brief class discussion sharing observations and thoughts.
By the time we got to the fourth worked problem, I had students work independently. I wanted to see my students’ thought processes and what conclusions they drew.
Step 3- Drawing conclusions
To close out this discovery lab activity, I asked students to reflect on what they did.
I gave them three questions to respond to:
- Which operations use the same steps?
- What is challenging about multiplying, dividing, adding, and subtracting numbers written in scientific notation?
- Which mathematical processes that we have learned so far this year are used in this process?
It made me happy to see how many students referred back to what we previously learned about the laws of exponents. They connected what happens in working with exponents to what they were doing with numbers written in scientific notation. That may seem like an obvious connection, but I’ve had so many students who didn’t realize this before.
Seeing what they understood after this inquiry activity, and what they didn’t, really help me make the direct instruction more targeted. While students’ answers weren’t always written the most clearly, I saw great math thoughts and realizations. Looking through their responses made my day.
Direct instruction and notes
After finishing our discovery lab, I knew my students were ready for diving into our notes. We used this foldable to talk about how to use each of the operations with numbers in scientific notation.
I have this foldable in 3 versions- one completely filled in, one with blanks for students to complete, and one blank for students to write their own notes. I used the pre-printed version and had students annotate their notes.
As we moved into practice, students referred back to their notes to keep on track. Then, we added a few handy tips to our notes. For example, students added arrows to show what was happening with the decimal point. I don’t like to talk about it “moving right” or “moving left” as I know too many students who get mixed up and can’t keep straight which way the decimal point moves. Instead, I reminded students that when you make the number bigger, then you make the exponent smaller. If you make the number smaller, then the exponent gets bigger. They really do remember this pattern after we go over it.
Another tip we added to our notes was to remind us when we adjust the exponent. For addition and subtraction we wrote, “Deal with decimal before” to remind us that we have to have the same exponent on both numbers before adding or subtracting. We chose the higher number on the exponent to be the common number between the two numbers as that seemed more manageable for students. For multiplication and division we wrote, “Deal with decimal after” to remind us to be sure to write our final answer in scientific notation.
One of my students really doesn’t like to write notes and use words to explain what he’s doing. Instead, he uses arrows and notations to show what happens. It works for him, so I encourage him to take his notes in a way that makes sense for him.
Watching students multiply with number in scientific notation I saw that they remembered and referred to what we learned about properties of exponents six weeks ago. The discovery lab also reinforced how to multiply with exponents. Between the discovery lab and our previous exponents unit, I never saw students make that common mistake this week of multiplying the exponents rather than adding them. A pleasant surprise, for sure!
At the end of the unit, my students this year did way better than my previous classes. Operations with scientific notation can be a tough topic because traditionally it deals so much with memorizing steps. And students struggle with that. But this approach of starting with a discovery lab and then working with our interactive notes seemed to bypass that pattern a bit. I even heard a few “this is easy”’s from students who traditionally struggle with math.
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